Pictures and trails: a new framework for the computation of shape and motion from perspective image sequences

Abstract

This paper presents a new framework for the computation of shape and motion from a sequence of images taken under perspective projection. The framework is based on two abstractions, the picture and trail loci, that represent respectively the set of all pictures of the same scene and the set of all trails that a point in the world can leave on the image for a given camera trajectory. These abstractions lead t o a remarkably clean relation between perspective and orthography. A shape and motion reconstruction method is developed for the case of a two-dimensional world, but all concepts also hold i n three dimensions. Experiments show that the method is rather immune to noise but critically dependent on camera calibration.

Robust Bundle Adjustment for Structure from Motion

“…Numerical experiments demonstrated the robustness of this approach. Similarly, Tomasi [8] Using a chessboard equipped with a mechanically tracked arm, we obtained a ground truth reconstruction and compared it with the results of BA using cost function (4) and a standard SBA.…”

Multi-view structure computation without explicitly estimating motion

“…Our method is largely inspired by intriguing idea of Tomasi [26] and Tomasi&Shi [27]. Yet, they applied different techniques are quite different.…”

Angle Independent Bundle Adjustment Refinement

“…Tomasi and Shi [11] proposed structurefrom-motion equations to compute the direction of heading of a camera --their equations did not involve camera angles. Subsequently, they described image changes through the angles between the projection rays [12]. This approach was used to reconstruct a twodimensional world and could theoretically be applied to a three-dimensional world although at significant additional complexity and with high-sensitivity to accurate camera calibration.…”