|
Name |
Venkatesh
K Subramanian (K |
|
|
Father’s Name |
K Subramanian |
|
|
Place & Date of Birth, Nationality |
|
|
|
Sex & Status |
Male, Married |
|
|
Permanent Address |
No.1769, 15th Phone: 080 6710482 |
|
Present Address |
Office |
207/ACES, Indian Phone: 0512 59 7468/7025 Fax: 0512 59 0064/0007 email: venkats@iitk.ac.in |
|
Residence |
No.354, Indian Institute of Technology, Phone: 0512 59 8354 |
|
|
Degree |
Institution |
University/Board |
Year of Passing |
Marks/CPI |
Subjects/Specialization |
|
SSLC |
Sri Aurobindo Memorial School,
Bangalore |
Karnataka Secondary Education and Examination Board |
1980 |
70.5% |
General |
|
PUC |
The National College (Jayanagar),
Bangalore |
Board of Pre-University Education, Karnataka |
1982 |
84.6% |
Physics, Chemistry, Mathematics, Biology |
|
BE |
|
Bangalore University |
1987 |
76.8% |
Electronics |
|
M.Tech |
IIT Kanpur |
IIT Kanpur |
1989 |
8.5 (CPI) |
Communication |
|
Ph.D |
IIT Kanpur |
IIT Kanpur |
1995 |
9.0 (CPI) |
Signal Processing |
Professional: Digital Communication; Communication System Theory; Non Uniform Sampling; Image Analysis and Processing (Conventional and Morphological); Multidimensional and Multivariate (Colour) Signal Representation; Transforms; Generalised Signal and System Theory.
Extra Professional: Theory of Games; Computerised Typesetting and Font Design; MeasurementTheory; Set Theory and Topology; Philosophy and Foundations of Mathematics; Philosophy and History of Science; Epistemology; Literature; History; Western Classical Music.
Abstract
A theory is proposed
for ordinal measurement over partially ordered relational systems, under
certain conditions and with certain assumptions. A decision criterion is
suggested that is based upon the principle of indifference. Following this is
the main representation theorem that establishes the feasibility of ordinal
measurement over the particular class of incomplete orders that have been
called linearisable orders. Further results
pertaining to the peculiar properties of the class of linearisable
orders are studied, and the class of automorphisms
for such a system is identified.
\noindent
Subsequently, the theory is extended to apply to product (multidimensional)
structures. each dimension of which is taken to be a linearizable
structure of the kind already studied. The salient features of the
multidimensional incomplete systems that have been called K-structures are
discussed. A representation theorem is given for additive conjoint measurement
over K-structures. It is shown that that the system of K-structures is a
semi-group. Finally, an algorithm is given for the decomposition of a
K-structure. The algorithm makes it possible to frame an alternative definition
of a K-structure.
Abstract
The thesis attempts to
generalise the current form of signal and system
theory by formulating it entirely in terms of set theory. The objective is to
express as many of the conventional notion of signal and system theory such as
signal symmetry, processor invariance, processor causality and processor
stability as possible within a set theoretic framework.
In the process of the
development, some entirely new concepts emerge, such as the {\it stasis\/} of a
signal, the {\it locality\/} of a processor, {\it etc.} It is shown that with
each processor is associated a certain point set topology on the signal space
called the processor's first preservance topology.
This topology is the first of a sequence of preservance
topologies defined on the power sets of higher and higher order of the signal
space. In the process of defining these higher preservance
topologies, a new set theoretic relation called subinclusion
is defined and applied.
The thesis goes to show
that from a topological viewpoint, processor invariance, linearity, locality
and stability are all very similar in their structural properties. This fact is
used to arrive at a generalisation from which all
these may be seen as very specific instances of a common phenomenon. This
latter fact is then used in turn to arrive at a purely set theoretic
formulation of the problem of signal representation and approximation. The
conventional representation theory applicable to linear time invariant systems,
that uses complex exponentials as its eigenfunctions
is demonstrated to be a special instance of the general theory.
Locality-Invariance
Theorem:
Given a processor with vista function W(d) and invarinace group Inv(p), the following is always true. Any u in Inv(p) is conformal on the vista function: W(u(d)) = u(W(d)) " d Î D.
This theorem is very significant as it brings out an intimate relationship between two notions that have been hitherto considered entirely unrelated. This might yield interesting results when the implications of the theorem that each invariance transformation will yield mutually isomorphic isolation topologies is investigated further.
Quasinclusion Based Set
Theory:
A
definition of quasinclusion as a generalisation
of subinclusion (as developed in the thesis for sets
of equal rank) now applicable to any two sets of arbitrary rank is the starting
point of the development. Quasi-union and quasi-intersection may be defined
along lines similar to their conventional counterparts, except for using quasinclusion rather than ordinary inclusion as the basis.
It turns out that the resulting operations have very interesting properties,
such as the non-uniqueness of the quasi-union and quasi-intersection. Thus also
emerges quasi-equivalence, the weak counterpart of set equality. The
quasi-power set is then defined as the set of all quasi-subsets. The
quasi-power set includes as a subset the ordinary power set. Among questions
presently under investigation is a conjecture that the cardinality of the
quasi-equivalence partition of the quasi-power set is the same as that of the
power set, and that one member of the power set is included in each class of
the partition.
Hypoprocessing:
Maps on the power sets of various (higher) orders of the signal space are termed as hypoprocessors. The processing effected by these entities is qualitatively different from that achieved by ordinary processors, which are their special instances. A hypoprocessor of the kth kind is distinguished by the nonexistence of all preservance topologies of order less than k. Possible questions of interest in this connection include a depiction of processors as relations on the signal space rather than as functions; a theory of hypoprocessing may yield the mathematical foundation for a study of this kind. The candidate has just recently started work on this area.
The `Law Of Nondiminishing
Symmetry':
This law is a by-product of the candidate's earlier studies in set theoretic signal processing. It constitutes a sort of negative result regarding the evolution of any system governed by invariant laws. The Nondiminishing Symmetry Law disallows certain kinds of state transitions in such systems, thus constraining the evolution of these systems to remain within a certain class of possible trajectories. When applied to physical systems, the Law permits one to make certain predictions regarding disallowed future states, and importantly, can do so even without exact information regarding the relevant governing laws, beyond their invariance properties. This Law of nondiminishing symmetry was originally formulated only for deterministic systems, but recent work, carried out over the last few months, has discovered a sufficient condition that allows its application on probabilistic systems. In its present form, it stands completed.
Future Research Plans In Related
Areas
l An analogue of the
Locality-Invariance theorem, that may be called the Stability-Linearity
Theorem, is under study. It essentially
attempts to prove that every transformation in the linearity group of a
processor will be conformal on the members of the neighbourhood
profile of that processor.
l Further results in Quasincusion
based Set Theory.
l Investigation of Hypoprocessing
and its implications for conventional System Theory..
Applied Areas
The following summarizes various projects undertaken
under the candidate’s supervision, both those completed and those presently in
progress. Those works that will be listed later under ‘Publications’ have been
omitted here.
The objective was to develop real-time or
near-real-time identification techniques to pinpoint the presence of
semi-transparent stationary objects such as icons in video data or a television
programme, and furthermore, to locate exactly and
extract the stationary component. Digitized, decompressed full-colour input at standard broadcast frame rates is assumed.
The approach taken is to evaluate differences of sufficiently temporally
uncorrelated video frames, threshold the difference image, and operate upon the
result with condensation-growing seed entities planted at the minima. This
estimates the spatial extent of the stationary component(s). With the spatial
extent known, the extraction of the semitransparent components is effected by
simple averaging. Subsequent to the identification, detection of presence or
absence in a given frame is a relatively simple task. Experimental results were
very encouraging and reliable performance was achieved.
The goal was to be able to record and retrieve 128kbps binary data on standard audio cassette tape. If this is implemented, CD quality audio music in mp3 format could be recorded, erased or played on a conventional audio cassette tape recorder. The experimental setup used for the trial was a commercially available cassette recorder interfaced with National Instruments E 6204 data acquisition card on a PC platform. But the sampling rate limitations of the DAQ card prevented successful recording/retrieval beyond 7kbps/channel. Though the results were encouraging, further development was dependent on the use of a DAQ with at least 2MSa/s capability which was very expensive (> Rs.90,000). The otherwise attractive and promising project had therefore to be shelved.
A theoretical basis for the search of the maximally compact packing configuration of identical copies of an object of arbitrary, possibly nonconvex, shape was sought. This involved the study of admissible shapes of stackable objects in 2-D and 3-D space, and the association with this of arbitrary nonconvex object packings. An algorithm was developed first for the 2-D case that achieved the optimal packing of the nonconvex objects, and is presently being extended to 3 dimensions. However, the algorithm is of exponential complexity with respect to the number of dimensions. The solution of this problem is apparently of interest to researches in solid state physics and solid state chemistry.
Face Recognition Package Based on Morphing and Tolerant Error Measures:
An
average face is obtained as the average of a sufficiently large population of
different faces: A face is described in the form of a 187-point vector of
salient points on the face that effectively characterize and distinguish an
individual’s face. A face database is created from frontal pictures of faces.
Each member of the database has to be calibrated and then its parameter vector
has to be manually evaluated by visually identifying the different salient
points from the image and measuring its coordinates. Once the database is
ready, any given test face image is first parametrized
(after calibration), and the parameter vector is compared against the database
vectors using a fast converging algorithm for a small ‘best match’ set of a few
(2 or 3) faces. At this stage, differencing techniques are resorted to to identify the final match. The package showed better than
80% accuracy on a database of about 50 faces.
Projects
Currently Being Supervised:
Appearance Interpolation and Object Recognition
Under Different Illuminations
Low Cost Computation of Omnistereo
Walkthroughs
Dedicated Architecture for Fast Huffman Decoding
3-axis Motion Estimation from Smeared Images
Tolerance Theory Based Change Detection and Change
Blindness
Hiding Techniques for Colour
Still Images and Video
Automatic Vehicle Identification, Tracking, and
Motion Estimation
Development of a system for blemish Identification,
Location, and Evaluation on HDTV CPTs and CDTs.
List of
Publications
Theoretical
(Under
Review: Signal Processing Journal -
Elsevier )
Abstract
We show that the two very distinct notions of linearity and time invariance in the conventional formulation of system theory have in fact a very similar structural basis at a fundamental level. The paper first develops a purely set-theoretic formulation of the signal processing problem in which signals and systems (processors) are viewed as very primitive entities, possessed of no more than the minimum structure necessary to serve our purposes. It is shown that every processor induces a certain sequence of topologies on the signal space, which we call its preservance topologies, each of which describes a somewhat different aspect of processor’s behaviour.
In this framework, a definition of processor invariance and of a restricted form of processor linearity are given and their respective topological characterisation is formulated. It is shown that both linearity and invariance yield exactly the same topological consequence, namely, a partition subtopology of the second preservance topology. To conclude, we show how our formulation, in spite of its generality, is capable of explaining the unique role played by complex expo-nentials as eigenfunctions of conventional linear time invariant processors.
(Signal Processing Journal – Elsevier: March
2000 )
Abstract
This paper formulates a general locality principle that assumes that every processor (system) on a set of signals may be studied in terms of its so-called locality properties. The entire discussion is carried out in a set theoretic framework, which the paper first proceeds to develop, in which signals and processors are simply functions on arbitrary sets, and operators on those functions, respectively. This measure ensures the validity of the results obtained over a very wide variety of contexts: the results will encompass, for example, both linear, time-invariant processing as well as morphological processing of multidimensional signals. In the process of the development, there emerges a distinguished subset of the domain that we call an isolation. The set of all isolations of the domain under a given processor is shown to constitute a topology on the domain. These isolations play a central role in the construction of so-called restricted systems that are homomorphic to the original signal space under processing by the processor in question. We finally study the question of signal representation using the restricted systems: it is shown that a representation constructed using any isolation cover is complete.
3 A Law of Nondiminishing
Symmetry
Abstract
We adopt the position that the evolution of any system with time nay be entirely captured as a succession of transitions of its state, where the state is a function of spatial coordinates (x,y,z) and has a value in the form of a vector consisting of all the various attributes of the system that are of interest to us. Under the following assumptions of the system’s behaviour, that it is closed, and most importantly, that it is law governed, certain results are arrived at whicjh are seen to set very definite constraints on the possible paths the evolution can possibly take. The entire discussion is carried out at a very general and mathematically primitive level that also admits of a probabilistic treatment of a problem; this ensures that the results obtained are applicable to a very wide variety of situations, including perhaps, the physical universe itself. The interesting aspect of the result is that it does not require specific knowledge of the laws that govern the system under study in order to make its predictions on the system’s evolution.
Applied
4
Spatial Domain Superresolution
Reconstruction from Several Degraded Frames
K S Sisodia, K S Venkatesh, Sumana Gupta SPCOM 2001, Bangalore
Abstract
Superresolution (SR) reconstruction for a linear space variant point spread function (PSF) is highly computationally intensive and is generally ill-conditioned. We propose a novel and simple algorithm for spatial domain recursive reconstruction of SR images from several undersampled, degraded frames blurred by a space varying medium that produces better reconstruction results than existing methods. After each update of the estimate, we use the a priori information that each pixel value is nonnegative in the source image. The algorithm may be used for reconstruction of an SR image from several frames obtained from multiple cameras with different sensor element array sizes with each frame degraded by a different PSF. Computational complexity may be further reduced by applying iterative methods.
5
Estimation of Motion and Depth from Smeared Images
Rajeev Bajpai, Sumana Gupta, K S Venkatesh, IEE Proc: Vision, Image and Signal Processing
(Under Revirew)
Abstract
A method for estimating motion from two successive frames of motion smeared images is described. The problem is treated as one of system identification. Motion smearing is modelled as a linear (space variant) system with an appropriate transfer function. An algorithm for estimating the transfer function is described. The motion vector is estimated from the support of the corresponding point spread function. Further, a new method for estimating depth and motion simultaneously is presented. The method uses the defocus and the motion-smear information present in the image frames. Both the methods are tested on simulated and real images.
6
Colour Quantization for
Video Sequences
D Godwin Gnanaraj, K S Venkatesh (Under
Preparation)
Abstract
In many display situations, devices allow only the display of a severely limited number of different colours. The need thus arises to find means to represent with least distortion images and video information that is inherently of far greater colour depth on such devices. We present fast, data dependent, colour palette design methods that directly use information presented in compressed (JPEG/MPEG) form to obviate the costs of decompression. The methods employ a complexity-graded family of sequential scalar quantization algorithms (a suboptimal variant of vector quantization) mediated by a temporal change quantification algorithm on a uniform colour representation space to achieve the best results at minimum cost. When applied to video, the temporal change quantification process allows the progressive refinement of the colour palette during intervals of smooth change.
Experience
Research Experience
|
No. |
Duration |
Organisation |
Areas |
|
1. |
1987-89 |
IIT Kanpur, EE Dept (M.Tech) |
Measurement
and Decisionmaking Theory. |
|
2. |
1989-95 |
IIT Kanpur, EE Dept (Ph.D) |
System
Theory in a Set Theoretic Framework. |
|
3. |
3/95-11/95 |
IISc Bangalore, ECE Dept (Research
Associate) |
Adaptive
Accoustic Noise Cancellation in Chan-nels with Long Delays and Sparse Responses. |
|
4. |
12/95-5/99 |
IIT Guwahati, ECE Dept
(Assistant Professor) |
System
Theory, Set Theory. |
|
5. |
5/99-now |
IIT Kanpur, EE Dept
(Assistant Professor) |
Supervised
several undergraduate and postgraduate research projects. Pl. see under head
“Current Research Activities” for details. Co-investigator
in the Image Performance and Display Evaluation Group at Samtel Center for Display Technology, IIT Kanpur; particular interest in
psychophysical/cognitive aspects of colour
perception and image and video visualization. |
Teaching Experience
|
No. |
Duration |
Organisation |
Areas |
|
|
1. |
1987-89 |
IIT Kanpur, EE Dept
(Teaching Asst.) |
Communication |
|
|
2. |
1989-95 |
IIT Kanpur, EE Dept (Teaching Asst.) |
Signals
and Systems, Networks and Systems, Electrical Sciences, Image Processing. |
|
|
3. |
12/95-5/99 |
IIT Guwahati, ECE Dept (Assistant Professor) |
Various subjects (see Details
of Courses Taught below) |
|
|
4. |
5/99-now |
IIT Kanpur, EE Dept
(Assistant Professor) |
Various subjects (see Details
of Courses Taught below) |
|
Details of Courses Taught at IIT
Guwahati and IIT Kanpur
|
No. |
Course
Name |
Course
No. |
Level |
No. Of Times |
Developed by you? |
IIT Guwahati
|
|||||
|
1. |
Electrical
Sciences-1 |
EC101
|
1st yr. UG |
4 |
Yes |
|
2. |
Electrical
Sciences-2 |
EC201 |
2nd yr. UG |
1 |
Yes |
|
3. |
Basic
Electronics Laboratory |
EC202 |
2nd yr. UG |
3 |
Yes |
|
4. |
Signals and
Systems |
EC220 |
2nd yr. UG |
3 |
Yes |
|
5. |
Digital
Communication |
EC330 |
3rd yr. UG |
1 |
Yes |
|
6. |
Communication System Engg. |
EC331 |
3rd yr. UG |
1 |
Yes |
|
7. |
Image
Processing |
EC624 |
1st sem PG |
1 |
Yes |
|
IIT Kanpur |
|||||
|
1. |
Signals,
Systems and Networks |
EE200 |
2nd yr. UG |
3 |
No |
|
2. |
High Speed DSP Architectures* |
EE606 |
1st sem PG |
1 |
No |
|
3. |
Mathematical Structures for Signals and Systems |
EE600 |
2nd sem PG |
1 |
No |
|
4. |
Avionics and Navigation* |
EE670 |
2nd sem PG |
1 |
No |
|
5. |
Mathematics for Control Systems* |
EE657 |
1st sem PG |
1 |
Yes |
|
6. |
Introduction to Information Systems* |
EE605 |
1st sem PG |
1 |
Yes |
* Shared With Other Instructors
Industrial Experience
|
No. |
Period |
Organisation |
Title
of Project |
Designation |
|
1. |
1986 |
Indian
Telephone Industries (ITI). Bangalore (BE Project) |
Digitally
Implemented Frequency Domain Speech Encryption. |
Project
Trainee |
Administrative Experience
|
No. |
Period |
Organisation |
Nature
of Responsibility |
|
1. |
1993-94 |
IIT Kanpur |
Member,
Institute Commercial Establishments Maintenance and Monitoring Committee. |
|
2. |
12/95-5/99 |
IIT Guwahati |
Convenor, Departmental Purchase Committee
and Lab Development Committee; Member of Institute Training and Placement
Committee. |
|
3. |
5/99-now |
IIT Kanpur |
Member,
Departmental Postgraduate Committee; Member, Institute Placement Committee. |
Development Activities at IIT GUWAHATI (1995-1999)
An Electronics Laboratory to support an introductory lab course in electronics as well as a more specialised departmental lab course for analog and digital circuits has been built up from scratch over the period Dec.95 to the present and is continuing. Presently, the laboratory is running an analog electronics course for students of the department as well as a digital hardware course for students of the Computer Sc. department. The candidate has designed and coordinated some of the lab courses, besides instructing and preparing course materials. He has also actively participated and continues to participate in lab development activities at various levels, from procurement of equipment, to design of laboratories layout, furniture and arrangements and supervision of the setting up process. The candidate, as Convenor, Departmental Lab Development committee was in charge of setting up 3 hardware labs and 1 software lab at the upcoming campus site.
A software lab with MICROSIM PSpice
Design package and MATLAB has also been set up by the candidate. Meanwhile,
work has started on the development of other labs; an Electrical Machines lab,
a high frequency lab, and a DSP hardware lab of sufficient sophistication to
meet the needs of the entire B.Tech Programme as well as development work for projects, are
being set up by the candidate. (Pl. Refer Item 11 G)