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A geometric framework for dynamic vision


Soatto, Stefano (1996) A geometric framework for dynamic vision. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/x87w-t943.


This thesis explores the problem of inferring information about the three-dimensional world from its projections onto a camera (images). Among all visual cues, we do not address "pictorial" ones, such as texture or shading. Instead, we concentrate on "dynamic" cues, which are associated with variations of the image over time. In order to eliminate pictorial cues, one may represent the world as a collection of geometric primitives, such as points, curves or surfaces in three-dimensional space. Then, from the two-dimensional motion of the projection of such primitives onto the image, one can infer the three-dimensional structure of the world and its motion relative to the viewer. "Three-dimensional structure from two-dimensional images" has now been a central theme in Computer Vision for over two decades, and tools from Linear Algebra and Projective Geometry have been widely employed to attack the problem as a "static" task. It is only in recent years that the role of time has started to be recognized, after the influential work of Dickmanns and his coworkers on vehicle guidance on freeways. We do not impose restrictions on the structure of the environment, and we cast the problem of general three-dimensional structure and motion estimation within the framework of Dynamical Systems. We show how different algebraic constraints on the image projections can be interpreted as nonlinear and implicit dynamical models whose (unknown) parameters live in peculiar differentiable manifolds that encode three-dimensional information. Recovering such three-dimensional information then amounts to identifying dynamical models while taking into account the geometry of the parameter manifolds.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Control and Dynamical Systems)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Perona, Pietro
Thesis Committee:
  • Perona, Pietro (chair)
  • Koch, Christof
  • Ponce, Jean
  • Marsden, Jerrold E.
  • Burdick, Joel Wakeman
  • Doyle, John Comstock
  • Morari, Manfred
  • Murray, Richard M.
Defense Date:17 May 1996
Record Number:CaltechETD:etd-01082008-103705
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68
Deposited By: Imported from ETD-db
Deposited On:10 Jan 2008
Last Modified:08 Nov 2023 00:44

Thesis Files

PDF (Soatto_s_1996.pdf) - Final Version
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