International Journal of Computer Vision

, Volume 29, Issue 3, pp 159–179

A Multibody Factorization Method for Independently Moving Objects

  • João Paulo Costeira
  • Takeo Kanade

DOI: 10.1023/A:1008000628999

Cite this article as:
Costeira, J.P. & Kanade, T. International Journal of Computer Vision (1998) 29: 159. doi:10.1023/A:1008000628999


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 them into 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. The theory works under a broad set of projection models (scaled orthography, paraperspective and affine) but they must be linear, so it excludes projective “cameras”.

computer vision image understanding 3D vision shape from motion motin analysis invariants 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • João Paulo Costeira
    • 1
  • Takeo Kanade
    • 2
  1. 1.Instituto de Sistemas e Robótica, Instituto Superior TécnicoLisboa CODEXPortugal. E-mail: Email
  2. 2.Carnegie Mellon UniversityPittsburghUSA. E-mail: Email

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