General Deformations of Point Configurations Viewed By a Pinhole Model Camera

TL;DR

This paper investigates the theoretical limits of reconstructing deforming point configurations from monocular images, analyzing how many views are needed and the conditions for unique solutions under affine and polynomial deformations.

Contribution

It provides a theoretical framework for understanding the minimal number of images required for unique reconstruction of deforming points with affine and polynomial models.

Findings

At least three images are needed for finite solutions in most cases.

The study covers both calibrated and uncalibrated camera scenarios.

Simple examples illustrate the solution conditions.

Abstract

This paper is a theoretical study of the following Non-Rigid Structure from Motion problem. What can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for affine and polynomial deformations with calibrated and uncalibrated cameras. We show that in general at least three images with quasi-identical two deformations are needed in order to have a finite set of solutions of the points' structure and calculate some simple examples.