Abstract The gender dentfcaton can be made to approxmately 95% accuracy when all the bones that the skull conssts of are present and well preserved. A dffcult problem that occurs for the medcal examner s that the favourable anatomcal condtons are not on often avalable. The large oval aperture, foramen magnum, whch perces the occptal bone that s stuated at the back and lower cranum was measured, as evaluaton of ths regon may be useful when examnng a fragmented skull. The manual measurements are dffcult to acheve and not often repeatable. The prelmnary nvestgaton establshes an easly reproducble vson system based on the ntellgent scssors system that wll extrapolate the partcular desred measurements from a 2D mage of the foramen magnum. The ntal study used 5 skulls from the UCD anthropologcal department to evaluate the robustness and accuracy of the system. Comparng them wth the standard manual measurements were used to assess the accuracy of the system. Then usng the depth from defocus method to obtan 3D mages the 2D technques for obtanng the data were transferred to evaluate the depth mages.
Table of Contents Abstract... Table of Fgures...3 Chapter : Introducton...4. Presentaton of tradtonal methods.5.2 Problem and Motvaton..8 Chapter 2: Lvewre Background and Implementaton 9 2. Lvewre...9 2.. Dynamc Programmng, Graph search...0 2.2 Overvew of the Fnal System 2 Chapter 3: Statstcal Analyss of 3D data.3 3. Depth from Defocus...3 3.2 Statstcal Analyss of 3D data - Orthographc Vew.5 3.2. Least Square Planar Fttng 5 3.2.2 Planar Projecton 6 3.3 Image Pxel Dmensons 8 Chapter 4: Measurement Code...20 4. Intal Code.20 4.2 2D Informaton Acquston...2 4.3 3D Range Acquston 24 Chapter 5: Calbraton 26 5. Scalng Factor 26 5.2 Testng the Scale 29 5.2. Testng the Scale for the Skull Images..30 5.3 Fnal Scale..3 Chapter 6: Testng..32 6. Determnng Robustness 32 6.. Slope Constrants...34 6..2 Robustness wth respect to the Mdsagttal Plane..35 6.2 2D Image Testng...39 6.3 3D Image Testng...4 6.3. Varyng the angle of Projecton.44 6.4 Gender Identfcaton...44 6.4. Analyss of 2D Results for Identfcaton..45 6.4.2 Analyss of 3D Results for Identfcaton..48 Concluson.5 References..52 2
Table of Fgures Fgure : The Base of the Skull..5 Fgure 2: Placement of mdsagttal plane wth respect to Foramen Magnum 6 Fgure 3: Anomales of Occptal Bone at Foramen Magnum 7 Fgure 4: Flow Chart of Lvewre 2D Dynamc Programme Graph Search Algorthm Fgure 5: Flow Chart of the Vson System.....2 Fgure 6: Actvely Illumnated Image and Computed Depth Image of Skull 6...4 Fgure 7: Flow Chart of 3D Informaton Computaton.4 Fgure 8: Rotatons constraned by the normal vector N to the object surface. 6 Fgure 9: 3D vew demonstratng Orthographc projecton..8 Fgure 0: Image of Reszng Image Dalogue Box.....9 Fgure : Intal Result Images 23 Fgure 2: Graphcal Interface of the Addtonal Measurement Functons..25 Fgure 3: Calbraton Image (Calb.bmp)..27 Fgure 4: Calbraton Image 2 (Calb2.bmp)..28 Fgure 5: 2D Results, LFM and WFM vs FMC..47 Fgure 6: 2D Results, Estmated FMA and Actual Area vs FMC 2.47 Fgure 7: 3D Results, LFM and WFM vs FMC.. 48 Fgure 8: 3D Results, Estmated FMA and Actual Area vs FMC 2.49 Fgure 9: Projected 3D Results, LFM and WFM vs FMC.. 49 Fgure 20: Projected 3D Results, Estmated FMA and Actual Area vs FMC 2.50 Table : Calbraton Results..30 Table 2: Length and Wdth Results and Coordnate Results for Skull 9..32 Table 3: Length and Wdth Results and Coordnate Results for Skull 9 tlted by 30 0..33 Table 4: Averaged Length and Wdth Results for Skulls 6,, 3 and 4...34 Table 5: Detectng LFM and WFM wth pxel dfference between axs coordnates 36 Table 6: Detectng LFM and WFM wth 2 pxel dfference between axs coordnates 37 Table 7: Detectng LFM and WFM wth 3 pxel dfference between axs coordnates...37 Table 8: Detectng LFM and WFM wth 4 pxel dfference between axs coordnates 37 Table 9: Detectng LFM and WFM wth 5 pxel dfference between axs coordnates 38 Table 0: Skull 6 2D Result..39 Table : Skull 9 2D Results 40 Table 2: Skull 2D Results..40 Table 3: Skull 3 2D Results..40 Table 4: Skull 4 2D Results..40 Table 5: Skull 6 3D Results 4 Table 6: Skull 9 3D Results 42 Table 7: Skull 3D Results..43 Table 8: Skull 3 3D Results..43 Table 9: Skull 4 3D Results..43 Table 20: Results from Best Angle for Projecton for each Tlted Image 44 Table 2: Anthropologsts Gender Identfcaton of the Skulls 45 Table 22: Fnal 2D Results, Notng and 3 has rotatonal errors 46 Table 23: Fnal 3D Results wth No Orthographc Vew appled and Depth Estmaton Errors.48 3
Chapter : Introducton Ths project s n collaboraton wth the UCD forensc Anthropology and Research group. Forensc anthropology s the applcaton of the scence of physcal anthropology to the legal process. The dentfcaton of skeletal badly decomposed or otherwse, undentfed human remans are mportant for both legal and humantaran reasons. Forensc anthropologsts apply standard scentfc technques developed n physcal anthropology to dentfy human remans, and to assst n the detecton of crme. Forensc anthropologsts frequently work n conjuncton wth forensc pathologsts and homcde nvestgators to dentfy a dead body and dscover evdence of foul play. In addton to assstng n locatng and recoverng suspcous remans, forensc anthropologsts work to suggest the age, sex, ancestry, stature, and unque features of a deceased person from the skeleton.[] In forensc scence and anthropology, the skull s more frequently and thoroughly nvestgated than any other secton of the human skeleton. For ths project the adult skull wll be used to determne the gender. The human skull s a complex structure and t conssts of the largest number of measurements and calculable ndces then most other bones n the human skeleton. In partcular the occptal regon of the skull s of hgh nterest. Artfcal Cranal Deformaton s an unnatural forced human alteraton of the skull. It permanently changes the orgnal genetcally defned cranal shape, alterng frontal facal morphology and other cranal bones. [2] The occptal s a bone at the nferor and posteror aspect of the skull, due to ts poston t s often found undamaged n human remans. For the project measurements were be taken at the cranal base of the skull as t has a number of features wth proportons that may be gender specfc. The human skull can be used to determne race by evaluaton and comparson of the anatomcal and morphologcal skull feature varatons. Thus there are sgnfcant 4
dfferences between Caucasod, Mongolod and Negrod skeletons through varatons of statstcal analyss. Success rates gender dentfcaton for Caucasod skulls generally yeld better results then Mongolod or Negrod. It s mportant to note that n ths project the Caucasod skull s the only source of testng.. Presentaton of tradtonal methods The man objectve of ths project s to create an mage processng based vson system that wll take specfc measurements, normally taken manually, from a dgtal mage of the occptal area. In ths secton the tradtonal method for extrapolatng the specfc measurements wll be addressed. Occptal bone s stuated at the back and lower cranum, t s trapezodal n shape and curved on tself. It s also perced by a large oval aperture.e. the foramen magnum, through whch the cranal cavty communcates wth the vertebrae canal.e. the spnal chord, as can be seen n the fgure of the posteror of the skull. It s ths area that wll be measured for further statstcal analyss. The fgure shows the skull vewed from an exteror vewpont. Fgure : The Base of the Skull [3] 5
The task of ths project was to take specfc measurements from dgtal mages. The program devsed for ths task wll be tested for dfferent Caucasod skulls suppled by the Unversty College Dubln, UCD, anthropologcal department. The measurements are morphologcal characterstcs of the human skull that can help n gender dentfcaton. These measurements nclude the maxmum length of the foramen magnum, LFM, and wdth of the foramen magnum, WFM. These dstances are to be taken n a smlar fashon to that of measurng wth callpers. To clarfy the length and wdth are measured wth respect to the mdsagttal plane. It s an nter-hemspherc fssure bsectng the human body. Ths plane gves an approxmate blateral symmetry to the skull, as the skull s never perfectly symmetrc. [4] The maxmum nternal length s measured along the plane. Were as the wdth s measured perpendcular to the plane. The clarfcaton of ths s shown f Fgure 2. Fgure 2: Placement of mdsagttal plane wth respect to Foramen Magnum Bason (ba) the mdlne pont on the anteror margn and Opsthon(o) the mdlne pont at the posteror margn of the foramen magnum. A more dffcult challenge s the measurng of the crcumference of the foramen magnum, FMC. No two skulls are dentcally formed due to the mutatonal processes nvolved durng DNA replcaton, and moss,.e. sexual reproducton stage. [5] As can be seen n fgure 2, partcularly B and C, the crcumference of the foramen magnum openng can be obstructed by occptal condyles dependng on the skull shape. 6
Fgure 3: Anomales of Occptal Bone at Foramen Magnum [6] A. The usual appearance of occptal bone at the foramen magnum, B. Precondylar tubercles, C. Thrd occptal condyle and D. Ossfcaton of the lgament of the odontod process of the axs The method that s manually appled to take the crcumference measurement nvolves the use of a strp of paper, whch s pressed around the edge of the foramen magnum crcumference. The ndentatons that trace the shape are then used to record the dstance that they cover over the paper. Ths rudmentary technque s n current use to detremne the undulatng edge surface of the foramen magnum. Obtanng the fourth and fnal measurement of the area, FMA s easly done, once the crcumference has been extrapolated. The area was obtaned by usng the followng basc equaton for the crcumference of the crcle, crcumfere nce( crcle) = 2 * π * R 7
As can be seen from the fgure on the prevous page the shape of the aperture may not actually be crcular but s taken to be an approxmaton. Ths s then could be translated nto the area formula, area( crcle) = π * R 2 There s another varaton to ths approach for fndng area, whch s documented n the Texera paper.[7] In ths case the area s estmated by obtanng the medum value between the half measures of the length and wdth..2 Problem and Motvaton The am of ths project was to produce an algorthm that s easly ncorporated n an anthropologst s feldwork. The hardware avalable may be lmted. For example there may not be suffcent means of lght control when takng an mage and also a smple dgtal camera may be the only means of mage acquston. Also the relablty of such measurements for gender dentfcaton are qute low wth normally about 80% accuracy. Ideally the ntroducton of a vson system may ncrease the robustness and relatve accuracy of sex determnaton from the foramen magnum. The methods used to acqure the measurements are qute elementary and wth the crcumference n partcularly qute cumbersome. Lvewre suppled the functonalty requred for the foramen magnum crcumference extracton from an mage. Ths allowed for the estmated area to be obtaned. Due to the precson nvolved when usng a vson system nstead of manual efforts the area could be found to a much closer approxmaton then the methods that have been documented prevously n the anthropologcal feld. Intally 2D mages were tested and then usng Depth from Defocus to generate the 3D mages the two dfferent methods were compared. The 3D mages were expected to yeld better results as the all the nformaton requred to measure the crcumference would be present. 8
Chapter 2: Lvewre Background and Implementaton There are a number of dfferent technques that have been appled n mage edtng. Most notably the Magc Wand and Actve Contours approaches. [8] Gven a user specfed sample pont or regon, Magc Wand computes a regon of connected pxels such that all the selected pxels fall wthn some adjustable tolerance of the sample statstc. In terms of algorthmc propertes, t seems somewhat slow, unntellgent, and unpredctable. Drawng an approxmate contour around an object ntalses Actve Contours. They are called snakes snce the contour appears to wggle and slde as t seeks a mnmum energy state combnng smoothness and mage features. By usng the result from one frame as the approxmate contour n the next frame, snakes can track a movng object through a vdeo sequence. Algorthmcally, snakes are fast, robust, seemngly ntellgent, and can be overrdden by nudgng on or pullng at portons of the snake durng mnmsaton. The Lvewre nteractve optmal path selecton tool s the technque used n ths nstance as the program s already been mplemented wthn the Vsons Systems Group and has dstnct advantages compared to the other technques, as t uses a dynamc programmng to fnd the optmal boundary of an object. 2. Lvewre The Lvewre program s a sem-automated procedure used for edge detecton and object extracton n an mage. [9] It allows for the user to nteractvely select the most sutable boundary, from a set of all optmal boundares emanatng from a seed pont, nteractve optmal 2D path selecton, by applyng smple gesture motons wth a mouse to extract the object quckly and accurately. It entals tranng facltes and automatc optmal feature and transform selecton methods so that these assgnments that can be made wth consstent effectveness n any applcaton. The user frst selects an ntal pont on the boundary. For any subsequent pont ndcated by the cursor, an optmal path from the ntal pont to the current pont s found and dsplayed n real tme. The user thus has a lve wre on hand, whch s moved by movng 9
the cursor. If the cursor goes close to the boundary, the lve wre snaps onto the boundary. At ths pont, f the lve wre descrbes the boundary approprately, the user deposts the cursor, whch now becomes the new startng pont and the process, contnues. Interactve dynamc tranng s employed to freeze unchangng segments and allows the user to nput addtonal seed ponts, ths s n case of any ambgutes n the edge of the object beng extracted. A few ponts are usually adequate to segment the whole 2D boundary. 2.. Dynamc Programmng, Graph search Lvewre mplements Dscrete Dynamc Programmng as a 2D graph-searchng problem for boundary detecton. The 2D dynamc programme search wndow s the entre mage. Actve ponts emanatng from the seed propagates faster where edge magntude local costs are lower,.e. the optmal path. The optmal graph search s based on the Djkstra algorthm. [9] It extends the boundary trackng method by utlsng the set of edge features. Path optmsaton s formulated as a graph search algorthm that computes the mnmumcost, n-lnk path from seed to all other edge pxels. The Canny Edge operator s appled to extract the edges. The gradent magntude cost feature lnks together the mnmum cumulatve cost path around the object begnnng wth the seed pxel. The neghbourng ponts of the seed pxel are then evaluated, wth the dagonal local costs havng been scaled by the Eucldean dstance,.e. 2. The neghbour of least cost s then expanded n the same manner wth the ncluson of the orgnal cost from the seed pont to that pont, the cumulatve feature. An mportant aspect to note s that the pont currently on the actve lst may change f even lower cumulatve costs are computed from ts nactvated neghbour. 0
Intalse Actve Lst Wth zero cost seed pxel, s Remove mnmum cost neghbour pxel q from actve lst Contnues f stll ponts to expand Mark q as expanded, process by computng total cost to neghbours r (.e. s to r) Remove hgher cost neghbours from lst If neghbour not on lst.e. mnmmum cost, Assgn ts total cost and place on actve lst Fgure 4: Flow Chart of Lvewre 2D Dynamc Programme Graph Search Algorthm The flow chart of Fgure 4 gves a vsual ndcaton of how the algorthm updates the neghbourng pxels wth respect to the cumulatve costs derved from the cost functon. As the process loops back t only does so f there are stll ponts on the mage to expand. It checks the cost of all the pxels that have a path to the seed pont s, whether an mmedate neghbour of the seed not removed from the lst or a neghbour of a mnmum cost cumulatve path pxel. By ths process t checks every possble path that emanates from the seed pxel fndng the lowest ones over the teratve approach.
2.2 Overvew of the Fnal System Fgure 5 gves an ndcaton of the sequence of the fnal mplementaton of the system. Intally the 2D or 3D mages are loaded. Then the Images area calbrated through the lvewre extracton of the scale appled to the mage detaled n Chapter 5. After calbratng the mages the edge extracton s appled to the mage and for the 2D case the crcumference, length, wdth and area can be drectly measured by the approach detaled n Chapter 4. The 3D case gves more nformaton and thus the correcton of vewpont dstortons can be nferred before the measurements are taken, the methods for whch are detaled n the next Chapter, 3. 2D or 3D Image Input (Apply Calbraton Intally) Edge Extracton of the Foramen Magnum (lvewre) Angle Calculaton of the 3D regon For 2D Image Skp the 3 Planar Steps Manual Angle Calculaton (f necessary) Surface Projecton of 3D Image Extract Measurements from 2D or 3D Image Fgure 5: Flow Chart of the Vson System, red dashed box ndcates exclusvely 3D operatons 2
Chapter 3: Statstcal Analyss of 3D data The 2D mages could be easly obtaned wth use of a smple dgtal or analogue camera wth a hgh enough resoluton for the nformaton to be transcrbed correctly after scalng. The camera used for the project s a Sony XC77, sold state CCD camera, mage resoluton 52 x 52. The problem wth 2D data resdes n the fact that ths data s very senstve to vewpont dstortons,.e. drecton you look at the surface of nterest. In 3D these dstortons can compensate for by projectng the extracted planar on a planar surface perpendcular on the optcal axs of the camera. Usng Depth from Defocus, DFD, Least Squares Planar Fttng and Planar Projecton ths was acheved. 3. Depth from Defocus The 3D nformaton can be obtaned usng varous technques. The depth from defocus method uses maxmal resemblance estmaton n a scene by examnng the local nformaton. Weak textures or texture-less scenes however have naccurate depth estmaton results. The soluton to ths problem s to ntroduce a texture onto the mage nvolvng the use of a structured lght. To employ a structured lght a slde projector generated a symmetrcal rectangular grd. The textural nformaton suppled from the grd was organsed n equally spaced lnes. The depth nformaton suppled by the depth from defocus allows 3Dscene nterpretaton. [0] Ths structured lght s nterpreted by measurng the apparent blurrng of the projected pattern. The resultng pattern of grey scale levels from the actvely llumnated mage s very spky and thus dffcult to analyse. The depth estmaton should have the same pattern. The strpes would not match perfectly at the borders of the mage, due to the change n dstance;.e. the depth estmaton s not contnuous when sudden changes n depth occur. 3
(a) Fgure 6: Actvely Illumnated Image and Computed Depth Image of Skull 6 (b) Structured Illumnated Image Apply Edge Focus Operator (Laplacan 7*7 kernel) Perform Map Interpolatons, merges the gaps Evaluate the Depth by strength of the sgnal Smooth the Depth Data (Gaussan Kernel) Fnal 3D Output Image Fgure 7: Flow Chart of 3D Informaton Computaton 4
Fgure 7 ndcates the procedure used for computng the 3D nformaton from the actvely llumnated 2D mage, an example of whch s shown n Fgure 6 (a). A Laplacan operator s appled to focus the edge nformaton n the mage. Two nterpolatons are performed to enhance and merge the gaps of the projected grd nformaton. From whch the strength of the sgnal can be obtaned and represent the z plane data, becomng effectvely a 3D mage. Gaussan kernels of standard devaton.5 smooth ths depth nformaton, to gve the fnal 3D output mage of Fgure 6 (b). 3.2 Statstcal Analyss of 3D data - Orthographc Vew The next am s to determne the spatal orentaton of the 3D mage. Ths was acheved by usng egenspace analyss to constran the object rotaton of the z component and estmatng the remanng rotatons by computng the normal to the surface from the object s range of data,.e. employng Least Square Planar Fttng. Ths s appled by the 3D > Orthographc vew command. 3.2. Least Square Planar Fttng Ths secton summates Least Square Planar Fttng of 3D data ponts of the form x, y and z, where z s functonally dependent on the x and y co-ordnates. In ths case the data for x and y s gven by the coordnate values n the mage and the z s the grey scale depth nformaton. Least square planar fttng works on the premse that when gven a set of sample data for the gven set of m ponts the planar coeffcents A, B and C can be determned. So that the sum of the squared errors between the z sample and the plane value Ax + By + C s mnmsed. [] Note the error s only measured n the z drecton. The error s defned as, m E ( A, B, C) = = [( ) ] 2 Ax + By + C z 5
Ths functon s non-negatve and the graph s hyper-parabolc whose vertex occurs when the gradent satsfes ) = (0,0,0 E. Ths leads to a system of three lnear equatons n A, B, C that can be solved easly. ( ) ( ) [ ]( ),, 2 0,0,0 m y x z C By Ax E = + + = = From ths equaton the followng matrx can be nferred, = = = = = = = = = = = = = m m m m m m m m m m m m z z y z x C B A y x y y y x x y x x 2 2 * Ths soluton provdes the least squares soluton of z = Ax + By + C. However usng a small number of ponts to compute the normal vector s emnently susceptble to error n depth estmaton. 3.2.2 Planar Projecton Fgure 8: Rotatons constraned by the normal vector N to the object surface [2] 6
The normal vector assocated wth [x,y,z] T s represented n homogeneous form as N=[n x,n y,n z,] T =[A,B,-,] T. The am s to transform a plane so that the normal vector les along the z drecton of the reference frame. The mage of the transformed plane can be smply formed by gnorng the z component of the transformed ponts. The rotaton about the z-axs s estmated usng Prncpal Component Analyss PCA analyss. [2] The desred transformaton s formulated as H = T 0 RY * RX * * T 0 Where T 0 s a transformaton that centres the pont Q about the orgn, and R X and R Y are rotatons about the x and y-axs respectvely. T 0 has the form, m x m = m y T0 = I M where the mean vector M = m = = m z m = m m m x y z and I s the Identty Matrx The rotatons about x and y-axs have the form R X 0 0 0 0 cos AX sn AX 0 = and 0 sn A cos A 0 X 0 0 0 X R Y = cos A 0 sn A 0 Y Y 0 0 0 sn A 0 cos A 0 Y Y 0 0 0 The rotaton angle about the y-axs s computed usng the transform N Rx = R X N = [n rx, n ry, n rz, ] T as A y s tan2 - (n rx,n rz ). Smlarly the x-axs s rotated wth respect to N Ry. 7
Note: That when rotatng about the y axs N becomes [n x,0,n z,] T or [A,0,-,] T.e. gnorng the y component and smlarly for the x rotatons N becomes [0,n y,n z,] T or [0,B,-,] T. Fgure 9: 3D vew demonstratng Orthographc projecton [2] Red-3D surface data ponts, Blue-Least square planar fttng of the ponts, Green-Transformed plane 3.3 Image Pxel Dmensons Due the camera specfcatons n whch the pxels were rectangular rather then square wth the vertcal axs beng larger then the horzontal axs n the rato 4/3. Therefore the mages were elongated along the y-axs. To acheve ths the current heght of the mage beng loaded was nferred to scale the mage aganst the desred heght or y value. The scale factor n ths case was 0.75 as the y-axs of each pxel was a thrd greater then the x-axs. Multplyng ths by the orgnal column value gves the user specfed length. Essentally each pxel s reduced or ncreased n the y drecton and ths s assgned to the new reszed output mage. 8
The program at each loadng of a new mage executes the dalogue box below. No entry of a resze factor wll cause the document to fal to load. If the camera dmensons are equal n both drectons,.e. the pxel dmensons are square; an nput of one wll not nduce a change n the mage. Fgure 0: Image of Reszng Image Dalogue Box 9
Chapter 4: Measurement Code As dscussed the Lvewre program was adapted to obtan the crcumference of the mages. Addtons to the code were then made to the program so t suppled the addtonal measurements, along wth calbraton code to gve the nformaton n metrc measurements. 4. Intal Code Intally a separate C program for testng the approach was set up. It conssted of devsng the followng matrx, test _ matrx = 2 3 4 5 2 4 6 8 0 3 6 9 2 5 4 8 2 6 20 5 0 5 20 25 The matrx was devsed to represent a set of pxels at dfferent grey scales. As the mage that s analysed wll consst of varyng grey scale pxels. The matrx was created by usng two for loops that updated the value at each coordnate of the matrx by multplyng the current row value plus by the current column value plus. Notng that the frst column and row are valued at zero.e. value at co-ordnate 0,0 s (0+)*(0+)=, up to the fnal column and fnal row value of four.e. value at co-ordnate 0,0 s (4+)*(4+)=25. The program found the largest dstance between coordnates that were at the value fve,.e. coordnates equal 0,4 and 4,0, and then proceeded to fnd the perpendcular wdth wth the values n the range 0 to 25,.e. coordnates equal,0 and 4,3. The dstance was evaluated usng the Eucldean dstance approach. Eucldean Dstance = ( x x y 2 2 ) + ( y ) 20
The perpendcular wdth was found by obtanng the slope of ths maxmum length lne usng ts coordnates, nvertng t, changng the sgn and only computng the wdth f the lne equalled ths nverted negated slope. Thus the maxmum length was 5.656854 pxels,.e. ( 0 2 2 4) + (4 0) and the maxmum wdth was 4.242640 pxels,.e. 4) + (0 2 ( 3) 2. The detecton of the lnes by the system were as follows, wth the length hghlghted by the round brackets and the wdth hghlghted by the square brackets. output _ test _ matrx = [2] 3 4 ( 5) 2 4 6 ( 8) 0 3 6 [( 9) ] 2 5 4 ( 8) 2 6 20 ( 5) 0 5 [20] 25 By prntng out the coordnates of each loop the progress and accuracy of the system could be montored and the results above collated wth the expected output. 4.2 2D Informaton Acquston The program was set up to work on a 2D dgtal mage. The orgnal skull used for testng was one that was used for teachng purposes n the anthropologcal department n UCD. It top half of the skull was sawn off so that the skull lay flat on a surface. For ths sample skull the contrast between the skull surface and the aperture was hgh. Due to the fact when lad on ts sde and the mage was taken the lght dd not ht the nner surface of the skull but ts rays shone through to the dstant background so ts llumnaton effects were mnmal Intally the code was added to the LveVew.cpp fle n the Lvewre program. Wthn the document ths meant the measurements were taken once the object had been extracted. A new functon lengthwdthpermeter was defned wthn the document and called upon after the object extracton, the defnton of whch s dscussed n the next paragraph. 2
However as ths functon was put nto use one the curve surroundng the object was closed and wthn the crteron for the lvewre extracton correspondng to the movement of the mouse t greatly ncreased the run tme needed to output the fnal closed mage, wth the measurements ncluded. At tmes takng up to forty seconds on partcularly large extracted objects n the mage to gve the measured segmented output mage, whch was the case for the orgnal sample mages used. It was decded to try and apply the measure once the output mage had been returned. It was dscovered ths also ncreased use-ablty to the operator as the measurements could be appled as when they desred. A Menu tem, Output Measurements > 2D Measure, was added to the graphcal nterface. Ths method was appled to the segmented output mage obtaned by Lvewre and the mage of the 2D edge extracton was then analysed by the system. The approach was adapted from the ntal test program to fnd the longest dstance that featured n the foramen magnum,.e. the aperture area. The extracted crcumference was represented by pxels valued at 255,.e. whte, on the segmented output mage. By scannng through the whte pxel coordnates n the mage and then fndng the longest Eucldean dstance to the other whte coordnates n the mage and thus perpendcular maxmum wdth. The Bresenham lne functon was used to apply two lnes representng the length and wdth. Ths takes n the segmented mage and draws a lne of a defned grey scale, ntally set to 200 for both, onto the mage between each par of x and y coordnates that were found to represent the maxmum measurement. Ths was partcularly useful when assessng the accuracy of the measurement acquston. 22
(c) (b) (c) Fgure : Intal Result Images: (a) Orgnal mage wth Lvewre Boundary Hghlghted, (b) Output Segmented Image and (c) Test Results of 2D Measure Note: Test Images were not Reszed The ntal mage results on the prevous page gve an ndcaton of how the perpendcular measures outputted. Further confnements n the calculatons were added later whch wll be dscussed n the testng secton of the report. The crcumference and area were obtaned from mage (b). As can be deduced the area was taken to nclude the whte pxels and the approxmately md grey pxels, grey scale 23
value 255 and 23 respectvely. Smlarly the crcumference requred the attanment of the number of whte edge pxels of the segmented mage (b). The fndngs of all the measures at ths pont of testng were stll n pxel format and of no relatve use to an anthropologst as the scale of the mage was unknown. As the Bresenham lne functon could not cope wth assessng a lne to be drawn wth no co-ordnate nputs as there was no segmented mage loaded to extrapolate the results. So only f a length had been detected would the code mplemented further. In other words the mage beng evaluated had been segmented. If a segmented mage was not extracted the program would smply yeld ether large or zero output answers, dependng on how the varables were ntalsed, and a blank mage. 4.3 3D Range Acquston The 3D mages were obtaned by usng the actve Depth from Defocus technque. Ths meant that the method used for obtanng the crcumference, length, wdth and estmated area of the skull for the 2D mages could be easly transcrbed for the 3D case. Ths s due to the fact the depth of the mage s represented by grey scales and s n fact the equvalent of a 2D mage wth 3D nformaton. Ths meant the segmented 3D edge mage could be analysed n the same manner. An addtonal menu tem was added to the programs fles whch was Output Measurements> 3D measure. However further analyss was appled to the 3D nformaton. As mentoned n Chapter 3 a transform could be appled to the 3D nformaton to elmnate any vewpont dstortons, so once the 3D nformaton was extracted the orthographc vew relatve to the depth nformaton,.e. z-axs, was extrapolated. Ths gave the planar projecton of the x and y coordnates of the 3D edge mage. Thus ths nformaton was used to deduce the planar nformaton wthout any tlt factor. Smply another functon was mplemented n called 3D orthogonal measure,.e menu tem Output Measurements> 3D Orthogonal Measure. 24
Fgure 2: Graphcal Interface of the Addtonal Measurement Functons 25
Chapter 5: Calbraton One of the most sgnfcant parts of ths project s the calbraton. It s hghly mportant to convert the pxel level nformaton nto metrc measurements that can defne exactly what the extracted nformaton s tellng the user. Intally the calbraton technque was to place a flat black square of known dmensons onto the surface of the skulls as close as possble to the planar surface at whch the nformaton was beng extracted. Two Calbraton Images were used to test how accurate the scalng of the mage was beng mplemented. The two mages were named Calb.bmp and Calb2.bmp. The former conssted of square compact dsc label wth dmensons 2cm x 2cm and the latter maged a square object wth a dark nner rectangular surface. Wth the exteror dmensons beng 5cm x 5cm and the nner rectangular surface 3.5cm x 2.3cm. As the mages were acqured wth the same camera as before they were scaled to reduce each y pxel dmenson by 0.25 to gve square pxel dmensons as the cameras resoluton elongated the mage. 5. Scalng Factor The nterface functon Scale was used to gve the fnal output measurements n centmetres. It calculated the number of pxels that depct one centmetre. Ths s done wth the use of Lvewre edge extracton along wth user nput,.e. the scalng factor, whch was requred by the program to evaluate the scale from the known dmensons of the square. Intally the Scale functon was calculated by an approach smlar to that of the foramen magnum length and wdth method. By fndng the largest dstance across the square.e. the hypotenuse, and gettng the length of the equal sdes. Ths method gave sgnfcantly changeable values for the scale of a sde due to the not always exact nature of the extracton and the skewed square mage. Often up to a few of pxels n dfference n the range 24 to 27 representng one centmetre for Calb.bmp. Takng ths nto account the measurements could be up to 2% naccurate. Ths led to the more relable 26
and effcent calbraton approach descrbed below for whch errors were sgnfcantly decreased. Scale worked by countng the number of pxels wthn the extracted closed output mage, thus gvng the area n pxels of the square. The wdth of the square was gven by fndng the square root of the pxel-defned area. Ths output value represented the known wdth of the object. Fnally the user defned nput scale factor was asked for by the system, ths allowed meant that the wdth was multpled by the factor to gve the pxel representaton of one centmetre. It s mportant to note at ths pont that the Scale or 2D Measure dd not use the whte pxels from the edge extracton for ther calculatons. Ths s sgnfcant and s dscussed n the next secton of ths chapter, 5.2, as nclusons of these gave varance n the results. Fgure 3: Calbraton Image (Calb.bmp) Lvewre Edge Image and Closed Output Image For the calbraton of the Calb.bmp mage the scale factor was entered n as 0.083333333,.e. one twelfth, to gve the number of pxels representng cm as the edge of the square was a length of 2cm. Ths yelded 27.376745 pxels representng cm,.e. 328.520928 equals 2cm. Applyng the 2D measure to the mage the outputted area yelded 43.99999cm 2 and the crcumference of the square came n at 48.2605cm. Both these results were qute close to those expected the exact area deally beng 44cm 2 27
and the crcumference beng 48cm long. The slght dscrepancy n the permeter appeared to be due to the human error that occurs n the sem-automated Lvewre approach. Fgure 4: Calbraton Image 2 (Calb2.bmp) Lvewre Edge Image and Closed Output Image For the mage Calb2.bmp the scale factor was 0.2 to gve the number of pxels representng cm as the edge of the square was a length of 5cm. Ths yelded 27.25437 pxels representng cm,.e. 36.07784 equalled 5cm. Smlarly applyng the 2D measure to the mage the outputted area yelded 24.999999cm 2 and the crcumference of the square came n at 9.73449cm. The apparent curved edges of the outer square ndcated that the scale factor would not be exact, as the area of the extrapolated edge mage would be less. Evdently the area gven s a good approxmaton as the method n obtanng t s smlar to the method used to fnd the scale. The change n permeter value to the expected 20cm ndcates not only human error, but also the drop n the scale factor. The scale was then used to evaluate the area and permeter of the nner rectangle that were 8.465cm 2 and.427338cm. These compared well wth the actual known values of 8.05cm 2 and.6cm. 28
5.2 Testng the Scale At tmes Lvewre appeared to produce an mage where the lower valued pxel at the edge was hghlghted to ndcate the presence of that edge. As the scale dd not take nto account the extra whte pxels t appeared to work fne wth the calbrated mages as ther square shapes conssted of a whte object on a black background and thus the approxmate md-grey pxel values took the whole object nto account. Ths lead to possble errors though when usng the scale on the rectangular nner mage of Calb2.bmp as ths was a black area wthn the whte 5cm*5cm regon. Meanng that a layer of whte pxels was n fact shaved from the total area of the shape. Ths would ndcate that the above area would actually be slghtly larger not smaller as s requred for an exact match of the known and vson system obtaned results. Ths nsnuated that when re-evaluatng the code the mage area should also nclude the whte hghlghted pxels as well as the md-grey level centre pxels. Due to the fact the aperture n the skulls worked on a smlar prncpal to the nner rectangle of the second mage,.e. the aperture beng darker then the skull edges. The scale also obeyed the same prncpal was as mentoned taken to be a black square whch lay upon the lghter surface of the skull. The next part deals wth whether or not the assumpton above would actually be held true when mplementng the functons. To do ths the whte pxels were not used when calculatng the scale for Calb2.bmp but n 2D measurements for the area. 0.2 as before multpled the 36.047786 pxels, representng the edge length of the square, to gve scale of 27.209558 pxels. As the scale factor was reduced the area of the mage was ncreased to 25.72262cm 2 and the permeter of the outer square remaned at a smlar value 9.662209cm. However the area of the nner rectangle ncreased 8.528283 cm 2 and the permeter ncreased.466559cm. Another approach could also be taken wth whte pxels used n the scale and 2D measurements for the area. The 27.605072 pxels ndcated centmetre,.e. 38.025360 * 0.2. The area was exact as expected at 24.999999 cm 2 were as the permeter decreased 29
9.525397cm. Smlarly a drop n the area and permeter of the nner rectangle occurred wth the ncreased scale to 8.290903 cm 2 and.37472 cm respectvely. 5.2. Testng the Scale for the Skull Images Another test was appled to the scale on one of the skulls, to see f ths concded wth the test results of Calb2.bmp. The mage of Skull 6 from the UCD collecton was used. A.5*.5cm square was produced by mll machne that guaranteed hgh accuracy, 0.000mm degree of error. The square was used to calbrate the mages so the pxeldefned wdth was reduced by two thrds,.e. a floatng pont number of 0.666666, to gve a cm scale. The results were as follows and they collaborated well wth the results above. SKULL 06 PIXELS =.5CM PIXELS = CM AREA (CM 2 ) CIRCUMFERENCE (CM) Known Measurements 2.25 6 Whte ncluded n Scale and 2D Measure 40.049969 26.69995 2.250005 5.692894 Whte not ncluded n Scale and 2D Measure 38.09994 25.394636 2.250005 5.86738 Whte ncluded n Scale only 39.962482 26.64627 2.034444 5.742892 Whte ncluded n 2D Measure only 38.052595 25.368370 2.484639 5.952294 Table : Calbraton Results of Skull 6 The elmnaton or ncluson of the whte pxels alters the results when obtanng the 2D measure results and lead to the decrease and ncrease n area respectvely. In actual fact the results above prove that the permeter and area values are workng accordngly wth the scale produced. I.e. the fnal two scale values only decrease or ncrease due to the excluson or ncluson of the whte edge pxels. 30
It s also noteworthy that these results gave lttle varance over a number of executons and recalculatons of the scale. At most the scale vared approxmately 0. pxels whch n relaton to the results above gave changes of at most approxmately 0.7%. 5.3 Fnal Scale On further testng of skull number 6 t was found that when testng the results on the foramen magnum the scale nclusve of the whte pxels was the best method to use. In turn the 2D measurements for area ncluded the whte pxels as they were consstently on target wth the manual results prevously taken. Notably f the scale s not calculated before measurng the output mage wll ndcate where the perpendcular measurements le but the output answers wll not be defned. Thus the program gves an output of zero for each, whch should ndcate to the user to calbrate the system. The scale was appled by dvdng the number of pxels comprsng the crcumference by t. Smlarly the scale dvded the length and wdth to gve an output n cm; the scale squared however dvded the area to gve an output n cm 2. Ths scale applcaton was then put n use for the 3D measure and 3D orthogonal measure on the graphcal nterface as the data s extracted n a smlar fashon. 3
Chapter 6: Testng The am of the project s to devse a system that wll generate reproducble results. For ths reason t was mportant to nvestgate the relablty and vablty of the two dmensonal approach n the forensc feld. Further testng of the 3D was mplemented to gve an dea of how any vewpont dstortons could be remeded. Fve Skulls were suppled by UCD for testng, numbered 6, 9,, 3 and 4. 6. Determnng Robustness The ntal testng of the program nvolved dong a seres of tests on each mage. A semautomatc Lvewre approach was appled to each mage, ten tmes n order to fnd the accuracy and any possble varatons that may occur when mplementng the program for the length and wdth measures. It was found upon numerous runs that the Foramen magnum length and wdth coordnates remaned n relatvely the same poston and yelded smlar results. The length wdth results for skull nne can be seen below. SKULL NO 9 LENGTH X Y X2 Y2 WIDTH X Y X2 Y2 36.62338 96 56 289 7 33.50649 24 20 255 25 37.0526 96 57 289 7 35.358 237 2 25 23 37.89474 96 56 287 88 32.7636 223 202 25 24 37.0526 96 57 288 76 33.55263 232 206 250 23 37.0526 96 57 289 7 33.55263 235 207 248 23 37.0526 96 57 289 7 33.55263 232 206 256 23 37.0526 96 57 289 7 33.55263 236 207 248 23 37.0526 96 56 289 7 33.55263 234 207 248 23 37.0526 96 57 286 85 32.7636 224 202 249 23 37.0526 96 55 289 70 34.73684 233 20 247 23 Average 37.3602 33.66644 Table 2: Length and Wdth Results and Coordnate Results for Skull 9 32
Due to the fact the applcaton s sem-automatc the edge detecton s never exactly reproduced. Slght co-ordnate dfferences were a result of ths. As can be magned the permeter yelded more sgnfcant errors at tmes due to the fact that areas were edges were to be detected were ambguous to the system. Tltng the mage by approxmately thrty degrees wth respect to the y-axs or mdsagttal plane gave dubous results n the 2D mages as would be expected. Due to vewpont dstortons the length reduced sgnfcantly, these beng dscussed further on n both 2D and 3D testng. SKULL NO 9 LENGTH X Y X2 Y2 WIDTH X Y X2 Y2 30.78947 85 66 262 72 33.94737 24 208 225 23 3.97368 85 6 264 78 33.55263 20 206 228 23 3.57895 85 67 264 78 34.342 26 209 228 23 3.97368 85 63 264 80 33.55763 20 206 228 23 30.78947 85 62 262 77 33.5789 20 206 224 23 3.97368 85 64 265 76 34.342 26 209 229 23 3.57895 85 68 264 80 33.94737 24 208 227 23 3.97368 87 54 266 7 33.94737 2 207 229 23 3.57895 86 59 264 75 35.358 25 208 233 2 3.57895 85 64 264 77 33.94737 24 208 228 23 Average 3.57895 33.99684 Table 3: Length and Wdth Results and Coordnate Results for Skull 9 tlted by 30degrees Checkng the robustness of the measures at ths pont dd yeld the fact however that the results that were acqured although farly robust n technque, slght rotatons on the results when compared to the mdsagttal plane meant the length and hence wdth of the foramen magnum were badly defned. As can be seen from Table 2 the fnal average results of the mage at approxmately 0 degrees were 37.3602 mm and 33.66644 mm for the length and wdth respectvely. Compared wth the desred results for Skull 9 mm of 34.43 and 30.43 mm they ndcate relatvely naccurate estmaton. 33
The other measurements compared n relatvely the same manner as skull 9 the results of whch are shown n the fgure on the next page, these results are an average of ten executons of the Lvewre edge extracton wth no sgnfcant angle, SKULL NO AVERAGE 2D LENGTH(LFM) IN MM 6 33.405 (33.4) 37.2773 (35.72) 3 40.272 (36.07) 4 36.9654 (36.48) AVERAGE 2D WIDTH(WFM) IN MM 28.83 (26.3) 38.62038 (33.93) 35.59524 (30.63) 3.6539 (28.74) AVERAGE 3D LENGTH(LFM) IN MM AVERAGE 3D WIDTH(WFM) IN MM 32.225 28.65 38.28947 36.55263 37.33784 32.7622 36.4557 3 Table 4: Averaged Length and Wdth Results for Skulls 6,, 3 and 4 Note: the brackets ndcate the measurements that have been already taken manually for comparsons. 6.. Slope Constrants The slope comparsons when appled to the test mage were ntally n nteger format, as the coordnates of the dstances were declared as ntegers. The approxmatons were good but f the slope of the maxmum length was zero, the wdth approxmaton would not le perpendcular to the length. By computng and comparng the slopes as double,.e. to 6 decmal places, the accuracy ncreased but by too much, as the wdth slope had to be very specfc and thus the wdest length detected was no where near t was expected vsually. As only a few possble coordnate would satsfy the negated nverted slope crteron. It was fnally decded to ntroduce a factor of 00 to the slopes and then applyng a double to nteger converson. Ths effectvely cut off the rest of the slope nformaton after two decmal places. The accuracy was suffcent to yeld good approxmatons. 34
6..2 Robustness wth respect to the Mdsagttal Plane Ideally the length of the foramen magnum should be relatvely close to the manual results as where t s determned s specfc. Were as the wdth results may be slghtly more ambguous when comparng, as there s a hgher degree of accuracy when fndng the wdth perpendcular to the length. As mentoned the length of the foramen magnum s actually placed on the mdsagttal plane that bsects the skull n half, so the problem wth ths approxmate lay n the fact there was no constrants on where the length would be detected. Intally when testng wth the nput mage of the test skull dd not appear to be effected by ths, as the foramen magnum aperture was farly ellptcal n shape. Not untl further testng of numerous skulls dd t become apparent that the shape of the aperture could become more sgnfcantly crcular and the slopes of the measures where slghtly naccurate n comparson wth the mdsagttal plane. To counteract these effects a confnement to how the program detected ts length was requred. A constrant could be appled along whchever mage axs the mdsagttal plane lay parallel to, for these test mages t was the along the x-axs. Lttle or no change n the y-axs coordnates of the length ndcates the length s parallel to the x-axs. So ntally the maxmum length was only detected where no change n the y coordnates,.e. y(j) y2(m) = 0, ths was too constrctve when tested on the mages. The lne of code applyng ths s hghlghted n yellow below. for(=4;<orgimage.row-4;++) for(nt j=4;j<orgimage.col-4;j++) f(mg2d[+j*orgimage.row] == 255) { for(nt k=4;k<orgimage.row-4;k++) for(nt m=4;m<orgimage.col-4;m++) f(mg2d[k+m*orgimage.row] ==255) //equal whte n mage { length2d = sqrt(((-k)*(-k))+((j-m)*(j-m))); f(abs((double)j-(double)m)<=0) //(nt)((orgimage.col)/00) { f(length2d>maxlength2d) { maxlength2d = length2d;max2d=;maxj2d=j;maxk2d=k;maxm2d=m; } } length2d = 0; } } 35
Allowng an ncrease n the dfference between y2 and y decreased the restrcton. A number of tests were appled ncrementng the absolute dfference by one each tme. Ths mpled that dfference of the coordnates could le between +/- pxel, +/-2 pxels etc. Ths was done for each mage as alteratons may have changed sgnfcantly. The mages were rotated by 90 degrees to see f the wdth was constraned to be parallel to the x-axs and thus detected frst, would t bear a dfferent output length of the foramen magnum. The mages were reszed and rotated by 90 degrees n Mcrosoft Photo Edtor. ORIGINAL IMAGE 90 0 ROTATED IMAGE +/-PIXELS SCALE (No. Pxels = cm) LFM WFM LFM WFM to y-axs to x-axs Skull no 6 27.68877 33.22653 27.448 33.22653 27.8096 Skull no 9 26.69995 34.8352 3.83526 34.8352 3.46073 Skull no 26.824505 36.90655 36.6097 36.90655 36.6097 Skull no 3 26.36367 37.49565 34.0527 37.49565 34.8739 Skull no 4 27.6639 34.39986 29.3304 34.7696 29.3304 Table 5: Detectng LFM and WFM wth pxel dfference between axs coordnates Note: some of the results are slghted dfferent when rotated due to slght gltches n the extracton rather then specfc changes n the measurements due to rotaton. The manual values for skull and 3 n partcular do not match well as the skulls are slghtly rotated n the mage wth respect to the mdsagttal plane, up to 20 degrees when analysng the mages. The plane lay approxmately parallel to the x-axs n the other mages ndcated by the preferred results. 36
+/-2PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no 6 27.656596 32.90354 27.477988 32.90354 27.477988 Skull no 9 26.633285 34.987 3.53948 34.987 3.53948 Skull no 26.882432 36.82702 36.08304 36.82702 36.35503 Skull no 3 26.05204 37.6822 34.6349 37.23436 34.54735 Skull no 4 27.72784 34.2802 29.22839 34.2802 29.22839 Table 6: Detectng LFM and WFM wth 2 pxel dfference between axs coordnates +/-3PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no 6 27.67266 32.88444 27.46393 32.88444 27.82530 Skull no 9 26.649967 34.89685 3.89497 34.89685 3.89497 Skull no 26.78305 36.96367 36.2693 36.96367 36.2693 Skull no 3 26.068259 37.5936 34.52474 37.5936 34.52474 Skull no 4 27.624437 34.7584 29.3286 34.7584 29.3286 Table 7: Detectng LFM and WFM wth 3 pxel dfference between axs coordnates +/-4PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no 6 27.664630 32.89399 27.043 32.89399 27.043 Skull no 9 26.633285 34.987 3.9495 34.987 3.9495 Skull no 26.932788 36.8956 35.7772 36.8956 35.7772 Skull no 3 26.02335 37.54453 34.09657 37.54453 34.09657 Skull no 4 27.72784 34.2802 29.22839 34.2802 29.22839 Table 8: Detectng LFM and WFM wth 4 pxel dfference between axs coordnates 37
+/-5PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no 6 27.64052 32.92268 27.3408 32.89399 27.49586 Skull no 9 26.66592 34.9406 3.93497 34.9406 3.93497 Skull no 26.824505 36.90655 36.6097 36.90655 36.6097 Skull no 3 26.068259 37.5936 34.44 37.5936 34.44 Skull no 4 27.656596 34.34985 28.9269 34.34985 29.037250 Table 9: Detectng LFM and WFM wth 5 pxel dfference between axs coordnates The algnment of the LFM wth ether axs bore practcally no dfference on the maxmum LFM detected. They dd not vary when approxmated to the nearest mllmetre. A constrant of a percentage of the heght of the mage, 52 pxels, was entered at a +/-%. Ths was deduced from the +/-5 pxel restrant on the detected length, wth respect to the axs ts parallel to, that gave lttle devaton n results but enough to counteract small rotatons. Choosng the constrant wth respect to the resoluton of the camera meant that the devaton would be n proporton to the dmensons of the mage loaded. If the mage specfcally extracted the occptal regon, rather then the whole skull as n the test mages, the restrant would be mnmal. Another approach was tred by wrtng the code for condyles n whch the slope of a lne equdstant from each of them would determne the slope for the length. Ths however was trcky and the program ran out of memory. The dea of the approach was to take the 20 mnmum y values along the upper most condyle and then take the 20 maxmum y values along the lower condyle. Rangng a set of x coordnates from 0 to 20 to put the y coordnates nto 2D. The dea then was to use the average value between each coordnate to then help determne the slope of the lne. Due to the unsymmetrcal nature of the condyles and mutatons however these mean dstances may not lead to good slope results 38
on further consderaton. The code s appended onto the lvewredoc.cpp fle though s nactvated. 6.2 2D Image Testng Ths secton deals wth applyng the extracton and calbraton to the 2D mages to obtan the desred measurements. 2D mages wth vewpont dstortons were also examned to dsplay the shortcomngs of 2D analyss. SKULL NO 6 LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 33.4 26.3 86 588.55 FMA (mm 2 ) Actual SCALE No Tlt 32.86537 27.8096 86.6779 597.87 65.6535 27.68872 Tlted by 30 0 30.33727 27.08685 79.09359 497.82 588.262 Table 0: Skull 6 2D Result Lookng at the results for Skull 6 n the table above t can be seen that as the estmated area of the aperture defned by the area of the crcle depends completely on the extracted crcumference, the results dffer slghtly to the manually estmated measures. Bad edge detecton by the user can greatly effect these partcular outputs. Often causng spkes n the output segmented mage that wll sgnfcantly ncrease the crcumference and hence the estmated area. However the better approxmaton of the area whch nvolves estmatng the area by countng the number of pxels that comprse the segmented mage dvded by the scale squared was less lkely to dffer dramatcally when the crcumference was badly extracted. The testng of the tlted mages produced notable changed results. As the tlt was along the x-axs of the mage, ths lay n conjuncton wth where the length of the foramen would be measured so the length was partcularly skewed. The results for the remanng skulls are tabulated on the next page. As mentoned skull and 3 were rotated sgnfcantly n the assocated mages and therefore the comparsons wth the manual 39
results do not relate well. Ths would be smply remeded by acqurng the mages agan wth more sgnfcance made on the algnment wth the mdsagttal plane. SKULL NO LFM WFM FMC FMA (mm 2 ) 9 Estmated Manual Results 34.43 30.43 95.75 729.57 FMA (mm 2 ) Actual SCALE No Tlt 34.8352 3.46073 96.62939 743.03 807.845 26.6659 Tlted by 30 0 30.4226 3.7378 9.2678 662.87 709.2805 Table : Skull 9 2D Results SKULL NO LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 35.72 33.93 04.69 872.7 FMA (mm 2 ) Actual SCALE No Tlt 36.88378 36.3865 07.2983 96.7 09.928 26.8407 Tlted by 30 0 34.27583 35.76609 02.5336 844.74 947.7626 Table 2: Skull 2D Results SKULL NO LFM WFM FMC FMA (mm 2 ) 3 Estmated Manual Results 36.07 30.63 98.74 775.85 FMA (mm 2 ) Actual SCALE No Tlt 37.52007 34.07435 05.2859 882.3 930.0508 26.936 Tlted by 30 0 34.07435 32.5429 97.62874 758.4825 807.267 Table 3: Skull 3 2D Results SKULL NO LFM WFM FMC FMA (mm 2 ) 4 Estmated Manual Results 36.48 28.74 94.02 703.45 FMA (mm 2 ) Actual SCALE No Tlt 34.7472 28.9544 92.6446 683.02 755.029 27.63248 Tlted by 30 0 34.37983 28.9544 92.2827 677.69 709.0527 Table 4: Skull 4 2D Results 40
6.3 3D Image Testng The analyss was then appled to the 3D data mages usng the same scale that was acqured for each skull n the 2D case. The 3D mages.e. 2D mages wth grd llumnaton, were computed usng 3D>Compute 3D n the Lvewre program. The least square planar fttng for extractng the angle requred for correct planar projecton was relatvely poorly recovered on ntal testng of the 3D mages. To mplement correct planar projecton the planar coeffcents were overwrtten to {0.6,0,0} for {a,b,c} ths ndcates a 30 degree projecton s requred. To do ths a dalogue box was added n the orthographc vew functon. Ths was mplemented after the planar fttng and the user defned tlt factor could be entered. If the user dd not want to overwrte the calculated coeffcents t was only necessary to CANCEL the pop-up box and the orthographc vew mplemented as normal. The projecton was also appled to the mages that were not tlted, as there s always a degree of human error. The angles outputted by the program ndcated the mages were slghtly tlted by or 2 degrees, although skulls 6 and 3 had slghtly hgher angles of about 3 or 4 degrees. SKULL NO 6 LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 33.4 26.3 86 588.55 FMA (mm 2 ) Actual SCALE No Tlt 30.69842 26.36453 83.06633 549.09 65.6535 27.68872 Orthogonal Vew 3.0598 26.72569 87.03906 602.86 600.7839 Tlted by 30 0 27.448 26.00337 76.92664 470.92 544.8272 Orthogonal Vew 3.789 2.636453 84.5096 568.35 60.436 Table 5: Skull 6 3D Results 4
SKULL NO 9 LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 34.43 30.43 95.75 729.57 FMA (mm 2 ) Actual SCALE No Tlt 33.835 3.55926 92.42355 679.76 788.4897 26.6659 Orthogonal Vew 34.892 3.93497 93.7496 690.86 769.575 Tlted by 30 0 3.7378 30.4226 97.88752 64.67 696.4435 Orthogonal Vew 36.4320 30.04702 95.39928 724.24 77.3496 Table 6: Skull 9 3D Results Note the results for the orthographc vew are slghtly exaggerated for the mages tlted by 30 degrees as they were tlted by a smple guestmaton usng a protractor. The 30 degrees orentaton s just apprecatve. Thus the mages tlt factor s ambguous and by forcng the planar coeffcents to mply a 30 0 planar projecton about the z-axs may cause dstortons as the angle may not have been ths large n the mage. Ths s partcularly notable n the results for Skull 9. However the results do ndcate that the mages projected to gve more accurate results. The valdty of ths approach s debatable however, as the user may not know the angle of the tlt and thus t would be preferable that the planar coeffcents and projecton were correctly formulated wthn the program. Instead of the approach of the user forcng the projecton angle. As mentoned n the statstcal analyss explanaton the number coeffcents cause problems n the angle estmaton. The tlt angle s relatvely poorly recovered due to the fact that the errors n depth estmaton around depth dscontnutes are sgnfcant and the number of ponts employed to estmate the planar s small. The mproved result for skull and 3 are only an ndcaton of ths and do not actually nfer that the 3D method used up to ths pont s better. Ways n whch to mprove the depth estmaton s dscussed n secton 6.3.. 42
SKULL NO LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 35.72 33.93 04.69 872.7 FMA (mm 2 ) Actual SCALE No Tlt 36.3865 33.5307 99.84699 793.34 922.6268 26.8407 Orthogonal Vew 36.52 33.90327 06.806 897.8 90.6675 Tlted by 30 0 32.4302 33.90327 9.27804 663.0 8.3064 Orthogonal Vew 37.6289 32.78558 99.47443 787.43 904.86 Table 7: Skull 3D Results SKULL NO 3 LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 36.07 30.63 98.74 775.85 FMA (mm 2 ) Actual SCALE No Tlt 35.22292 30.62863 90.7373 655.8 787.288 26.936 Orthogonal Vew 36.3749 30.62863 93.03445 688.78 788.8942 Tlted by 30 0 34.84006 30.62863 94.56588 7.64 800.767 Orthogonal Vew 40.58293 3.048 00.696 806.82 89.207 Table 8: Skull 3 3D Results SKULL NO 4 LFM WFM FMC FMA (mm 2 ) Estmated Manual Results 36.48 28.74 94.02 703.45 FMA (mm 2 ) Actual SCALE No Tlt 34.7472 28.58954 89.38756 635.35 722.2803 27.63248 Orthogonal Vew 35.0362 29.3333 90.47324 65.37 703.42 Tlted by 30 0 30.0399 28.58954 86.49242 595.3 64.7359 Orthogonal Vew 35.4655 28.58954 94.8595 75.4 7.482 Table 9: Skull 4 3D Results 43
6.3. Varyng the angle of Projecton As the 3D results from the rectfed tlted mages were stll naccurate, further testng was appled to the 3D mages by applyng varyng degrees of planar projecton. Dfferent degrees for the projecton were appled. The angles that generated the best results for each mage are ndcated n Table 20. As can be seen the angle vared sgnfcantly for each. SKULL NO ANGLE LFM WFM FMC FMA FMA SCALE (mm 2 ) (mm 2 ) Estmated Actual 6-34.992 33.2367 26.3727 85.9805 588.29 628.5396 27.68069 (Manual) (33.4) (26.3) (86) (588.55) 9-28.808 34.987 29.28666 96.6203 735.23 745.633 26.63329 (Manual) (34.43) (30.43) (95.75) (729.57) -24.23 36.08304 32.7353 02.2297 832.7572 832.7508 26.88243 (Manual) (35.72) (33.93) (04.69) (872.7) 3-6.70 36.38335 30.6386 94.5967 72.08 795.5688 26.085 (Manual) (36.07) (30.63) (98.74) (775.85) 4-33.0239 36.06357 28.2958 94.8478 75.8779 75.7096 27.72882 (Manual) (36.48) (28.74) (94.02) (703.45) Table 20: Results from Best Angle for Projecton for each Tlted Image There were stll notable dfferences however the results do ndcate how the 3D data has the capacty for extractng the data requred by projectng the mage. Skull No 3 n partcular had a very low crcumference measurement, n fact the angle at 30 0 yelded a better value of 96.2863mm but the LFM and WFM were naccurate at 40.5965mm and 3.0259mm respectvely. The nformaton s stll somewhat naccurate due to depth estmaton errors. There are a number of approaches that would mprove the depth estmaton calculated by lvewre. The most obvous strategy would be to use a more powerful lght projector to compensate 44
for the drop n sgnal strength n areas wth dark colours or a lght projector wth a lens wth a smaller depth of feld. Also a camera wth a hgher resoluton would mprove the estmaton, as the mages would be sharper. Usng a better qualty range sensor,.e. stereo or trangulaton-based laser scanners would also mprove the results of the system. 6.4 Gender Identfcaton The gender of each of the skulls has not actually been offcally determned. These samples are used for test purposes by the UCD forensc anthropology department. Nevertheless Dr Jason Last dd ndcate dd gve an ndcaton of what he as a forensc anthropologst would beleve the gender of each sample to be, by takng nto account other more obvously gender dentfable features of the skull. Normally three or more anthropologsts apply these methods for dentfcaton and thus they would collaborate ther results. SKULL NO GENDER 6 Female 9 Male Male 3 Male 4 Female Table 2: Anthropologsts Gender Identfcaton of the Skulls, wth approx 90% accuracy 6.4. Analyss of 2D Results for Identfcaton The results had notceable sgnfcance, both manually and expermentally. Generally the female skulls had more ellptcal foramen magnum wth the male beng closer to a crcular shape. Ths s realsed n the dfferences between the length and wdth. The length s sgnfcant larger then the wdth for females. The area however both the estmated and the more accurate fndngs were partcular notable. As the female samples 45
appeared have a smaller area then the male, though skull 9 may be partcular dubous f gong on area alone. As t bears the ellptcal qualtes substantally both qualtes may be used to nfer ts gender. Both of these fndngs have been drawn attenton to by prevous authors n medcne and forenscs as ndcated n the Texera paper [7]. Plots of the results of the table above exhbt these assumptons more clearly, gvng an ndcaton of how the gender could be dstngushed. SKULL NO 6 (Manual) 9 (Manual) (Manual) 3 (Manual) 4 (Manual) LFM 32.86537 (33.4) 34.8352 (34.43) 36.88378 (35.72) 37.52007 (36.07) 34.7472 (36.48) WFM 27.8096 (26.3) 3.46073 (30.43) 36.3865 (33.93) 34.07435 (30.63) 28.9544 (28.74) FMC 86.6779 (86) 96.62939 (95.75) 07.2983 (04.69) 05.2859 (98.74) 92.6446 (94.02) FMA (mm 2 ) Estmated 597.87 (588.55) 743.03 (729.57) 96.7 (872.7) 882.3 (775.85) 683.02 (703.45) FMA (mm 2 ) Actual 65.6535 807.845 09.928 930.0508 755.029 Table 22: Fnal 2D Results, Notng and 3 has rotatonal errors Plottng the length and wdth aganst the crcumference ndcates that the dfference n length and wdth may be drectly related to gender, see Fgure 5. Also the crcumference ncreases n the male skulls, as the dstances become closer,.e. the foramen magnum s more crcular. Skull 9, whch s consdered male, s less dstngushable by these results as the crcumference s smaller at 96.62939, although t does exhbt more smlar length and wdth dstances. Skull and 3 had slghtly ncreased length and wdth results when compared wth the manual results due to rotatonal effects. There was a notable varance n the length and wdth n Skull 3 but when referenced wth the crcumference the graph would have yelded the results for 3 n a smlar poston to Fgure 5. 46
Fgure 5: 2D Results, LFM and WFM vs FMC The plot n Fgure 6 dsplays that the male samples exhbt larger areas. Smlarly the area of skull 9, both the crcle-based estmaton and the more accurate result, sways the results closer to the female classfcaton. Cross Referencng the data from the two plots may allow for sex determnaton to be more accurate. Fgure 6: 2D Results, Estmated FMA and Actual Area vs FMC 2 47
6.4.2 Analyss of 3D Results for Identfcaton Smlarly the 3D data was examned. The results were less conclusve then the 2D data, whch was explaned n the prevous testng secton, 6.3. There are stll ndcatons of larger areas and more crcularty wth male samples. The dfference n length and wdth n Skull 6 has the greatest change from the 2D results. As can be seen from Fgures 7 and 8 errors n depth estmaton have sgnfcantly altered the results for Skull 3. The crcumference n partcular has greatly reduced. SKULL NO LFM WFM FMC FMA (mm 2 ) Estmated FMA (mm 2 ) Actual 6 30.69842 26.36453 83.06633 549.09 65.6535 9 33.835 3.55926 92.42355 679.76 788.4897 36.3865 33.5307 99.84699 793.34 922.6268 3 35.22292 30.62863 90.7373 655.8 787.288 4 34.7472 28.58954 89.38756 635.35 722.2803 Table 23: Fnal 3D Results wth No Orthographc Vew appled and Depth Estmaton Errors Fgure 7: 3D Results, LFM and WFM vs FMC 48
Fgure 8: 3D Results, Estmated FMA and Actual Area vs FMC 2 The forced tlt results from Table 20 were plotted lkewse, dsplayed n Fgures 9 and 20. To gve an ndcaton of the best 3D results recovered. As prevously ndcated Skull 3 crcumference recovery s notably much less then ts manual value of 98.74, although the length and wdth measurements are deal. Fgure 9: Projected 3D Results, LFM and WFM vs FMC 49
Fgure 20: Projected 3D Results, Estmated FMA and Actual Area vs FMC 2 Wth the excepton of Skull 3 the 3D mages yeld good results and show the greater possbltes nvolved wth 3D magng. However for the task n hand and wth the methods appled the 2D approach gave suffcently accurate results. There are many enhancements that could be nferred to obtanng the 3D range of data that would make the 3D approach ultmately the best. 50
7 Concluson The 2D approxmate s more accurate when compared wth the 3D results, however as ndcated, mprovements could be made n the 3D mages. Another advantage to the 2D approach s that t s easer to reproduce the data because of the equpment nvolved. The only equpment requred would be a suffcently hgh-resoluton dgtal camera to obtan the mages and a PC to run lvewre. The tlt factor that may be a problem could be dealt wth by employng a sprt level to gauge that no tlt exsts when acqurng an mage of a skull. The most sgnfcant fndng however s that the mage processng allows for a farly accurate generaton of the area of the skull. The approach dscussed n Chapter s estmated on the bass of an area of a crcle and s a very crude apprasal. Ths fndng should bear sgnfcance n future anthropologcal endeavours. Further work could nclude apprasng how crcular or ellptcal the foramen magnum s. The devatons from each shape may help determne the gender accurately. An mproved method n the determnaton of the mdsagttal plane could also be appled by determnng the best bsectng lne of the foramen magnum nto equal halves. The analyss of the fndngs s purely conjecture and a larger range of skulls would be requred to examne fully the possble trats exhbted by ether sex n ths regon of the skull. It would enable statstcal examnaton of how vald these presumptons may be and note the error that may occur when testng dubous samples. Ths examnaton alone does not valdate the accuracy of the dentfcaton, only presents a system that may help n future analyss of larger homogeneous sample groups. 5
References [] An Overvew of Forensc Anthropology, Jessca Kefer http://serendp.brynmawr.edu/bology/b03/f0/web/kefer.html [2] Gender Practces of Artfcal Cranal Deformaton http://ehlt.flnders.edu.au/archaeology/gender/998/owen/essay.htm#ref [3] Dagram Showng Anthropometrc landmarks, Aello and Dean 990, http://mac-huws.lut.ac.uk/~ws/lectures/evolutonary-anatomy/the%20skull.pdf [4] Robust Mdsagttal Plane Extracton from Normal and Pathologcal 3-D Neuroradology Images Yanx Lu*, Member, IEEE, Robert T. Collns, Member, IEEE, and Wllam E. Rothfus [5] Sex Determnaton of Fragmentary Crana by Analyss of the Cranal Base Thomas Dean Holland, Amercan Journal of physcal Anthropology 70:203-208 (986) [6] Anomales of Occptal Bone at Foramen Magnum (Occptal Condyles) llustrated Encyclopeda of Human Anatomc Varaton: Opus V: Skeletal Systems Ronald A. Bergman, PhD, Adel K. Aff, MD, MS and Ryosuke Myauch, MD [7] Sex Identfcaton utlzng the sze of the Foramen Magnum W.R.G. Texera, M.D., Ph.D., Amercan Journal of Forensc Medcne and Pathology, Volume 3 No 3 (982) [8] Vson-Asssted Image Edtng, Erc N. Mortensen Brgham Young Unversty 52
[9] Intellgent Scssors for Image Composton, Erc N. Mortensen and Wllam A. Barrett [0] A vdeo-rate range sensor based on depth from defocus Ovdu Ghta, Paul F. Whelan, Optcs and Laser Technology Volume: 33, Issue: 3, Aprl, 200 [] Least Squares Fttng of Data, Davd Eberly,Magc Software, Inc.,http://www.magc-software.com [2] Pose Estmaton for objects wth planar surfaces usng egnmage and range data analyss Ovdu Ghta, John Mallon, Paul Whelan, Davd Vernon, Natonal Unversty of Ireland Maynooth 53