On-going research projects

Discrete Computer Vision

Discrete geometry meets computer vision:
reformulation of multiple-view geometry for digital image analysis

in collabolation with Assoc. Prof. A. Sugimoto at NII
since April 2003.

Project overview

The problem of inferring 3D information of a scene from a set of its images has a long history in computer vision. Multiple-view geometry enables us to understand geometric relationships between different views of an object in space, and lies in the basis of 3D reconstruction techniques in the field of computer vision. The conventional multi-view geometry is formulated in continuous spaces, namely, assumes that the smallest unit of images is a point. In applications, however, we cannot deal with points because digital images involve some digitization process and the smallest unit of digital images is not a point but a pixel.

In digital images, two different errors exist: digitization errors and observation errors. They are originally different from each other because they are generated in different mechanisms. This project aims at discriminating the two kinds of errors, focusing on pixels as the smallest unit of digital images. In other words, we reformulate the conventional multiple-view geometry based on a pixel as the smallest unit of images and propose a discrete multiple-view geometry. Our formulation is established through projections from the continuous 3D space to discrete image planes.

Such formulation for discrete computer vision will contribute to computer vision literatures in the following topics:

  1. giving theoretically grounded reasons to existing empirical knowledge obtained from practical experiences: for examples, optimal allocation of cameras for 3D reconstruction;
  2. clarifying the limitation of precision in camera calibration and in 3D reconstruction due to digitization errors;
  3. proposing computationally efficient algorithms with the help of discrete and/or computational geometry.
We expect, of course, that our contribution will go beyond the above listed topics.


Conference articles [29].


Yukiko Kenmochi
Last updated: 2/16/2005