Object & Shape Based Medical Image Analysis
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
Abstract
Viewing 3D objects from a medial point of view allows one to focus on
the object’s 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.
Bibliographies
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.
People
Faculty involved in this research, with their principal department, are
Last update: 14 February 1997