Surface Reconstruction of the Human Nasal Cavity from CT-Data for Fluid Mechanical Analysis of Breathing Problems

Transcription

1 Surface Reconstruction of the Human Nasal Cavity from CT-Data for Fluid Mechanical Analysis of Breathing Problems Andreas Lintermann January 22, / 65

2 1 Introduction / 65

3 Motivation Objectives Motivation Motivation everybodies nasal cavity is different big differences between races breathing problems caused by a cold / allergy / abnormalism / deformation 4/ 65

4 Motivation Objectives Motivation Motivation everybodies nasal cavity is different big differences between races breathing problems caused by a cold / allergy / abnormalism / deformation 4/ 65

5 Motivation Objectives Motivation Anatomy septum turbinates mucous membranes protect lung by heating up air moisturing air cleaning air olfactory organ sense of smell involved in sense of taste paranasal sinuses Images from 5/ 65

6 Motivation Objectives Motivation Surgery and arising problems surgery in nasal cavity is the most frequent surgery in otolaryngology physiological functions suffer: damage or loss of sense of smell damage of sense of taste no breathing improvements 6/ 65

7 Motivation Objectives Major goals Tasks increase surgery success rate enhance the patients physiological functions predict results of a surgery find optimal surgery procedure for the individual patient Idea from Schlöndorff et al. [AKME + 90] perform a virtual surgery and evaluate results to find optimal surgery procedure 7/ 65

8 Acquiring CT-data Introduction Motivation Objectives scan of the patient s body hounsfield mapping Volume Reconstruction Photo of CT-scanner from 8/ 65

9 Motivation Objectives Steps to a virtual surgery CT-data of patient s head Flow simulations CFD solver Flow visualization Real surgery? A surface of the nasal cavity is extracted Virtual surgery / mesh editing 9/ 65

10 Motivation Objectives Objectives Software objectives implementation and design of a surface extraction software quality analysis of: the applied algorithms the provided CT-data 10/ 65

11 Motivation Objectives Objectives - Surface Reconstruction Open questions concerning the surface reconstruction how to obtain a 3D-model from 2D-CT-slices?? 11/ 65

12 Motivation Objectives Objectives - Surface Reconstruction Open questions concerning the surface reconstruction how to obtain a 3D-model from 2D-CT-slices? how to extract the region of interest (the nasal cavity)?? 11/ 65

13 Motivation Objectives Objectives - Accuracy Investigation Issues influencing surface-accuracy low CT-resolutions provide inaccurate surfaces analysis of the accuracy dependent on CT-resolutions vs. 12/ 65

14 Motivation Objectives Objectives - Accuracy Investigation Issues influencing surface-accuracy low CT-resolutions provide inaccurate surfaces analysis of the accuracy dependent on CT-resolutions unsharp features prevent interface detection of ROI evaluation of image-filters vs. 12/ 65

15 Motivation Objectives Objectives - Accuracy Investigation Issues influencing surface-accuracy reconstruction algorithm provides a stair-step surface-approximation smoothing is necessary introducing further inaccuracies analysis of the introduced errors and smoothing algorithms 13/ 65

16 Motivation Objectives State of the art Current applications and MITK itk-snap uses Geodesic Active Contours for segmentation slow convergence segmentation not bound to nasal cavity OsiriX uses Seeded Region Growing for segmentation no surface extraction segmentation not bound to nasal cavity MevisLab uses network interface for data flow no source code available MITK is a public domain solution uses VTK and ITK allows direct interface development for the grid generator easy extensibility (e.g. accuracy tools) 14/ 65

17 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing initial CT-image Image Preprocessing Surface Reconstruction Segmentation Surface Postprocessing Nasal cavity surface 16/ 65

18 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Image preprocessing steps initial CT-image Image preprocessing crop image object insertion processed image image image filters 18/ 65

19 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Image Filtering results Filters 3x3 conv. 12: A shift-scale: H (v) = γ (H (v) + H σ) 19/ 65

20 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Output image preprocessing 20/ 65

21 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Segmentation steps - Region Growing preprocessed image Segmentation set seed points set lower/upper threshold uses itkconnectedthresholdimagefilter Seeded Region Growing [AB94] not all segmented merge binary image binary image(s) 22/ 65

22 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Segmentation result 23/ 65

23 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Surface reconstruction steps Surface Reconstruction vtkmarchingcubes [LC87] binary image surface mitk::imagetosurfacefilter 25/ 65

24 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Marching Cubes result 26/ 65

25 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Surface postprocessing steps Surface postprocessing surface Smoothing processed surface surface cutting surface Decimation not good enough Smoothness evaluation 28/ 65

26 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Laplacian Smoothing [Tau95] with vtksmoothpolydatafilter v new c = v old c + λ v i N(v old c ) ( vi vc old ) N (vc old ), 0 < λ 1 v old c v i+1 v i v i+1 29/ 65

27 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Laplacian Smoothing [Tau95] with vtksmoothpolydatafilter v new c = v old c + λ v i N(v old c ) ( vi vc old ) N (vc old ), 0 < λ 1 v old c v new c v i 1 i+1 v i v i+1 29/ 65

28 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Windowed Sinc Function Smoothing Preparation [TZG96] express Laplacian Smoothing [Tau95] by matrix multiplication v i v = v i + λ v i = (I + λu) v perform eigen-analysis of U obtain eigenvalues λ i and eigenvectors e i obtain DFT (e i basis in Fourier space) and transfer function v = e i c i,c i =Fourier coefficients i (I + λu) v (1 + λ i λ) c = (1 λω) c 30/ 65

29 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Windowed Sinc Function Smoothing Ideal low-pass filter [TZG96] set a pass-band defining the deletion of high frequencies f (k i ) = perfect low-pass filter (1-λω) (1-λω) 3 ( 1, 0 k i ρ b 0, ρ b < k i 2 f(k i ) k i 31/ 65

30 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Problems of the ideal low-pass filter Approximation with polynomial [TZG96] for a large numer of vertices, the eigen-analysis of U becomes difficult replace transfer function by analytic approximation to the ideal low-pass filter with Chebychev-polynomials 1.2 perfect low-pass filter Chebychev-Approx. with deg= f(k i ) k i 32/ 65

31 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Chebychev-Approximation Adjustments and requirements approximation has to be windowed with weights to obtain f (0) = 1 and prevent Gibbs Phenomenon narrow pass-band requires high degree polynomial 1.2 perfect low-pass filter Chebychev-Approx. with deg= f(k i ) k i 33/ 65

32 Image Preprocessing Segmentation Surface Reconstruction Surface Postprocessing Smoothing result 34/ 65

33 Method analysis overview Image from a surface Reconstruction pipeline Error calculation prior surface Image Generator Error calulation image generated surface Reconstruction pipeline 36/ 65

34 From a surface to an image Image from a surface Reconstruction pipeline Error calculation Image generator surface Calculate MBB set resolution generate image image post-processing image 38/ 65

35 Image from a surface Reconstruction pipeline Error calculation The generated minimal bounding box 39/ 65

36 Introduction Image generation - SAT Image from a surface Reconstruction pipeline Error calculation y y x x 42/ 65

37 Image from a surface Reconstruction pipeline Error calculation Obtaining a real CT-image approximation Region identification perform region growing on outer region set region values to: outer region: 1 interface: 0 inner region: -1 44/ 65

38 Image from a surface Reconstruction pipeline Error calculation Obtaining a real CT-image approximation 45/ 65

39 Image from a surface Reconstruction pipeline Error calculation Obtaining a real CT-image approximation 45/ 65

40 Image from a surface Reconstruction pipeline Error calculation Obtaining a real CT-image approximation 45/ 65

41 Image from a surface Reconstruction pipeline Error calculation Obtaining a real CT-image approximation 45/ 65

42 Generated CT-image example Image from a surface Reconstruction pipeline Error calculation 46/ 65

43 Error calculation Introduction Image from a surface Reconstruction pipeline Error calculation Error metrics calculate distance between original surface and output surface use a two-sided mean squared distance error metric 0 1 ξ 1 X d (S gen,v) 2 + V orig + V gen v V orig use a two-side mean distance error metric ξ 2 = V orig X v V orig q d (S gen,v) V gen X w V gen d X w V gen 1 `Sorig, w 2A 1 q d `Sorig,w 2A 49/ 65

44 Image from a surface Reconstruction pipeline Error calculation Obtaining minimal distances Finding minimal distances for a vertex v o use kd-tree [Ben90] to find closest vertex in other surface finding vertex v c is in log-time instead of linear in V i closest point lies on triangle fan around v c check all triangles in triangle fan for minimal distance 50/ 65

45 Obtaining minimal distances Image from a surface Reconstruction pipeline Error calculation 51/ 65

46 Obtaining minimal distances Image from a surface Reconstruction pipeline Error calculation 51/ 65

47 Resolution dependencies Resolution dependencies Error metrics related to voxel extents Smoothing analysis Sphere error metric use a sphere error metric: ξ s = 1 V gen 1 1 X v n c(i) 2 V gen r n=0 53/ 65

48 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Error produced by Marching Cubes (sphere image) 54/ 65

49 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Error metrics in relation to voxel extents Preparation and calculation shrink surface by 1 voxel extent instead of scaling calculate ξ 1 and ξ 2 for both surfaces 55/ 65

50 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Smoothing Analysis Preparation choose previously generated approximating CT-image with HU l = 1024 HU i = 185 HU u = 655 generate surfaces from the following segmentations: Segmentation lower th. τ l upper th. τ u Is Is Is Is Is / 65

51 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Laplacian Smoothing τ u = -285 τ u = -185 τ u = -85 τ u = 115 τ u = 215 error ξ 2 in voxel units iteration steps 57/ 65

52 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Windowed Sinc Function Smoothing b = 0.05 b = 0.25 b = error ξ 2 in voxel units iteration steps 58/ 65

53 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Laplacian vs. Windowed Sinc Function Smoothing 1.2 Laplace smoothing, λ=0.1 WSF smoothing, b= error ξ 2 in voxel units iteration steps 59/ 65

54 Resolution dependencies Error metrics related to voxel extents Smoothing analysis Laplacian vs. Windowed Sinc Function Smoothing av. max. curvature original av. max. curvature WSF, b=0.25 av. max. curvature laplace, λ= max. curvature iteration steps 60/ 65

55 and Conclusion References and Conclusion surface extraction image preprocessing (cropping, object insertion, filtering) CT-image preprocessing with a 3x3-convolution filter or a shift-scale filter yielded best results segmentation with Seeded Region Growing surface extraction with Marching Cubes surface post-processing (smoothing and curvature analysis) use Windowed Sinc Function Smoothing with - a pass-band of iterations monitor smoothing by evaluating surface curvature 62/ 65

56 and Conclusion References and Conclusion Accuracy analysis resolution dependencies higher resolutions provide lower errors smoothing analysis advantages of Windowed Sinc Function Smoothing prevents shrinkage produces lower errors while keeping constant curvature 63/ 65

57 and Conclusion References Thank you for your attention! 64/ 65

58 References Introduction and Conclusion References [AKME + 90] Ludwig Adams, Werner Krybus, Dietrich Meyer-Ebrecht, Rainer Rueger, Joachim M. Gilsbach, Ralph Moesges, and Georg Schlöndorff. Computer-Assisted Surgery. IEEE Computer Graphics and Applications, 10(3):43 51, May [Ben90] Jon Louis Bentley. K-d trees for semidynamic point sets. In SCG 90: Proceedings of the sixth annual symposium on Computational geometry, pages , New York, NY, USA, ACM. [Tau95] Gabriel Taubin. A signal processing approach to fair surface design. In SIGGRAPH 95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, pages , New York, NY, USA, ACM. [TZG96] Gabriel Taubin, Tong Zhang, and Gene H. Golub. Optimal Surface Smoothing as Filter Design. In ECCV 96: Proceedings of the 4th European Conference on Computer Vision-Volume I, pages , London, UK, Springer-Verlag. [AB94] R. Adams and L. Bischof, Seeded Region Growing. In IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 6, pages , IEEE Computer Society, 1994,Washington, DC, USA. [LC87] William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3D surface construction algorithm, In ACM SIGGRAPH Computer Graphics, Vol. 21, pages , ACM, 1987, New York, USA. 65/ 65