Object & Shape Based Medical Image Analysis Old Well

The University of North Carolina at Chapel Hill
College of Arts and Sciences
Department of Computer Science
Medical Image Display & Analysis Group

Object & Shape Based
Medical Image Analysis

Slide Presentations

Object Shape Tutorial , Stephen M. Pizer

Object-Intrinsic Coordinates and the Associated Non-Euclidean Geometry , Stephen M. Pizer, Andrew Thall


Viewing 3D objects from a medial point of view allows one to focus on the objectís decomposition into figures. Viewing figures from a first order medial point of view, i.e., adding to the medial surface and the radius function their first derivatives, leads to a medial-centric view of both the object surface and of 3-space that allows not only global but local shape information to be accessed, as a result of local magnification equivariance. The result for a single figure object is an object intrinsic coordinate system in which distance is decomposed into distance along the medial surface and distance along boundary normals from the medial locus up to any external focal surface. Moreover, both distances are measured proportional to medial radius. This leads to a frame fitted to the medial surface according to this geometry, as well as to frames fitted to each point in space. The way in which this yields correspondences in position, local frame (orientation), and local ruler under figural deformation and thus to possibilities for shape statistics will be discussed. A discussion of figurally based coordinates for objects made from multiple attached figures will follow. Finally, the issues of defining these object-intrinsic for the interstitial space between multiple objects will be briefly introduced.




Links in the text below point to sections of a Select Bibliography on Object Segregation and Shape Representation by Cores or Medialness. The Select Bibliography includes citations that present the best and most recent papers in each topic, and it contains a fairly fine subdivision of topic areas. A Full Bibliography for this research area is also avaialable.

Applications and Objectives

A group led by Kenan Professor Stephen M. Pizer researches methods related to the analysis of medical images in terms of the objects in them and their shape. Application objectives include the extraction of objects, registration of images based on object matching, measurement of object shape change, and 3D display of objects. Application areas include planning and verification of radiotherapy, planning and delivery of neurosurgery, thoracic surgery, and biopsy, and diagnosis of schizophrenia via measurement of shape change of brain organs.

Image Analysis Approach

The image analysis approach is based on extracting and using models of object shape that include skeletal middles of figures, i.e., medial loci (see Fig.). These medial loci are frequently linked to the locus forming the object boundary. The figures are frequently linked to subfigures representing protrusions and indentations in their parent figures. Just as boundaries are described as loci of position that locally have high values of behaving like a boundary (boundariness), medial loci are described as loci of position & width that locally have high values of behaving like a skeletal middle of a figure (medialness). Medialness is defined in terms of convolution kernels at many positions and scales (in scale space), with scales, i.e., kernel widths, that are a significant fraction of the figure's radial width.

***Figure to be inserted here soon***

Fig. The medial loci, in this case cores, for two figures and one's subfigure in an image object

The Core as Medial Locus

Model formation from one or more reference images and interactive object extraction from an image are done via cores, which are ridges of medialness. Core definition is based on invariance to zoom, and core extraction for an image figure is based either on interactive stimulation at an approximate position and width or on extracting subfigure cores on the approximate boundaries isomorphic to cores. The singularities of ridges and object-relative geometry of scale space are mathematical subjects under study.

Model-Based Image Analysis

Model-based object segmentation or registration, based on linked medial and boundary loci, uses methods of deformable loci. These optimize an objective function involving two components. The first component measures consistency with knowledge as to shape, richly reflected through the links in a way based on the theory of Markov random fields. The second component measures the consistency of the locus with image information by integrating boundariness on the boundary locus and medialness on the medial locus. Via approaches of statistical pattern recognition, multiscale geometric operators tailored to application-specific aspects of shape and able as well to measure aspects of absolute intensity and texture can be included in this measure of consistency of the loci with the image. Measurement of shape variation from a model is accomplished through the difference of the links from the model, relative to the variabilities of the links that were found in a training set. Here is a recent paper. on medical image segmentation using deformable M-Reps.

Models of Human Vision

Models of the extraction and representation of objects by human vision are based on cores and medialness. We have been studying psychophysically how the human visual system represents object shape and sets of objects.

Three Dimensional Images and Graphics

Most work to date has been on 2D images, but recently work on 3D images has begun. 3D object rendering avoiding occlusion with the use of a medial model is being studied.


Faculty involved in this research, with their principal department, are

Last update: 14 February 1997