Shape Analysis Group
Astrocyte Geometry
Characterizing astrocyte shape and mitocondrial spatial distribution using geometric formalisms
Embryoic Cardiomyocyte Geometry
Analyzing the evolution of nuclear shape, orientation, and arrangement of mammilian hearts during embryonic development
Topological Optimization Using Diffeomorphic Interpolation
Exploring an efficient geometry-based method of transforming a bunny into a circle
Finding Sheets in Fibrous Structures
Modeling sheet-like geometry in fibrous biological structures by minimizing non-holonomicity.
Moving Frames
Modeling spatio-temporal fiber rotation in the heart wall using moving frames
Generalized Helicoids for Modeling Hair Geometry
Modeling fiber geometry using minimal surfaces for realistic hair and fur rendering
Background
I am a Professor of Computer Science at McGill University, a member of McGill's Centre for Intelligent Machines, and an associate member of the Dept. of Mathematics and Statistics, the Goodman Cancer Research Centre, and MILA. Together with Keith Murai of the Dept. of Neurology and Neurosurgery I hold an FRQS Dual Chair in AI and Health. I work in shape analysis, with a particular interest in areas at the interface between disciplines - computer vision, neuroscience, bio-medicine, machine learning and perception. My doctoral work at Brown University was on curve evolution based methods for the analysis of visual form. I graduated from Cathedral and John Connon High School in Bombay and obtained my undergraduate degree in Electrical Engineering from Lafayette College. I presently serve as the Field Chief Editor of Frontiers in Computer Science. In this role I am seeking to promote work that highlights the theoretical, algorithmic and applied aspects of our field, while also considering its impact on other disciplines.
The Shape Analysis Group – Spring 2025
Research
The shape of an object lies at the interface between vision and
cognition, yet general purpose theories of shape have been notoriously difficult to
formulate. Drawing on techniques from singularity theory, partial
differential equations, geometric flows and graph theory, our group is broadly
concerned with the problem of shape analysis in computational
vision, visual perception, bio-medicine, neuroscience and robotics. A key theme is the development of "generic" models, to support a notion of similarity between qualitatively similar
shapes. Distinct from current trends in computer vision in representation learning from data using black box methods, we are interested in learning representations which are informed by regularities of the physical world and the objects within it. A key focus has been on the use of mathematical tools from differential geometry and group theory to allow for appropriate levels of abstraction of visual form.
I am particularly interested in biological shape analysis using applied mathematics and computer vision. Students interested primarily in neural network based approaches, deep learning, applied machine learning, applications of computer vision and black box methods should seek other colleagues with expertise in these areas.