---
title: "A General Expression of the Fundamental Matrix for Both Perspective and Affine Cameras"
authors:
  - "Zhengyou Zhang"
  - "Gang Xu"
doi: ""
url: "https://ijcai.org/proceedings/1997/216"
pdf: "https://ijcai.org/proceedings/1997/0216.pdf"
venue: "Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence"
year: 1997
pages: "1502-1509"
track: "Vision"
keywords:
---

# A General Expression of the Fundamental Matrix for Both Perspective and Affine Cameras

Zhengyou Zhang, Gang Xu

*Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence*, pages 1502-1509.

## Abstract

This paper addresses the recov ery of structure and motion from two uncalibrated images of a scene under full perspective or under affine projection. Epipolar geometry, projective reconstruction, and affine reconstruction are elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A general expression of the fundamental matrix is derived which is valid for any projection mod el without lens distortion (including full perspective and affine camera). A new technique for affine reconstruction from two affine images is developed , which consists in first estim ating the affine epipol ar geometry and then performing a triangu l ation for each point match with respect to an implicit common affine basis. This technique is very efficient.