AIM-407
Annotated Production Systems: A Model for Skill Acquisition
Author[s]: Ira P. Goldstein and Eric Grimson
Date: February 1977PS Download: ftp://publications.ai.mit.edu/ai-publications/0-499/AIM-407.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-407.pdfAbstract: Annotated Production Systems provide a
procedural model for skill acquisition by
augmenting a production model of the skill
with formal commentary describing plans,
bugs, and interraltionships between various
productions. This commentary supports
processes of efficient interpretation, self-
debugging and self-improvement. The theory
of annotated productions is developed by
analyzing the skill of attitude instrument flying.
An annotated production interpreter has been
written that executes skill models which
control a flight simulator. Preliminary evidence
indicates that annotated productions
effectively model certain bugs and certain
learning behaviors characteristic of student
pilots.
AIM-510
Differential Geometry, Surface Patches and Convergence Methods
Author[s]: W.E.L. Grimson
Date: February 1979PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-510.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-510.pdfAbstract: The problem of constructing a surface from
the information provided by the Marr-Poggio
theory of human stereo vision is investigated.
It is argued that not only does this theory
provide explicit boundary conditions at certain
points in the image, but that the imaging
process also provides implicit conditions on
all other points in the image. This argument is
used to derive conditions on possible
algorithms for computing the surface.
Additional constraining principles are applied
to the problem; specifically that the process
be performable by a local-support parallel
network. Some mathematical tools,
differential geometry, Coons surface patches
and iterative methods of convergence,
relevant to the problem of constructing the
surface are outlined. Specific methods for
actually computing the surface are examined.
AIM-565
A Computer Implementation of a Theory of Human Stereo Vision
Author[s]: W.E.L. Grimson
Date: January 1980PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-565.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-565.pdfAbstract: Recently, Marr and Poggio (1979) presented a
theory of human stereo vision. An
implementation of that theory is presented
and consists of five steps: (1) The left and
right images are each filtered with masks of
four sizes that increase with eccentricity; the
shape of these masks is given by $
abla^{2}G$, the laplacian of a gaussian
function. (2) Zero-crossing in the filtered
images are found along horizontal scan lines.
(3) For each mask size, matching takes place
between zero-crossings of the same sign and
roughly the same orientation in the two
images, for a range of disparities up to about
the width of the mask's central region.
Within this disparity range, Marr and Poggio
showed that false targets pose only a simple
problem. (4) The output of the wide masks
can control vergence movements, thus
causing small masks to come into low
resolution to dealing with small disparities at
a high resolution. (5) When a
correspondence is achieved, it is stored in a
dynamic buffer, called the 2 1/2 dimensional
sketch. To support the sufficiency of the Marr-
Poggio model of human stereo vision, the
implementation was tested on a wide range
of stereograms from the human stereopsis
literature. The performance of the
implementation is illustrated and compared
with human perception. As well, statistical
assumptions made by Marr and Poggio are
supported by comparison with statistics found
in practice. Finally, the process of
implementing the theory has led to the
clarification and refinement of a number of
details within the theory; these are discussed
in detail.
AIM-613
A Computational Theory of Visual Surface Interpolation
Author[s]: W.E.L. Grimson
Date: June 1981PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-613.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-613.pdfAbstract: Computational theories of structure from
motion [Ulman, 1979] and stereo vision [Marr
and Poggio, 1979] only specify the
computation of three-dimensional surface
information at special points in the image. Yet,
the visual perception is clearly of complete
surfaces. In order to account for this, a
computational theory of the interpolation of
surfaces from visual information is presented.
AIM-663
The Implicit Constraints of the Primal Sketch
Author[s]: W.E.L Grimson
Date: October 1981PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-663.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-663.pdfAbstract: Computational theories of structure-from-
motion and stereo vision only specify the
computation of three-dimensional surface
information at points in the image at which the
irradiance changes. Yet, the visual perception
is clearly of complete surfaces, and this
perception is consistent for different
observers. Since mathematically the class of
surfaces which could pass through the known
boundary points provided by the stereo
system is infinite and contains widely varying
surfaces, the visual system must incorporate
some additional constraints besides the
known points in order to compute the
complete surface. Using the image irradiance
equation, we derive the surface consistency
constraint, informally referred to as no news is
good news. The constraint implies that the
surface must agree with the information from
stereo or motion correspondence, and not
vary radically between these points. An explicit
form of this surface consistency constraint is
derived, by relating the probability of a zero-
crossing in a region of the image to the
variation in the local surface orientation of the
surface, provided that the surface albedo and
the illumination are roughly constant. The
surface consistency constraint can be used to
derive an algorithm for reconstructing the
surface that “best” fits the surface information
provided by stereo or motion correspondence.
AIM-666
The Perception of Subjective Surfaces
Author[s]: Michael Brady and W. Eric L. Grimson
Date: November 1981PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-666.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-665.pdfAbstract: It is proposed that subjective contours are an
artifact of the perception of natural three-
dimensional surfaces. A recent theory of
surface interpolation implies that “subjective
surfaces” are constructed in the visual system
by interpolation between three-dimensional
values arising from interpretation of a variety
of surface cues. We show that subjective
surfaces can take any form, including singly
and doubly curved surfaces, as well as the
commonly discussed fronto-parallel planes.
In addition, it is necessary in the context of
computational vision to make explicit the
discontinuities, both in depth and in surface
orientation, in the surfaces constructed by
interpolation. It is proposed that subjective
surfaces and subjective contours are
demonstrated. The role played by figure
completion and enhanced brightness contrast
in the determination of subjective surfaces is
discussed. All considerations of surface
perception apply equally to subjective
surfaces.
AIM-697
Binocular Shading and Visual Surface Reconstruction
Author[s]: W.E.L. Grimson
Date: August 1982PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-697.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-697.pdfAbstract: Zero-crossing or feature-point based stereo
algorithms can, by definition, determine
explicit depth information only at particular
points on the image. To compute a complete
surface description, this sparse depth map
must be interpolated. A computational theory
of this interpolation or reconstruction process,
based on a surface consistency constraint,
has previously been proposed. In order to
provide stronger boundary conditions for the
interpolation process, other visual cues to
surface shape are examined in this paper. In
particular, it is shown that, in principle,
shading information from the two views can
be used to determine the orientation of the
surface normal along the feature-point
contours, as well as the parameters of the
reflective properties of the surface material.
The numerical stability of the resulting
equations is also examined.
AIM-738
Model-Based Recognition and Localization from Sparse Range or Tactile Data
Author[s]: W. Eric L. Grimson and Tomas Lozano-Perez
Date: August 1983PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-738.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-738.pdfAbstract: This paper discusses how local
measurements of three-dimensional
positions and surface normals (recorded by a
set of tactile sensors, or by three-dimensional
range sensors), may be used to identify and
locate objects, from among a set of known
objects. The objects are modeled as
polyhedra having up to six degrees of freedom
relative to the sensors. We show that
inconsistent hypotheses about pairings
between sensed points and object surfaces
can be discarded efficiently by using local
constraints on: distances between faces,
angles between face normals, and angles
(relative to the surface normals) of vectors
between sensed points. We show by
simulation and by mathematical bounds that
the number of hypotheses consistent with
these constraints is small. We also show how
to recover the position and orientation of the
object from the sense data. The algorithm’s
performance on data obtained from a
triangulation range sensor is illustrated.
AIM-744
Constructing a Depth Map from Images
Author[s]: Katsushi Ikeuchi
Date: August 1983PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-744.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-744.pdfAbstract: This paper describes two methods for
constructing a depth map from images. Each
method has two stages. First, one or more
needle maps are determined using a pair of
images. This process employs either the
Marr-Poggio-Grimson stereo and shape-from-
shading, or, instead, photometric stereo.
Secondly, a depth map is constructed from
the needle map or needle maps computed by
the first stage. Both methods make use of an
iterative relaxation method to obtain the final
depth map.
AIM-762
Computational Experiments with a Feature Based Stereo Algorithm
Author[s]: W. Eric L. Grimson
Date: January 1984PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-762.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-762.pdfAbstract: Computational models of the human stereo
system can provide insight into general
information processing constraints that apply
to any stereo system, either artificial or
biological. In 1977, Marr and Poggio proposed
one such computational model, that was
characterized as matching certain feature
points in difference-of-Gaussian filtered
images, and using the information obtained
by matching coarser resolution of
representations to restrict the search space
for matching finer resolution representations.
An implementation of the algorithm and its
testing on a range of images was reported in
1980. Since then a number psychophysical
experiments have suggested possible
refinements to the model and modifications to
the algorithm. As well, recent computational
experiments applying the algorithm to a variety
of natural images, especially aerial
photographs, have led to a number of
modifications. In this article, we present a
version of the Marr-Poggio-Grimson algorithm
that embodies these modifications and
illustrate its performance on a series of
natural images.
AIM-763A
The Combinatorics of Local Constraints in Model-Based Recognition and Localization from Sparse Data
Author[s]: W. Eric L. Grimson
Date: March 1986PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-763a.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-763a.pdfAbstract: The problem of recognizing what objects are
where in the workspace of a robot can be cast
as one of searching for a consistent matching
between sensory data elements and
equivalent model elements. In principle, this
search space is enormous and to control the
potential combinatorial explosion, constraints
between the data and model elements are
needed. We derive a set of constraints for
sparse sensory data that are applicable to a
wide variety of sensors and examine their
characteristics. We then use known bounds
on the complexity of constraint satisfaction
problems together with explicit estimates of
the effectiveness of the constraints derived for
the case of sparse, noisy three-dimensional
sensory data to obtain general theoretical
bounds on the number of interpretations
expected to be consistent with the data. We
show that these bounds are consistent with
empirical results reported previously. The
results are used to demonstrate the graceful
degradation of the recognition technique with
the presence of noise in the data, and to
predict the number of data points needed in
general to uniquely determine the object
being sensed.
AIM-841
Recognition and Localization of Overlapping Parts from Sparse Data
Author[s]: W. Eric L. Grimson and Tomas Lozano-Perez
Date: June 1985PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-841.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-841.pdfAbstract: This paper discusses how sparse local
measurements of positions and surface
normals may be used to identify and locate
overlapping objects. The objects are
modeled as polyhedra (or polygons) having
up to six degreed of positional freedom
relative to the sensors. The approach
operated by examining all hypotheses about
pairings between sensed data and object
surfaces and efficiently discarding
inconsistent ones by using local constraints
on: distances between faces, angles between
face normals, and angles (relative to the
surface normals) of vectors between sensed
points. The method described here is an
extension of a method for recognition and
localization of non-overlapping parts
previously described in [Grimson and Lozano-
Perez 84] and [Gaston and Lozano-Perez 84].
AIM-855
Sensing Strategies for Disambiguating Among Multiple Objects in Known Poses
Author[s]: W. Eric L. Grimson
Date: August 1985PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-855.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-855.pdfAbstract: The need for intelligent interaction of a robot
with its environment frequently requires
sensing of the environment. Further, the need
for rapid execution requires that the interaction
between sensing and action take place using
as little sensory data as possible, while still
being reliable. Previous work has developed
a technique for rapidly determining the
feasible poses of an object from sparse,
noisy, occluded sensory data. In this paper,
we examine techniques for acquiring position
and surface orientation data about points on
the surfaces of objects, with the intent of
selecting sensory points that will force a
unique interpretation of the pose of the object
with as few data points as possible. Under
some simple assumptions about the sensing
geometry, we derive a technique for predicting
optimal sensing positions. The technique
has been implemented and tested. To fully
specify the algorithm, we need estimates of
the error in estimating the position and
orientation of the object, and we derive
analytic expressions for such error for the
case of one particular approach to object
recognition.
AIM-983
On the Recognition of Curved Objects
Author[s]: W. Eric L. Grimson
Date: July 1987PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-983.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-983.pdfAbstract: Determining the identity and pose of occluded
objects from noisy data is a critical part of a
system's intelligent interaction with an
unstructured environment. Previous work has
shown that local measurements of the
position and surface orientation of small
patches of an object's surface may be used in
a constrained search process to solve this
problem for the case of rigid polygonal objects
using two-dimensional sensory data, or rigid
polyhedral objects using three-dimensional
data. This note extends the recognition
system to deal with the problem of
recognizing and locating curved objects. The
extension is done in two dimensions, and
applies to the recognition of two-dimensional
objects from two-dimensional data, or to the
recognition of three-dimensional objects in
stable positions from two- dimensional data.
AIM-985
On the Recognition of Parameterized Objects
Author[s]: W. Eric L. Grimson
Date: October 1987PS Download: ftp://publications.ai.mit.edu/ai-publications/500-999/AIM-985.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-985.pdfAbstract: Determining the identity and pose of occluded
objects from noisy data is a critical step in
interacting intelligently with an unstructured
environment. Previous work has shown that
local measurements of position and surface
orientation may be used in a constrained
search process to solve this problem, for the
case of rigid objects, either two-dimensional
or three-dimensional. This paper considers
the more general problem of recognizing and
locating objects that can vary in parameterized
ways. We consider objects with rotational,
translational, or scaling degrees of freedom,
and objects that undergo stretching
transformations. We show that the
constrained search method can be extended
to handle the recognition and localization of
such generalized classes of object families.
AIM-1019
The Combinatorics of Object Recognition in Cluttered Environments Using Constrained Search
Author[s]: W. Eric L. Grimson
Date: February 1988PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1019.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1019.pdfAbstract: When clustering techniques such as the
Hough transform are used to isolate likely
subspaces of the search space, empirical
performance in cluttered scenes improves
considerably. In this paper we establish
formal bounds on the combinatorics of this
approach. Under some simple assumptions,
we show that the expected complexity of
recognizing isolated objects is quadratic in
the number of model and sensory fragments,
but that the expected complexity of recognizing
objects in cluttered environments is
exponential in the size of the correct
interpretation. We also provide formal bounds
on the efficacy of using the Hough transform
to preselect likely subspaces, showing that
the problem remains exponential, but that in
practical terms, the size of the problem is
significantly decreased.
AIM-1044
On the Sensitivity of the Hough Transform for Object Recognition
Author[s]: W. Eric L. Grimson and David Huttenlocher
Date: May 1988PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1044.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1044.pdfAbstract: A common method for finding an object's
pose is the generalized Hough transform,
which accumulates evidence for possible
coordinate transformations in a parameter
space and takes large clusters of similar
transformations as evidence of a correct
solution. We analyze this approach by deriving
theoretical bounds on the set of
transformations consistent with each data-
model feature pairing, and by deriving
bounds on the likelihood of false peaks in the
parameter space, as a function of noise,
occlusion, and tessellation effects. We argue
that blithely applying such methods to
complex recognition tasks is a risky
proposition, as the probability of false
positives can be very high.
AIM-1110
On the Verification of Hypothesized Matches in Model-Based Recognition
Author[s]: W. Eric L. Grimson and Daniel P. Huttenlocher
Date: May 1989PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1110.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1110.pdfAbstract: In model-based recognition, ad hoc
techniques are used to decide if a match of
data to model is correct. Generally an
empirically determined threshold is placed on
the fraction of model features that must be
matched. We rigorously derive conditions
under which to accept a match, relating the
probability of a random match to the fraction of
model features accounted for, as a function of
the number of model features, number of
image features and the sensor noise. We
analyze some existing recognition systems
and show that our method yields results
comparable with experimental data.
AIM-1111
The Combinatorics of Heuristic Search Termination for Object Recognition in Cluttered Environments
Author[s]: W. Eric L. Grimson
Date: May 1989PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1111.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1111.pdfAbstract: Many recognition systems use constrained
search to locate objects in cluttered
environments. Earlier analysis showed that
the expected search is quadratic in the
number of model and data features, if all the
data comes from one object, but is
exponential when spurious data is included.
To overcome this, many methods terminate
search once an interpretation that is "good
enough" is found. We formally examine the
combinatorics of this, showing that correct
termination procedures dramatically reduce
search. We provide conditions on the object
model and the scene clutter such that the
expected search is quartic. These results are
shown to agree with empirical data for
cluttered object recognition.
AIM-1226
The Effect of Indexing on the Complexity of Object Recognition
Author[s]: W. Eric L. Grimson
Date: April 1990PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1226.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1226.pdfAbstract: Many current recognition systems use constrained search to locate objects in cluttered environments. Previous formal analysis has shown that the expected amount of search is quadratic in the number of model and data features, if all the data is known to come from a sinlge object, but is exponential when spurious data is included. If one can group the data into subsets likely to have come from a single object, then terminating the search once a "good enough" interpretation is found reduces the expected search to cubic. Without successful grouping, terminated search is still exponential. These results apply to finding instances of a known object in the data. In this paper, we turn to the problem of selecting models from a library, and examine the combinatorics of determining that a candidate object is not present in the data. We show that the expected search is again exponential, implying that naïve approaches to indexing are likely to carry an expensive overhead, since an exponential amount of work is needed to week out each of the incorrect models. The analytic results are shown to be in agreement with empirical data for cluttered object recognition.
AIM-1250
Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment
Author[s]: W. Eric L. Grimson, Daniel P. Huttenlocher and David W. Jacobs
Date: August 1991PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1250.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1250.pdfAbstract: Affine transformations are often used in
recognition systems, to approximate the
effects of perspective projection. The
underlying mathematics is for exact feature
data, with no positional uncertainty. In
practice, heuristics are added to handle
uncertainty. We provide a precise analysis of
affine point matching, obtaining an expression
for the range of affine-invariant values
consistent with bounded uncertainty. This
analysis reveals that the range of affine-
invariant values depends on the actual $x$-
$y$-positions of the features, i.e. with
uncertainty, affine representations are not
invariant with respect to the Cartesian
coordinate system. We analyze the effect of
this on geometric hashing and alignment
recognition methods.
AIM-1362
Recognizing 3D Ojbects of 2D Images: An Error Analysis
Author[s]: W. Eric Grimson, Daniel P. Huttenlocher and T. D. Alter
Date: July 1992PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1362.ps.ZPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1362.pdfAbstract: Many object recognition systems use a small
number of pairings of data and model
features to compute the 3D transformation
from a model coordinate frame into the
sensor coordinate system. With perfect image
data, these systems work well. With uncertain
image data, however, their performance is
less clear. We examine the effects of 2D
sensor uncertainty on the computation of 3D
model transformations. We use this analysis
to bound the uncertainty in the transformation
parameters, and the uncertainty associated
with transforming other model features into
the image. We also examine the impact of the
such transformation uncertainty on
recognition methods.
AIM-1435
Why Stereo Vision is Not Always About 3D Reconstruction
Author[s]: W. Eric L. Grimson
Date: July 1993PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1435.ps.ZPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1435.pdfAbstract: It is commonly assumed that the goal of
stereovision is computing explicit 3D scene
reconstructions. We show that very accurate
camera calibration is needed to support this,
and that such accurate calibration is difficult
to achieve and maintain. We argue that for
tasks like recognition, figure/ground
separation is more important than 3D depth
reconstruction, and demonstrate a stereo
algorithm that supports figure/ground
separation without 3D reconstruction.
AIM-1463
Object Recognition By Alignment Using Invariant Projections of Planar Surfaces
Author[s]: Kanji Nagao and W. Eric L. Grimson
Date: February 1994PS Download: ftp://publications.ai.mit.edu/ai-publications/1000-1499/AIM-1463.ps.ZPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1463.pdfAbstract: In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.
AIM-1523
Recognizing 3D Object Using Photometric Invariant
Author[s]: Kenji Nagao and Eric Grimson
Date: April 22, 1995PS Download: ftp://publications.ai.mit.edu/ai-publications/1500-1999/AIM-1523.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1523.pdfAbstract: In this paper we describe a new efficient
algorithm for recognizing 3D objects by
combining photometric and geometric
invariants. Some photometric properties are
derived, that are invariant to the changes of
illumination and to relative object motion with
respect to the camera and/or the lighting
source in 3D space. We argue that
conventional color constancy algorithms can
not be used in the recognition of 3D objects.
Further we show recognition does not require
a full constancy of colors, rather, it only needs
something that remains unchanged under the
varying light conditions sand poses of the
objects. Combining the derived color
invariants and the spatial constraints on the
object surfaces, we identify corresponding
positions in the model and the data space
coordinates, using centroid invariance of
corresponding groups of feature positions.
Tests are given to show the stability and
efficiency of our approach to 3D object
recognition.
AIM-1662
Co-dimension 2 Geodesic Active Contours for MRA Segmentation
Author[s]: Liana M. Lorigo, Olivier Faugeras, W.E.L. Grimson, Renaud Keriven, Ron Kikinis, Carl-Fredrik Westin
Date: August 11, 1999PS Download: ftp://publications.ai.mit.edu/ai-publications/1500-1999/AIM-1662.psPDF Download: ftp://publications.ai.mit.edu/ai-publications/pdf/AIM-1662.pdfAbstract: Automatic and semi-automatic magnetic resonance angiography (MRA)s segmentation techniques can potentially save radiologists larges amounts of time required for manual segmentation and cans facilitate further data analysis. The proposed MRAs segmentation method uses a mathematical modeling technique whichs is well-suited to the complicated curve-like structure of bloods vessels. We define the segmentation task as ans energy minimization over all 3D curves and use a level set methods to search for a solution. Ours approach is an extension of previous level set segmentations techniques to higher co-dimension.