Extracting Branching Object Geometry via Cores Doctoral Dissertation Defense Yoni Fridman August 17, 2004 Advisor: Stephen Pizer Doctoral Dissertation

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  • Slide 1
  • Extracting Branching Object Geometry via Cores Doctoral Dissertation Defense Yoni Fridman August 17, 2004 Advisor: Stephen Pizer Doctoral Dissertation Defense Yoni Fridman August 17, 2004 Advisor: Stephen Pizer
  • Slide 2
  • OutlineOutline Motivation, Background, and Thesis Statement Cores in 3D Handling Branching Objects with Cores Ends of Cores Evaluation and Results Scientific Contributions and Future Work Motivation, Background, and Thesis Statement Cores in 3D Handling Branching Objects with Cores Ends of Cores Evaluation and Results Scientific Contributions and Future Work
  • Slide 3
  • Motivation: Endovascular Embolization Driving problem: Endovascular embolization of a cerebral aneurysm Endovascular embolization Courtesy Toronto Brain Vascular Malformation Study Group http://brainavm.uhnres.utoronto.ca/ Aneurysm in a DSA projection image
  • Slide 4
  • Motivation: Endovascular Embolization Difficulty: How to guide catheter to aneurysm In 2D, projection overlap makes geometry of vasculature ambiguous In 3D, information lost when viewing 1 slice at a time Difficulty: How to guide catheter to aneurysm In 2D, projection overlap makes geometry of vasculature ambiguous In 3D, information lost when viewing 1 slice at a time Axial slice of head MRA data Aneurysm in a DSA projection image
  • Slide 5
  • GoalGoal Automatically extract representations of anatomic objects from medical images 3D vessel tree representation Axial projection image of head MRA data
  • Slide 6
  • Motivation: Radiation Treatment Planning Driving problem: 3D radiation treatment planning Tumor in axial slice of abdominal CT data Courtesy Shands Health Care
  • Slide 7
  • GoalGoal Automatically extract representations of anatomic objects from medical images 3D kidney representation Tumor in axial slice of abdominal CT data Courtesy Shands Health Care
  • Slide 8
  • Blums medial axis The medial axis is a formulation that describes objects by focusing on their middles Can be thought of as a skeleton or backbone Pioneered by Blum (Blum 1967, Blum & Nagle 1978) for biological structures The medial axis is a formulation that describes objects by focusing on their middles Can be thought of as a skeleton or backbone Pioneered by Blum (Blum 1967, Blum & Nagle 1978) for biological structures An object and its medial axis
  • Slide 9
  • Overview of Cores (in 2D) A core is a medial axis of an object at scale (i.e., in a blurred image) Why at scale? To reduce image noise So small indentations and protrusions on the object boundary are not reflected in the core A core is a medial axis of an object at scale (i.e., in a blurred image) Why at scale? To reduce image noise So small indentations and protrusions on the object boundary are not reflected in the core A synthetic object and its core
  • Slide 10
  • Overview of Cores (in 2D) A core is a medial axis of an object at scale (i.e., in a blurred image) Each location on the core stores orientation and radius information A core is a medial axis of an object at scale (i.e., in a blurred image) Each location on the core stores orientation and radius information A synthetic object and its core
  • Slide 11
  • Cores as Object Representations An objects core provides a discrete representation, at scale, of the object This can be seen by taking the union of disks centered along the core, with the given radii This representation is computed automatically An objects core provides a discrete representation, at scale, of the object This can be seen by taking the union of disks centered along the core, with the given radii This representation is computed automatically Recreating an object from its core
  • Slide 12
  • Types of Cores Two mathematically distinct types of cores have been studied: 1. Maximum convexity cores (Morse 1994, Eberly 1996, Damon 1998, Miller 1998, Damon 1999, Keller 1999) 2. Optimum parameter cores (Furst 1999, Aylward & Bullitt 2002) This dissertation deals with optimum parameter cores; details later Two mathematically distinct types of cores have been studied: 1. Maximum convexity cores (Morse 1994, Eberly 1996, Damon 1998, Miller 1998, Damon 1999, Keller 1999) 2. Optimum parameter cores (Furst 1999, Aylward & Bullitt 2002) This dissertation deals with optimum parameter cores; details later
  • Slide 13
  • Thesis Statement Optimum parameter cores with branch- handling and end-detection provide an effective means for extracting the branching geometry of tubular structures from 3D medical images and for extracting the branching geometry of general structures from relatively low noise 3D medical images.
  • Slide 14
  • OutlineOutline Motivation, Background, and Thesis Statement Cores in 3D Handling Branching Objects with Cores Ends of Cores Evaluation and Results Scientific Contributions and Future Work Motivation, Background, and Thesis Statement Cores in 3D Handling Branching Objects with Cores Ends of Cores Evaluation and Results Scientific Contributions and Future Work
  • Slide 15
  • Core Computation Optimize the derivative of Gaussians fit to the image by varying location, radius, and orientation Take a step forward and iterate Optimize the derivative of Gaussians fit to the image by varying location, radius, and orientation Take a step forward and iterate Initialize a medial atom and place a derivative of a Gaussian at the tips of two spokes Computing the core of a synthetic object
  • Slide 16
  • Cores of 3D objects are generically 2D (sheets). Objects represented by 2D cores are called slabs Special case: Cores of tubes are 1D (curves) Cores of 3D objects are generically 2D (sheets). Objects represented by 2D cores are called slabs Special case: Cores of tubes are 1D (curves) Cores in 3D Slabs and Tubes
  • Slide 17
  • What is a Medial Atom? A medial atom m = (x, r, F, ) is an oriented position with two spokes. In 3D (Morse 1994, Fritsch et al. 1995, Pizer et al. 1998, Furst 1999, Pizer et al. 2003) A medial atom m = (x, r, F, ) is an oriented position with two spokes. In 3D (Morse 1994, Fritsch et al. 1995, Pizer et al. 1998, Furst 1999, Pizer et al. 2003) x is its location in 3-space r is its radius, or the length of two spokes, p and s F is a frame that defines its orientation b is the bisector of the spokes is its object angle x r p s b Medial atom geometry
  • Slide 18
  • My Medial Atoms I constrain to /2, so m = (x, r, F) This improves the resistance of core computation I constrain to /2, so m = (x, r, F) This improves the resistance of core computation to image noise It is also less natural and affects core computation in other ways I quantify these effects in the dissertation and show that the constraint is beneficial overall x r p s b My medial atom geometry
  • Slide 19
  • What is the Medialness of a Medial Atom m? Medialness M(m) is a scalar function that measures the fit of a medial atom to image data A kernel K(m) is created from m by placing two directional derivatives of volumetric Gaussians, one at each spoke tip, with the derivatives taken in the spoke directions Medialness M(m) is a scalar function that measures the fit of a medial atom to image data A kernel K(m) is created from m by placing two directional derivatives of volumetric Gaussians, one at each spoke tip, with the derivatives taken in the spoke directions x p s M(m) is then computed by integrating image intensities as weighted by K(m)
  • Slide 20
  • Maximizing Medialness Given an approximate atom m = (x, r, F), find x, r, and F that maximize M(m) Let x = (s, t, u) and F = (az, alt, ) u is in the spoke direction and (s, t) span the normal plane az and alt are the azimuth and altitude of b, is spin about b Maximize with respect to position and then parameters: This defines the optimum parameter cores I use Given an approximate atom m = (x, r, F), find x, r, and F that maximize M(m) Let x = (s, t, u) and F = (az, alt, ) u is in the spoke direction and (s, t) span the normal plane az and alt are the azimuth and altitude of b, is spin about b Maximize with respect to position and then parameters: This defines the optimum parameter cores I use
  • Slide 21
  • Core-FollowingCore-Following Now we need to follow a 2D sheet cant simply step forward Rather, march along a grid Now we need to follow a 2D sheet cant simply step forward Rather, march along a grid Following the 2D core of a slab in 3D 2D core of a kidney
  • Slide 22
  • Core-FollowingCore-Following I add two features to core-following that improve its resistance to noise: 1. When optimizing medialness, I penalize significant changes in radius and/or orientation between neighboring atoms 2. I compute the core at a coarse sampling (taking large steps between atoms) and then refine the sampling I add two features to core-following that improve its resistance to noise: 1. When optimizing medialness, I penalize significant changes in radius and/or orientation between neighboring atoms 2. I compute the core at a coarse sampling (taking large steps between atoms) and then refine the sampling Refining a core
  • Slide 23
  • Cores of Tubes Cores of tubes are computed using medial atoms with a set of (8) concentric spokes The resulting core is a curve Problem: Euclidean optimi

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