Abstract
This paper addresses the computational role that the construction of a complete surface representation may play in the recovery of 3-D structure from motion. We first discuss the need to integrate surface reconstruction with the structure-from-motion process, both on computational and perceptual grounds. We then present a model that combines a feature-based structure-from-motion algorithm with a smooth surface interpolation mechanism. This model allows multiple surfaces to be represented in a given viewing direction, incorporates constraints on surface structure from object boundaries, and segregates image features onto multiple surfaces on the basis of their 2-D image motion. We present the results of computer simulations that relate the qualitative behavior of this model to psychophysical observations. In a companion paper, we discuss further perceptual observations regarding the possible role of surface reconstruction in the human recovery of 3-D structure from motion.
Highlights
This section further justifies a number of aspects of the surface reconstruction process: (l) the separation of the SFM and surface interpolation components of the 3-D recovery process; (2) the grouping of points by their 2-D motion for surface reconstruction; (3) the interpolation of the "smoothest" surface consistent with the sparse 3-D data; and (4) the use of boundary constraints for surface reconstruction
Even if the processes analyzing different 3-D cues produce a dense representation of 3-D shape directly, it may be simpler to analyze the various cues somewhat independently and integrate 3-D information derived from each cue at a level that constructs a common surface representation, rather than tightly linking the 3-D recovery processes themselves. [It has been suggested that the Bayesian approach provides a useful framework for reliable integration of various depth cues.]
This paper addressed the computational role that the construction of a complete surface representation plays in the recovery of 3-D structure from motion
Summary
An important tool for the perceptual study of the recovery of three-dimensional (3-D) structure from motion has been the dynamic random-dot pattern, in which a random collection of points is moved across a two-dimensional (2-D) computer display in a way that is consistent with the projection of points from the surface of a 3-D object moving in space. Dosher et al (1989a) showed that subjects can discriminate between different complex 3-D surfaces in moving dot displays in which each dot has a lifetime of only two frames, performance may improve for a larger number of frames (Landy et al, 1991) To account for these phenomena, a mechanism is required that allows the representation underlying the 3-D percept to be preserved when the moving points disappear, and allows new points appearing in different image locations to improve the representation of 3-D shape. If interpolation is required to interpret SFM displays with short point lifetimes, this observation suggests an ability to interpolate across multiple surfaces simultaneously In another demonstration, Ramachandran et al (1988) present a display of two superimposed planes of random dots moving in opposite directions. Later sections elaborate on the justifications of the model, and present the details of the implementation of this model that was used to conduct our computer simulations
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