Hybrid Segmentation Fuzzy Connectedness Voronoi Diagram

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					                      Hybrid Segmentation:
                      Fuzzy Connectedness
                        Voronoi Diagram
                          Classification
                      and Deformable Model

Celina Imielińska
Yinpeng Jin
Elsa Angelini
Andrew Laine
Columbia University
Hybrid Segmentation Engine
                Fuzzy Connectedness with Voronoi
                 Diagram and Deformable Model
       use (simple) 3D fuzzy connectedness to generate statistics
        for homogeneity operator
       run Voronoi Diagram-classification algorithm
       use deformable model to determine final (3D) boundary




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                 Overview:
     SimpleFuzzyConnectednessImageFilter
   Compared to “VectorialFuzzy…”:
- Non-scale-based.
- Non-iterative.
- Only one seed in the target region.
   Basic Idea:
- Fuzzy Affinity between two nearby pixels based on their similarity
   and their similarity with the estimated object.
- Define Strength of a path and Fuzzy Connectedness between two
   arbitrary pixels within the image based on the Fuzzy Affinity.
- Compute Fuzzy Connectedness value of each pixels to the seed
   point (via dynamic programming): A Fuzzy Map.
- Thresholding on the Fuzzy Map to give a object that strongly
   connected to the seed point (segmentation result).

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              Fuzzy Connectedness Segmentation
                            itkImageToImageFilter


             itkSimpleFuzzyConnectednessImageFilterBase



itkSimpleFuzzyConnectednessScalarImageFilter   itkSimpleFuzzyConnectednessRGBImageFilter



 • itkSimpleFuzzyConnectednessImageFilterBase:
   Base class for simple fuzzy connectedness segmentation.
 • itkSimpleFuzzyConnectednessScalarImageFilter:
   Implementation of FC segmentation of single channel (gray scale) image.
 • itkSimpleFuzzyConnectednessRGBImageFilter:
   Implementation of FC segmentation of three channel (RGB) image.
 • Classes can be derived from the base class by defining other affinity function,
    and targeting on an arbitrary number of channels.
                            Overview:
                  VoronoiDiagramImageFilter(2D)
      Algorithm:
 1. Given initial number of seed points. (default 200 random points, can be changed
       by SetSeeds or SetNumberOfSeeds).
 2. Compute the Voronoi Diagram based on the seed points.
 3. Classify each Voronoi region as internal/external by homogeneity operator.
 4. Define boundary region as “external” that have at least one “internal” neighbors,
      then add seed points to those boundary region (if it is large enough: this gives
      another parameter the minimum region, default as 20 pixels, can be changed
      by SetMinRegion).
 5. Goto 2 until certain steps have been run, or no more seed points can be added.
      Parameters:
 - Initial number of seeds, MinRegion, Running Mode, Output Mode.
 - Others depend on the homogeneity operator.
 - One parameter for the hybrid framework so far: UseBackGroundInAprior.


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     Voronoi Diagram Classification Algorithm
                        itkImageToImageFilter


              itkVoronoiSegmentationImageFilterBase



 itkVoronoiSegmentationImageFilter      itkVoronoiSegmentationRGBImageFilter


• itkVoronoiSegmentationImageFilterBase:
  Base class for segmentation based on Voronoi diagram.
• itkVoronoiSegmenationImageFilter:
  Implementation of VD segmentation of single channel (gray scale) image.
• itkVoronoiSegmentationRGBImageFilter:
  Implementation of VD segmentation of three channel (RGB) image.
• Classes can be derived from the base class by defining other homogeneity
  measurement, and targeting on arbitrary number of channels.
Classes Checked-in for Implementation
       of Voronoi Diagram

  itkCellInterface             itkMesh


  itkPolygonCell        itkVoronoiDiagram2D


               itkMeshSource


      itkVoronoiDiagram2DGenerator
             Working Alone:
      SimpleFuzzyConnectednessImageFilter


                          Input: itkImage object
Parameters:
Estimated mean
and variance
                     SimpleFuzzyConnectednessImageFilter
of the object
(other parameters)

                          Output: itkImage object
                               (binary mask)
                  Working Alone:
           VoronoiSegmenationImageFilter

Parameters:
                       Input:: itkImage object
Estimated mean
and variance
of the object
                  VoronoiSegmentationImageFilter
      or
 A-prior::
 Binary Mask      Output:: itkImage object
                        (binary object mask)
                    or (binary boundary delineate))
      Hybrid Segmentation: (simple) Fuzzy
      Connectedness + Voronoi Diagram
                      Input: itkImage object

SimpleFuzzyConnectednessImageFilter


        A-prior:
        Binary Mask     VoronoiSegmentationImageFilter


                        Output: itkImage object
                              (binary object mask)
                          or (binary boundary delineate)
   Hybrid Segmentation: (simple) Fuzzy Connectedness
       + Voronoi Diagram + Deformable Model
                       Input: itkImage object

SimpleFuzzyConnectednessImageFilter


         A-prior:
         Binary Mask      VoronoiSegmentationImageFilter


    Output: itkImage object               Deformable
         binary mask                        Model

              Output: itkMesh object or binary object mask
   FC/VD
Fuzzy
Connectedness/
Voronoi Diagram
Classification




                  Visible Human Male Data - Segmentation of temporalis muscle
                 (simple) Fuzzy Connectedness with
                           Voronoi Diagram




Fuzzy                 Binary image from   Voronoi Diagram        Final boundary:
Connectedness:        which we generate   with yellow boundary   a subgraph of the
Fuzzy map             homogeneity         Voronoi regions        Delaunay triangulation
                      statistics          (Visible Human data)
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                    Sample Parameters
        Hybrid Method: SimpleFuzzy + VoronoiDiagram
                (Visible Human Male visceral adipose tissue)




                  Fuzzy Connectedness:
                                                 Voronoi Diagram:
                  Mean={201.0, 179.2, 127.6}
                                                 MeanPctErr=0.35 for all chanels.
                  Var={289.9, 389.8, 223.8}
                  Computed from a small sample   VarPctErr=2.0 for all chanels.
                  region within the object.
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Hybrid Segmentation: (simple) Fuzzy +
Voronoi Diagram + Deformable Model

                                        Color
                                        Raw data




                                        FC/VD




                                        FC/VD/
                                        CC/DM




                                        Hand
                                        segm.
                Hybrid Method: (simple) Fuzzy +
              Voronoi Diagram + Deformable Model




            (Click to open QT-VR object)                           (Click to open QT-VR object)
                  FC/VD                                                  FC/VD/CC/DM




     Visible Human
     Female Jaw



                                    (Click to open QT-VR object)

                                     Hand Segmentation
Columbia University
    Integrated System for Quantification of Adipose
           Tissue from Whole Body MRI scans
       (A. Laine, C. Imielińska, S. Heymsfield, W. Shen, Y. Jin, E. Angelini
             Columbia University and St. Luke’s Roosevelt Hospital)




   Build an integrated imaging system to
    improve the overall performance of
    acquisition, segmentation, quantification and
    analysis of adipose tissues in humans
    obtained from whole body MRI scans


Columbia University
  Integrated System for Quantification of Adipose
         Tissue from Whole Body MRI scans




Segmented Whole-body                        Reconstructed 3D body
   MRI scan                                 Composition from
(St. Luke’s-Roosevelt Hospital              Segmented whole body MRI scan
Obesity Research Center – Dr. Heymsfield)
       Integrated System for Quantification of Adipose
              Tissue from Whole Body MRI scans
      Segmentation of adipose tissue using hybrid segmentation algorithm




Input data –          Training – (simple   Segmented Image Smoothed segmented
                      FC): Tissue          VD classification Image – adipose
MRI T1 image                                                 tissue
                      homogeneity
                                                             (visceral and
                                                             Subcutaneous)


Columbia University
              Integrated System for Quantification
      of Adipose Tissue from Whole Body MRI scans
     Segmentation of adipose tissue using hybrid segmentation algorithm




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      Demo: Hybrid Segmentation




Fuzzy Connectedness   Voronoi Diagram Classification
            Demo 2: Hybrid Segmentation: SPECT data
    Fuzzy Connectedness with Voronoi Diagram Classification




             LoadRawImage               Training

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              Demo: Hybrid Segmentation: SPECT data




             Fuzzy Segmentation        Fuzzy Scene


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               Demo: Hybrid Segmentation: SPECT data




Loading Voronoi Classification   Voronoi Classification: Object   Voronoi Classification: Boundary




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              Demo: Hybrid Segmentation: SPECT data




                 Result 1                   Result 2


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                                Related Publications
1. Angelini, E.; Imielinska,C.; Jin, Y.; Laine,A., “Improving statistics for hybrid segmentation of high-
resolution multichannel images”, SPIE International Symposium on Medical Imaging 2002, Image
Processing Conference.

2. Jin, Y.; Imielinska,C.; Laine,A., “A Homogeneity-Based Speed Term for Level-set Shape Detection”, SPIE
International
    Symposium on Medical Imaging 2002, Image Processing Conference.

3. J.K. Udupa, V.R. Leblanc, H. Schmidt, C. Imielinska, K.P. Saha, G.J. Grevera, Y. Zhuge, P. Molholt, L.
Currie, Y.
Jin, “A Methodology for Evaluating Image Segmentation Algorithms”, SPIE Medical Imaging, San Diego,
2002.

4. .Imielinska, C.; Metaxas, D.; Udupa, J.; Jin, Y.; Chen, T., "Hybrid Segmentation of Anatomical Data",
   MICCAI 2001 conference, Utrecht, The Netherlands, 14-17 October 2001.
5. Imielinska, C.; Metaxas, D.; Udupa, J.; Jin, Y.; Chen, T., "Hybrid Segmentation of the Visible Human
Data", in the Proceedings of the Third Visible Human Project Conference, Bethesda, MD, October 5-6, 2000.

6. Imielinska, C.; Downes, M; and Yuan, W., "Semi-Automated Color Segmentation of Anatomical Tissue",
Journal of Computerized Medical Imaging and Graphics, 24(2000), 173-180, April, 2000.
                              Related Publications
7. J.K. Udupa, and S. Samarasekera: “Fuzzy Connectedness and Object Definition: Theory, Algorithms, and
Applications in Image Segmentation,” Graphical Models and Image Processing, 58(3):246-261, 1996.

8. P. Saha and J.K. Udupa: “Scale-based Fuzzy Connected Image Segmentation: Theory, Algorithms and
Validation,” Computer Vision and Image Understanding, 77(2):145-174, 2000.

9. P.K. Saha and J.K. Udupa: “Relative Fuzzy Connectedness Among Multiple Objects: Theory, Algorithms
and Applications in Image Segmentation,” Computer Vision and Image Understanding, 82(1):42-56, 2001.

10. P.K. Saha and J.K. Udupa: “Fuzzy Connected Object Delineation: Axiomatic Path Strength Definition
and the Case of Multiple Seeds,” Computer Vision and Image Understanding, 83:275-295, 2001.

11. J.K. Udupa, P.K. Saha and R.A. Lotufo: “Relative Fuzzy Connectedness and Object Definition: Theory,
algorithms, and Applications in Image Segmentation,” IEEE Transactions on Pattern Analysis and Machine
Intelligence, 24:1485-1500, 2002.

12. L.G. Nyul, A.F. Falcao and J.K. Udupa: “Fuzzy-Connected 3D Image Segmentation at Interactive
Speeds,” Graphical Models and Image Processing, accepted.

13. Deformable Model Techniques for Graphics and Medical Applications'', D. Metaxas. Computer Graphics
International, Geneva, Switzerland, June 23, 2000.

14. Image Segmentation based on the Integration of Markov Random Fields and Deformable Models'', T.
Chen and D. Metaxas. Procs MICCAI 2000, Pittsburgh, PA, October 11-14, 2000.