Abstract. Dublin City University

Transcription

1 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.

2 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 Dynamc Programmng, Graph search Overvew of the Fnal System 2 Chapter 3: Statstcal Analyss of 3D data.3 3. Depth from Defocus Statstcal Analyss of 3D data - Orthographc Vew Least Square Planar Fttng Planar Projecton Image Pxel Dmensons 8 Chapter 4: Measurement Code Intal Code D Informaton Acquston D Range Acquston 24 Chapter 5: Calbraton Scalng Factor Testng the Scale Testng the Scale for the Skull Images Fnal Scale..3 Chapter 6: Testng Determnng Robustness Slope Constrants Robustness wth respect to the Mdsagttal Plane D Image Testng D Image Testng Varyng the angle of Projecton Gender Identfcaton Analyss of 2D Results for Identfcaton Analyss of 3D Results for Identfcaton..48 Concluson.5 References..52 2

3 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 Fgure 6: Actvely Illumnated Image and Computed Depth Image of Skull 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 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 Table 3: Length and Wdth Results and Coordnate Results for Skull 9 tlted by Table 4: Averaged Length and Wdth Results for Skulls 6,, 3 and 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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.

12 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

13 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

14 (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

15 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 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

16 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 Planar Projecton Fgure 8: Rotatons constraned by the normal vector N to the object surface [2] 6

17 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 cos AX sn AX 0 = and 0 sn A cos A 0 X X R Y = cos A 0 sn A 0 Y Y sn A 0 cos A 0 Y Y 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

18 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

19 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

20 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 = 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

21 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 pxels,.e. ( ) + (4 0) and the maxmum wdth was 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) ( 8) [( 9) ] ( 8) ( 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 D 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

22 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

23 (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

24 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 D 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

25 Fgure 2: Graphcal Interface of the Addtonal Measurement Functons 25

26 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

27 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 ,.e. one twelfth, to gve the number of pxels representng cm as the edge of the square was a length of 2cm. Ths yelded pxels representng cm,.e equals 2cm. Applyng the 2D measure to the mage the outputted area yelded cm 2 and the crcumference of the square came n at cm. Both these results were qute close to those expected the exact area deally beng 44cm 2 27

28 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 pxels representng cm,.e equalled 5cm. Smlarly applyng the 2D measure to the mage the outputted area yelded cm 2 and the crcumference of the square came n at cm. 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 cm. These compared well wth the actual known values of 8.05cm 2 and.6cm. 28

29 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 pxels, representng the edge length of the square, to gve scale of pxels. As the scale factor was reduced the area of the mage was ncreased to cm 2 and the permeter of the outer square remaned at a smlar value cm. However the area of the nner rectangle ncreased cm 2 and the permeter ncreased cm. Another approach could also be taken wth whte pxels used n the scale and 2D measurements for the area. The pxels ndcated centmetre,.e * 0.2. The area was exact as expected at cm 2 were as the permeter decreased 29

30 cm. Smlarly a drop n the area and permeter of the nner rectangle occurred wth the ncreased scale to cm 2 and cm respectvely 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 , 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 Whte ncluded n Scale and 2D Measure Whte not ncluded n Scale and 2D Measure Whte ncluded n Scale only Whte ncluded n 2D Measure only 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

31 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

32 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 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 Y Average Table 2: Length and Wdth Results and Coordnate Results for Skull 9 32

33 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 Y Average 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 mm and mm for the length and wdth respectvely. Compared wth the desred results for Skull 9 mm of and mm they ndcate relatvely naccurate estmaton. 33

34 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 (33.4) (35.72) (36.07) (36.48) AVERAGE 2D WIDTH(WFM) IN MM (26.3) (33.93) (30.63) (28.74) AVERAGE 3D LENGTH(LFM) IN MM AVERAGE 3D WIDTH(WFM) IN MM 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

35 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

36 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 Skull no Skull no Skull no Skull no 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

37 +/-2PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no Skull no Skull no Skull no Skull no 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 Skull no Skull no Skull no Skull no 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 Skull no Skull no Skull no Skull no Table 8: Detectng LFM and WFM wth 4 pxel dfference between axs coordnates 37

38 +/-5PIXELS SCALE (No. Pxels = cm) ORIGINAL IMAGE 90 0 ROTATED IMAGE LFM WFM LFM WFM to x-axs to y-axs Skull no Skull no Skull no Skull no Skull no 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