A Multi-body Factorization Method for Motion Analysis

Joao Costeira and Takeo Kanade
tech. report CMU-CS-TR-94-220, Computer Science Department, Carnegie Mellon University, September, 1994


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Abstract
The structure-from-motion problem has been extensively studied in the field of computer vision. Yet, the bulk of the existing work assumes that the scene contains only a single moving object. The more realistic case where an unknown number of objects move in the scene has received little attention, especially for its theoretical treatment. In this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images. The method does not require prior knowledge of the number of objects, nor is dependent on any grouping of features into an object at the image level. For this purpose, we introduce a mathematical construct of object shapes, called the shape interaction matrix, which is invariant to both the object motions and the selection of coordinate systems. This invariant structure is computable solely from the observed trajectories of image features without grouping theminto individual objects. Once the matrix is computed, it allows for segmenting features into objects by the process of transforming it into a canonical form, as well as recovering the shape and motion of each object.

Notes
Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Text Reference
Joao Costeira and Takeo Kanade, "A Multi-body Factorization Method for Motion Analysis," tech. report CMU-CS-TR-94-220, Computer Science Department, Carnegie Mellon University, September, 1994

BibTeX Reference
@techreport{Kanade_1994_2097,
   author = "Joao Costeira and Takeo Kanade",
   title = "A Multi-body Factorization Method for Motion Analysis",
   booktitle = "",
   institution = "Computer Science Department",
   month = "September",
   year = "1994",
   number= "CMU-CS-TR-94-220",
   address= "Pittsburgh, PA",
}