Research Profile

My research interests and accomplishments can be broadly classified into the following categories:

**(A) CAD Model based
Machine Vision**

** Summary**:
My research in CAD Model based Machine Vision has centered around the design
and analysis of algorithms for the recognition and localization of three
dimensional objects from range and intensity images. I have designed surface
matching algorithms [8] and recognition/localization algorithms based on
the Generalized Hough Transform (GHT) [7]. I have investigated hypergraph
based representation schemes and designed efficient algorithms based on
hypergraph monomorphism for three dimensional object recognition and localization
[2]. I have investigated means of improving the robustness and accuracy
of range image segmentation algorithms by an appropriate combination of
edge- and surface based segmentation approaches [6]. I have also explored
means by which the various stages of range image understanding viz., segmentation,
feature extraction and recognition and localization can be synergistically
integrated in a range image understanding system [4,11].

Along more theoretical lines, I have been interested in analyzing the sensitivity of recognition/localization algorithms to errors in segmentation and feature extraction [9]. In particular, I have studied the impact of qualitative feature labeling on the performance of the GHT [5]. Qualitative feature labeling was shown to result in the formulation of a weighted GHT (WGHT) wherein the weights are looked upon as fuzzy membership values for the fuzzy sets defined by the qualitative feature labels [3]. The WGHT was shown both analytically and experimentally to perform better than the GHT [3]. I have also addressed issues concerning knowledge representation and control in CAD model based machine vision systems. In particular, the modeling of model based machine vision systems as coupled systems (i.e., knowledge based systems in which symbolic and numerical computing are integrated) in an object oriented representation framework was addressed in [39,40]. I am currently exploring issues concerning the design of hierarchical indexing/hashing structures for CAD model based vision using object models represented as attributed relational hypergraphs.

**(B) Parallel Processing
for Computer Vision**

** Summary**:
My research in parallel processing for Computer Vision is focused on issues
concerning the parallelization of recognition and localization algorithms
on prototypical SIMD and MIMD multiprocessor architectures as well as special
purpose architectures. I have addressed issues concerning parallelization
of three-dimensional object recognition and localization algorithms on
a fine-grained SIMD architecture such as the Connection Machine CM-2 [18]
and on a coarse grained MIMD architecture such as the Intel iPSC hypercube
[16,17]and a PVM based cluster of workstations. I have also investigated
special purpose architectures for computer vision and the mapping of computer
vision algorithms on these architectures. In collaboration with two colleagues,
a novel architecture was proposed and designed, which was termed as the
Reconfigurable Multi-Ring Network (RMRN). The RMRN has been shown to be
a highly efficient, scalable, cost effective and physically compact multiprocessor
system suitable for active robot vision on autonomous or dexterous robotic
platforms [24]. The theoretical properties of the RMRN were rigorously
proved in [20,21]. Procedural primitives for data broadcast, data circulation,
sort, data concentrate, data accumulate and circular shift were designed
and analyzed in [23]. These procedural primitives were used as building
blocks for parallel algorithms for low- and intermediate level vision such
as the FFT, convolution and template matching [23], stereo correlation
[24]and the Hough Transform [19,20,26]. The architecture was shown to be
well suited for problems in machine and robot vision [24,27]. On the theoretical
side, I am currently investigating quantitative performance criteria for
the evaluation of parallel and distributed recognition and localization
algorithms on prototypical multiprocessor architectures and special purpose
multiprocessor architectures such as the RMRN.

**(C) Evolutionary
Computation, Stochastic Optimization and Neural Networks for Low level
Vision**

** Summary**:
My current research interests in low level vision are focused on the design
and analysis of stochastic optimization techniques for low level vision
problems such as edge detection, Gestalt clustering, image segmentation
and surface reconstruction. Evolutionary and stochastic optimization techniques
such as genetic algorithms, simulated annealing, microcanonical annealing
and the random cost algorithm have been investigated in this context. The
research thus far has resulted in the design of an edge detection technique
using a genetic algorithm (GA) [33,34] and evolutionary algorithms for
image segmentation [35]and figure-ground separation [36,37]. The research
in [35] and [36] has resulted in the formulation and implementation
of novel hybrid stochastic optimization algorithms that combine the positive
aspects of stochastic hill climbing and evolutionary computation while
alleviating their individual shortcomings.

I am also investigating neural networks and multiscale stochastic optimization algorithms in the context of low level vision. The neural networks of specific interest are stochastic Hopfield networks, Boltzmann networks and Self Organizing Feature Maps. I am particularly interested in the design of multiscale or hierarchical versions of the aforementioned neural networks. The research thus far has resulted in the design of a Multi-Layer Self-Organizing Feature Map (MLSOFM) for image segmentation [28]-[32]. The MLSOFM combines the ideas of and with those of image segmentation. It is distinctly different from previous approaches to image segmentation using neural networks in that it naturally alleviates the problems of under segmentation and over segmentation endemic to most image segmentation algorithms. The MLSOFM has proved successful in multiscale segmentation of intensity, range and multispectral magnetic resonance (MR) images. Multiscale versions of stochastic Hopfield networks and Boltzmann networks are also being investigated.

**(D) Computer Vision
and Parallel Processing Applications**

** Summary**:
I have also investigated various applications of computer vision algorithms
to practical problems. As a co-principal investigator on a USDA funded
collaborative project with the School of Forestry at the University of
Georgia, I have dealt with the processing and analysis of cross-sectional
CT images of log samples using machine vision algorithms [13]-[15]. The
goal is to detect and classify the internal log defects and render
a 3-D reconstruction of the log that clearly shows its internal defects.
The knowledge of the internal defects is used to formulate an optimal lumber
production strategy that maximizes the yield and grade of the resulting
lumber while minimizing wastage.

I have also applied parallel processing, computer vision and image processing techniques to problems in computational biology and biomedicine. As a principal investigator on a USDA funded collaborative project with the Department of Genetics at the University of Georgia, I have examined problems related to chromosome reconstruction or physical mapping from short and possibly noisy (error containing) DNA fragments. The problem was modeled as one of signal/image reconstruction for which a optimization algorithms based on simulated annealing and microcanonical annealing have been designed and implemented on prototypical MIMD and SIMD architectures such as the Intel iPSC hypercube [42] and the MasPar MP-2 [44] and on a PVM based cluster of workstations. As a co-principal investigator on an NSF funded collaborative project with the Applied Genetics Technology Center at the University of Georgia, I am investigating algorithms for analysis of DNA microarray images. The goal of this project is to quantify gene expression, detect and quantify clusters of gene expression values arising from homologous (similar) genes and track the changes in cluster characteristics over time using algorithms from image morphology.

In collaboration with researchers at the Medical College of Georgia, I have investigated parallel algorithms for entropy computation of experimental heart rate and electrocardiac potential (EKG) data. Heart rate entropy has been shown to be indicative of cardiovascular health but entropy computation has proved computationally intensive even for modest size data sets. Data parallel implementations on the MasPar MP-2 [48] and a PVM based cluster of workstations [51] has yielded impressive speedups and shown the viability of using parallel computing for real time monitoring of cardiovascular activity, especially during surgery. This research presents a novel and challenging applications area for design and development of parallel algorithms.

**(E) Content based
Retrieval in Visual Information Systems**

** Summary**:
Recently, I have been investigating issues related to organization and
content based retrieval of video and image data in visual information systems.
The approach taken is one based on extraction of content based metadata
from the underlying image/video data. The ultimate goal is to allow the
user to pose queries using high level metadata that encapsulates the semantics
of the underlying problem/application domain. Current work deals with metadata
extraction from image and video data with emphasis on the direct processing
of compressed images (JPEG) and compressed video streams (MPEG) [49,50].
In particular, a motion based algorithm for the parsing of compressed video
was proposed and implemented in and an integrated video parsing algorithm
that combined motion based, luminance based and chrominance based information
was proposed and implemented in [50]. Both algorithms were capable
of processing video data in real time (at rates in excess of 30 frames/sec)
with the integrated video parsing exhibiting superior results in terms
of miss rate and false alarm rate. Generation of indexing/hashing structures
for efficient content based retrieval is also being investigated. The long
term
goal of this research is to permit integrated access to multimedia data
which includes video, image, text and audio data.

Each of the aforementioned categories are elaborated upon in the following sections.

(A) CAD Model based Machine Vision

My research in this
area has centered around design and analysis of algorithms for the recognition
and localization of three dimensional objects from range and intensity
images.

As part of my doctoral
research, I developed Hough Transform based algorithms for matching surfaces
embedded in 3-D space [8]. Subsequently, I generalized these surface matching
algorithms for the purpose of recognition and localization of three dimensional
rigid objects composed of curved quadric surfaces from range images [7].
These recognition and localization algorithms were based on the generalized
Hough Transform and were found to be robust in that they were capable of
recognizing and localizing three dimensional objects in range images that
contained multiple objects with instances of partial occlusion [7].

While on the faculty of the Department of Computer Science at the University
of Georgia, I continued to build on my previous research in the design
and analysis of recognition and localization algorithms for model based
machine vision. My earlier algorithms based on the generalized Hough Transform
[7] were computationally intensive. In an effort to address the combinatorial
complexity of object recognition and localization in multiple object scenes
with partial occlusion, I investigated hypergraph based representation
schemes for rigid 3-D objects composed of curved quadric surfaces and recognition/localization
algorithms based on hypergraph monomorphism [2]. The hypergraph representation
presented in [2] was viewpoint independent resulting in substantial
memory savings for the object model database. The resulting hypergraph
monomorphism algorithm integrated both relational constraints and the rigid
pose constraint and had a low polynomial order complexity (O(n^{2})
where n is the number of scene features) even in multiple object scenes
with partial occlusion as compared to the worst case exponential complexity
of straightforward graph monomorphism algorithms. I also designed an algorithm
for incrementally constructing the hypergraph representation of an object
model from range images of the object from different viewpoints. The hypergraph
monomorphism and the hypergraph construction algorithms were designed to
correct errors in the initial segmentation of the range image [2].

I have investigated ways of improving the robustness and accuracy of existing
range image segmentation techniques. Most conventional range image segmentation
algorithms could be classified as either surface based or edge based, depending
on whether they extract the parameters of the underlying surface or the
surface discontinuities, respectively. The primary drawback of edge based
segmentation techniques is the inevitable fragmentation of the edges in
the presence of noise. Surface based segmentation techniques, on the other
hand, can result in over segmentation or under segmentation of the image.
In collaboration with my graduate student, I designed a range image segmentation
algorithm that integrated both surface and edge information [6]. In this
algorithm, the geometric parameters of the surface regions are used to
hypothesize the presence of a surface discontinuity and accurately compute
its parametric form. The presence of the surface discontinuity in the image
is used to confirm the hypothesis whereas its absence is used as a cue
to merge the appropriate regions. Experiments on range images demonstrated
that the synergetic integration of surface and edge information results
in a robust and accurate segmentation algorithm capable of alleviating
the individual shortcomings of edge based and region based segmentation
techniques [6].

I have also investigated means by which the various stages in range image
understanding, viz. segmentation, feature extraction, recognition and localization,
could be synergistically integrated in a range image understanding system.
Conventional approaches to range image understanding have treated these
stages in isolation with a largely bottom up flow of control and data through
the three stages. Strictly bottom up approaches are fragile in the
face of errors in segmentation due to noise and limitations on sensor resolution
and accuracy. Synergetic interaction of these three stages is essential
for an image understanding system to exhibit robust behavior [4].
In collaboration with my graduate student, I designed and implemented a
range image understanding system that attempts to exploit the synergy between
the various stages in the image understanding process [4,11]. The salient
features of the range image understanding system were: (i) a synergetic
combination of edge- and surface based segmentation processes that results
in more accurate segmentation than would have been possible with either
of them alone and (ii) the ability to correct errors made during segmentation
in the recognition and localization stages. Experimental results on range
images demonstrated the validity of our approach. An efficient algorithm
for pose verification of hypothesized objects in the range image was also
designed [10]. The pose verification algorithm used feature matching and
cast the pose verification problem as one of optimal assignment (also known
as the *Hungarian marriage problem *in combinatorics). The pose
verification algorithm was found to be far more robust to small errors
in the computed pose when compared with pose verification algorithms
that relied on straightforward depth comparison.

Along more theoretical lines, I have analyzed the sensitivity of recognition
and localization algorithms to errors in segmentation and feature extraction.
In [9], I analyzed the sensitivity of the generalized Hough
Transform (GHT) to errors in segmentation and feature extraction in the
context of 3-D object recognition and localization. The 3-D objects under
consideration were rigid objects composed of piece wise smooth quadric
surfaces. The features were resulting from extended features such
as axes of symmetry, centroids etc. derived from the piece wise smooth
quadric surfaces. The sensitivity of the computed pose to errors in the
angle of the dihedral feature junctions was analyzed. A redundant representation
of the Hough space was seen to reduce the sensitivity of the computed pose
to these errors. The effect of qualitative feature labeling (i.e., assigning
qualitative attributes to scene features) on the robustness of the GHT
was also analyzed [5]. Qualitative feature labeling was seen to result
in a reduction in the search space of scene interpretation hypotheses and
also the number of spurious interpretations explored by the GHT.

Grimson and Huttenlocher [12] have suggested two criteria by which
the performance of the GHT can be judged: (i) the redundancy factor of
the GHT i.e. the number of Hough buckets into which a computed transform
value is fragmented due to the finite resolution of the sensor and
finite quantization of the Hough space and (ii) the probability of occurrence
of spurious peaks of significant magnitude due to random accumulation of
evidence in the Hough space. It is desirable that both the redundancy factor
and the probability of occurrence of random spurious peaks of significant
magnitude be as low as possible. The straightforward GHT, however, shows
a high probability of spurious peaks of significant magnitude even for
small values of the redundancy factor and small magnitude of the search
space of scene interpretations. Qualitative labeling of scene features
was shown to result in the formulation of a weighted Generalized Hough
Transform (WGHT) where each match of a scene feature with a model feature
was assigned a weight based on the qualitative attributes assigned to the
scene feature. These weights were looked upon as membership function values
for the fuzzy sets defined by these qualitative attributes. A fuzzy probabilistic
model for the WGHT was formulated in . Analytical expressions for the redundancy
factor and the probability of random accumulation of spurious votes
were derived for the WGHT using a statistical occupancy model and compared
with the corresponding expressions for the straightforward GHT [3]. Experimental
results on intensity and range images showed that the WGHT performed better
than the conventional GHT in terms of the aforementioned criteria.

I have also addressed issues related to knowledge representation and control
in CAD model based vision systems. Most problems in CAD model based vision
could be looked upon as a trade-off between the complexity of representation
and the complexity of control (i.e., the constraint propagation/satisfaction
technique used). The choice of representation granularity (i.e.,
global features vs. local features) and constraint propagation/satisfaction
technique greatly impacts the performance of the vision system. Typical
shortcomings of most CAD model based vision systems are:

- Restriction to a single level of representation granularity
- Use of constraint propagation techniques based on matching of features at a single level of representation granularity
- Inflexible control strategies
- Inadequate integration of numerical and symbolic processing.

My research in CAD model based vision resulted in the publication of a book entitled , coauthored with Dr. M. Suk, published by Springer-Verlag [1]. Currently, I am investigating efficient indexing/hashing techniques for CAD model based machine vision. Techniques for generating hierarchical indexing and hashing structures from object models represented as attributed relational hypergraphs are being explored. Means of incorporating sensor models, illumination models and task specific constraints within the hierarchical indexing/hashing structures are being studied. These indexing and hashing structures will be extended to allow for indexing/hashing into a database of pre-compiled recognition strategies. Issues on optimizing the hierarchical indexing/hashing structures by exploitation of object symmetries and salience will be addressed. Means of using these hierarchical indexing/hashing structures for CAD model based machine vision via an evidential reasoning approach based on the Dempster-Shafer theory will be explored.

(B) Parallel Processing for Computer Vision

My research interests
in parallel processing for computer vision are largely focused on the parallelization
of recognition and localization algorithms for 3-D machine vision. I have
explored means of parallelizing the recognition and localization algorithms
that I designed on prototypical SIMD and MIMD multiprocessor architectures.
Recognition and localization algorithms based on the GHT [7] were found
to be well suited for parallelization on a fine grained SIMD architecture
such as the Connection Machine CM-2. In [18], issues on exploiting fine
grained parallelism on the CM-2 at every stage of 3-D object recognition
and localization such as segmentation, feature extraction matching, pose
determination and pose verification were tackled. Experimental results
on the CM-2 brought out the advantages of exploiting fine grained parallelism
for 3-D machine vision using recognition and localization techniques based
on the GHT. In [16,17]parallelization of recognition and localization
algorithms based on Interpretation Tree (I.T.) search on a coarse grained
MIMD hypercube (Intel iPSC/2) was explored. Three strategies for mapping
the I.T. search process on the MIMD hypercube were designed. The performance
of the parallel I.T. search for each of these mapping strategies was analyzed
in terms of parameters such as speed-up, processor utilization, interprocessor
communication overhead and load sharing between processors. It was shown
how the requirement for uniform load sharing leads to increased interprocessor
communication overhead.

In collaboration with my colleagues Dr. Arabnia and Dr. Smith in the Department
of Computer Science at the University of Georgia, I have investigated special
purpose architectures for computer vision and the mapping of computer vision
algorithms on these architectures. The architecture that we proposed is
termed as the Reconfigurable Multi-Ring Network (RMRN). In [21,23]
the properties of the RMRN architecture were investigated and rigorously
proved. Briefly, the RMRN_{n} consists of 2^{n} processors
connected in a ring, but with the capability for reconfiguration, under
software control, into R rings of D processors each, with corresponding
elements of each ring linked in a pipelined manner, for any R and D whose
product is 2^{n}. The total number of processors could be any composite
number, but using the natural choice of a power of 2 maximizes the number
of possible configurations and also lends itself to ease of mapping algorithms
onto the RMRN. Some of the salient properties of the RMRN are:

**(i)
**All 2-D mesh topologies of size 2^{i} x 2^{j} are
subsets of the RMRN_{n} where i + j = n. This enables algorithms
for 2-D mesh/toroidal architectures of various sizes to be mapped onto
the RMRN in O(1) time.

**(ii)
**The
*n-cube *(i.e. a hypercube with N = 2^{n} processors) can
embed all possible configurations of the RMRN_{n} (though not simultaneously).
This enables the hypercube to simulate the behavior and function of the
RMRN.

**(iii)
**Any
algorithm which uses the communication links along a single dimension of
the at any given point in time can be mapped to the RMRN_{n}
in O(1) time. This enables an important and fairly wide class of algorithms
for the to be mapped very efficiently onto the RMRN_{n}.

**(iv)
**In
any configuration the RMRN can be recursively decomposed into sub configurations
with the connectivity pattern preserved within each sub configuration.
Thus the RMRN_{n} can be recursively decomposed in a manner similar
to the *n-cube*.

**(v)
**The RMRN is highly scalable since the degree of connectivity of each
processor is fixed. This ensures that the number of interprocessor communication
links scales as O(N) with network size whereas the diameter of the
RMRN scales as O(log_{2} N) with network size.

Procedural primitives for data broadcast, data circulation, sort, data
concentrate, data accumulate and circular shift have been designed and
analyzed [23]. These procedural primitives have been used as building blocks
for parallel algorithms for low- and intermediate level vision such as
the FFT, convolution and template matching [23] and the Hough Transform
[19,26]. The architecture is well suited for problems in machine and robot
vision [24,27]. Efforts are currently underway towards building the hardware
for the RMRN using custom VLSI. Complex problems in intermediate- and high
level vision such as binocular stereo, surface reconstruction, image segmentation
and object recognition are also being considered along with other problems
in robotics such as path and trajectory planning and motion control. For
the compute bound problems in active robot vision, the RMRN promises
to offer an efficient, inexpensive, scalable and physically compact multiprocessor
system that could be used on mobile and dexterous robotic platforms [24].

On the theoretical side, I am currently investigating quantitative performance
criteria for the evaluation of parallel and dist ributed recognition and
localization algorithms

on prototypical multiprocessor
architectures and special multiprocessor architectures such as the RMRN.
A rigorous analysis of the impact of architectural design parameters such
as processor bandwidth, memory bandwidth, interprocessor communication
bandwidth, interconnection topology and synchronization bandwidth on the
performance of the parallel/distributed recognition and localization algorithms
is currently underway. A quantitative analysis of the performance of the
parallel/distributed recognition and localization algorithms in terms of
parallel processing parameters such as speedup, load distribution and load
balancing overhead, search overhead, synchronization overhead, interprocessor
communication overhead, efficiency of parallelism and scalability is being
attempted. Quantitative relations between these parallel processing parameters
and physical, statistical and geometrical scene parameters such as finite
image resolution, scene clutter, gray level quantization, quantization
geometry, sensor noise and errors introduced by the feature extraction
process are being studied.

(C) Evolutionary Computation, Stochastic Optimization and Neural Networks for Low level Vision

My current research
interests in low level vision are focused on the design and analysis of
evolutionary and stochastic optimization algorithms for low level vision
problems such as edge detection, Gestalt clustering, image segmentation
and surface reconstruction. The evolutionary algorithms under investigation
include the various variants of the genetic algorithm (GA) whereas the
stochastic optimization algorithms under investigation include simulated
annealing, microcanonical annealing and the random cost algorithm. The
research thus far has resulted in GA based techniques for edge detection
[33,34], image segmentation [35]and figure-ground separation [36].

The GA is an evolutionary search/optimization technique, the conceptual
basis of which lies in Darwin's , better known as . The GA repres ents
each candidate solution as a chromosome and traverses the search space
by constructing better chromosomes (solutions) from an existing population
of chromosomes using operators such as selection, crossover and mutation
that mimic the process of natural evolution. Although GA's have found successful
applications in a variety of problem domains, their application to vision
problems has been somewhat limited.

The GA based edge detection algorithm in [33] treats candidate edge configurations
as two-dimensional chromosomes with assigned fitness values. In [34]crossover,
mutation and meta-level operators for the GA are designed which enable
exploration of better edge configurations using a population of existing
edge configurations. The GA with various combinations of meta-level operators
was tested on synthetic and real intensity images. The performance of the
GA was compared both qualitatively and quantitatively with hill climbing
based and simulated annealing based edge detection approaches. The GA based
edge detection technique was shown to perform very well in terms of robustness
to noise, rate of convergence and quality of the final edge image [33].
The GA produced edge images comparable in quality to those produced by
simulated annealing but exhibited a faster rate of convergence. Although
hill climbing was seen to exhibit a faster rate of convergence than the
GA or simulated annealing, it did not exhibit the same robustness to noise,
resulting in a greater degradation of the final edge image with increased
noise levels.

In [35] the GA based edge detection approach was extended to the problem
of image segmentation. A suitable fitness function to quantify the quality
of the segmented image and the corresponding GA operators were designed
and implemented. In [36]the GA was investigated in the context of
figure-ground separation. The figure-ground separation problem was modeled
as an Ising system from quantum physics and the fitness function for the
GA was derived from the Ising energy function. Although GA's are inherently
parallel, premature convergence to local minima and the need to maintain
large population sizes were seen to present significant problems. Stochastic
annealing techniques, on the other hand, are computationally intensive
and not as easily parallelizable. But they guarantee asymptotic convergence
to a global minimum if certain conditions on the annealing schedule are
satisfied. In [35,36]evolutionary stochastic optimization algorithms
that combine the positive aspects of stochastic annealing and evolutionary
computation while alleviating the individual shortcomings of both were
proposed and implemented. The evolutionary stochastic optimization algorithms
were seen to outperform their pure evolutionary and pure stochastic annealing
counterparts. Hierarchical or multiscale evolutionary and stochastic optimization
techniques in the context of low level vision problems are currently being
investigated.

I have also investigated neural implementations of low level vision algorithms.
The neural networks of specific interest are stochastic Hopfield networks,
Boltzmann networks and Self Organizing Feature Maps. I am particularly
interested in the design of multiscale or hierarchical versions of the
aforementioned neural networks. The research thus far has resulted in the
design of a Multi-Layer Self-Organizing Feature Map (MLSOFM) for image
segmentation [28]-[32]. One of the shortcomings of the conventional single
layer Self-Organizing Feature Map (SOFM) is that the number of neural units
in the feature map has to be close to the number of regions in the final
segmentation. Since, one typically does not know the number of regions
in the final segmentation a priori, the SOFM often yields an under
segmented or over segmented image. The MLSOFM consists of multiple SOFM
layers organized in a pyramidal fashion. The problem of image segmentation
is formulated as one of vector quantization and mapped onto the MLSOFM.
The MLSOFM combines the ideas of and with those of image segmentation.
It is distinctly different from previous approaches to image segmentation
using neural networks. The MLSOFM generates an which represents the
segmentation of the image at multiple scales of abstraction. Traversal
of the abstraction tree results in the desired segmented image. Since the
neural units in each layer of the MLSOFM do not have to be specified a
priori, the MLSOFM can be seen to alleviate a major shortcoming of the
SOFM in the context of image segmentation. The MLSOFM has been successfully
applied to the segmentation of intensity, range and multi-spectral magnetic
resonance (MR) images. The MLSOFM is currently being extended for use in
hierarchical image coding and semantics preserving compression of images
[29,32]. Also, multiscale versions of stochastic Hopfield networks and
Boltzmann networks are being explored for the purpose of Gestalt clustering
and image segmentation.

(D) Computer Vision and Parallel Processing Applications

I have also explored practical applications of computer
vision and parallel processing. As a co-principal investigator on a USDA
funded collaborative project with the School of Forestry at the University
of Georgia, I have dealt with the processing and analysis of cross-sectional
CT images of log samples using machine vision techniques [13,14,15]. These
CT images are analyzed for the detection and localization of defects such
as holes, knots, cracks, wood decay, bark and pitch pockets etc. The nature
of the defects and the ring structure deduced from each CT image are used
to construct a 3-D model of the log sample. The 3-D model is used to simulate
various sawing patterns and to determine the optimal lumber processing
strategy that would maximize the resulting lumber yield. This would enable
the saw mill to maximize the grade and yield of the produced lumber, minimize
wood wastage and conserve valuable forest resources. The research in this
project thus far has resulted in the internal defect classification and
3-D reconstruction of logs of premium hardwood species [13,15]. Initial
simulations of algorithms for optimal lumber processing strategy determination
have yielded very encouraging results [14]. Current research is aimed at
further refinement of algorithms for internal defect detection and localization
and for optimal lumber processing strategy determination. The role
of parallel computing in real time CT scanning of logs and for subsequent
image analysis and optimal lumber processing strategy determination is
also being investigated.

I have also investigated applications
of computer vision and parallel computing to problems in computational
biology and biomedicine. As the principal investigator on a USDA funded
collaborative project with the Department of Genetics at the University
of Georgia, I have investigated algorithms for reconstruction of chromosomes
from short and possibly noisy (i.e., error containing) DNA fragments. The
problem is modeled as one of image/signal reconstruction in the presence
of noise. A likelihood function is defined for the relative ordering of
the DNA fragments and their pair wise spacing in the presence of noise.
A maximum likelihood estimation (MLE) procedure that recovers the relative
ordering of the DNA fragments and their pair wise spacing is then defined.
The MLE procedure is shown to be computationally intensive and intractable
involving both, combinatorial and continuous optimization, thus calling
for the use of parallel computing. An earlier (and simpler) version of
the chromosome reconstruction problem was modeled along the classical Traveling
Salesman Problem (TSP) which is known to be intractable. Parallel implementations
of chromosome reconstruction algorithms based on the MLE approach and the
TSP approach on an SIMD architecture (MasPar MP-2), MIMD architecture (Intel
iPSC/860) and a PVM based cluster of workstations was seen to yield very
good speedups. As co-principal investigator on an NSF funded collaborative
project with the Applied Genetics Technology Center at the University of
Georgia, I am currently investigating algorithms for the analysis of DNA
microarray images used for the measurement of gene expression. The goals
of this project are to detect and characterize clusters of gene expression
patterns when multiple genes are jointly expressed in response to a stimulus,
detect differential gene expression patterns using morphological operators,
detect and track temporal patterns in gene expression values and characterize
background noise due to cross-hybridizations.

In collaboration with researchers
at the Medical College of Georgia, I have investigated parallel algorithms
for entropy computation of heart rate and electrocardiac potential (EKG)
data. The short term goal of the research is to use the computed entropy
as a retrospective diagnostic tool whereas the long term goal is on-line
entropy computation during surgery and recovery. A wide variety of dynamic
systems such as the human heart, which were earlier considered stochastic
or periodic have been re-classified as chaotic. Chaotic systems are deterministic,
not stochastic. Entropy is a diagnostic statistic that characterizes the
level of chaos within a dynamic system. Zero entropy indicates a periodic
system, very high positive values of entropy (approaching infinity) indicates
a random system and finite positive values of entropy indicates a chaotic
system. The research focused on the parallel computation of Kolmogorov
entropy using the algorithm of Grassberger and Procaccia. Entropy computation
has proved computationally intensive even for modest size data sets. Data
parallel implementations on an SIMD machine (MasPar MP-2) [47,48] and control
parallel implementations [51]on a PVM based cluster of workstations gave
impressive speedups. The current implementations, though suitable for off-line
analysis of electrocardiac data, fall short of the requirements for real
time cardiovascular monitoring. This research presents a novel and challenging
applications area for design and development of parallel algorithms. An
immediate application of the research is to aid the anesthesiologist in
assessing risk associated with recovery of ambulatory surgery patients
using EKG data. The proper analysis of heart rate and EKG data would greatly
reduce unnecessary hospitalization costs and also potential risks arising
from imprudent patient discharges. Future research will look into design
of special purpose hardware in the form of application specific integrated
circuits (ASICs) for the real time computation of heart rate entropy.

(E) Content based Retrieval in Visual Information Systems

Some of my more recent research deals with various issues
related to the organization and content based retrieval of video and image
data in visual information systems. This research is a crucial component
in providing integrated high level access to multimedia information. The
current research has focused on automatic parsing of video data for extraction
of content based metadata. The content based metadata represents the image/video
contents at a higher level of abstraction and can be used to provide an
indexing mechanism into an image/video database.

The video parsing algorithms developed
in [49,50]detect shot boundaries, special cinematographic effects such
as fades, dissolves and image morphs, predominant camera motion such as
zoom and pan, and predominant object motion such as translation and rotation.
Both pixel based and feature based approaches have been investigated with
an emphasis on direct analysis of compressed video data (MPEG). In [49]
a motion based video parsing algorithm was proposed and implemented. The
algorithm was shown to be fairly robust in its detection of shot boundaries,
fades and dissolves. On a 200MHz SUN UltraSparc-1 workstation, a C++ implementation
of the video parsing algorithm was shown to be capable of processing video
streams at a rate of 60 frames/sec, making it suitable for real time (30
frames/sec) video parsing applications. In [50] a video parsing algorithm
that integrated luminance based, chrominance based and motion based information
was proposed and implemented. In addition to shot boundaries, fades
and dissolves, the algorithm was also capable of detecting pans, zooms
and predominant object motion. The algorithm was seen to be more robust
than those that used luminance, chrominance or motion information in isolation.
In a quantitative study, the integrated video parsing algorithm was shown
to outperform strict luminance based, chrominance based and motion based
video parsing algorithms in terms of percentage of misses and percentage
of false alarms. The processing rate of the integrated video parsing algorithm
was 48 frames/sec on a 200MHz SUN UltraSparc-1 workstation (20% slower
than the strict motion based algorithm) but still suitable for real time
applications. The immediate goal of this project is to formulate and implement
representation schemes (in the form of key frames and mosaics) for distinct
video shots detected by the video parsing process. These representations
will be used to provide an indexing mechanism to an image/video database.
The long term goal is to support high level integrated access to multimedia
data which may include text, video, images and audio data.

References

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[32] S.M. Bhandarkar, J. Koh and M. Suk, **A
Hierarchical Neural Network and Its Application to Image Segmentation,**
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[33] S.M. Bhandarkar, Y. Zhang and W.D. Potter,
**An
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[34] S.M. Bhandarkar, Y. Zhang and W.D. Potter,
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[37] S.M. Bhandarkar and X. Zeng, **
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[41] S.M. Bhandarkar, S. Chirravuri, S. Machaka
and J. Arnold, **Parallel Computing for Chromosome Reconstruction via
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[42] S.M. Bhandarkar,** Parallel Processing
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[43] S.M. Bhandarkar and S. Machaka, **Chromosome
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[44] S.M. Bhandarkar and S. Chirravuri, **A
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[45] S.M. Bhandarkar, S. Machaka, S.S. Shete
and J. Arnold, **Parallel Computation of a Maximum Likelihood Estimator
for Physical Mapping of Chromosomes**, *Journal of Parallel and Distributed
Computing*, under review.

[46] P. Grassberger and I. Procaccia, **Estimation
of the Kolmogorov Entropy from a Chaotic Signal**, *Physical Review*,
Vol. 28, 1983, pp. 2591-2593.

[47] S. Chirravuri, S.M. Bhandarkar and D.
Whitmire, **A Massively Parallel Algorithm for K2 Entropy Computation:
Case Studies of Model Systems and Data,** *Intl. Journal of Supercomputing
Appl. and High Perf. Computing *, Vol. 9, No. 4, 1995, pp. 296-311.

[48] S.M. Bhandarkar, S. Chirravuri, and D.
Whitmire, **Analysis of Heart Rate Variability on a Massively Parallel
Processor,** *Proc. Intl. Conf. Parallel Processing, Bloomingdale*,
IL, Aug. 12-16, 1996, Vol. 2, pp. 166-169.

[49] S.M. Bhandarkar and A.A. Khombadia, **Motion
based Parsing of Compressed Video**, Proc*. IEEE Intl. Wkshp. Multimedia
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[50] S.M. Bhandarkar, Y.S. Warke and A. A.
Khombadia, **Integrated Parsing of Compressed Video**, *Proc. Intl.
Conf. Visual Inf. Mgmt. Sys.*, Amsterdam, The Netherlands, June 2-4,
1999, pp. 269-276.

[51] S.M. Bhandarkar, S. Chirravuri and S.
Machaka, **Cluster Computing for Biomedical Applications**, in *Cluster
Computing: Theory and Applications*, Prentice-Hall Inc., Upper Saddle
River, NJ, June 1999, Chapter 29, pp. 604-624.