Center-of-mass variation under projective transformation

Accurate feature detection and localization is fundamentally important to computer vision, and feature locations act as input to many algorithms including camera calibration, structure recovery, and motion estimation. Unfortunately, feature localizers in common use are typically not projectively invariant even in the idealized case of a continuous image. This results in feature location estimates that contain bias which can influence the higher level algorithms that make use of them. While this behavior has been studied in the case of ellipse centroids and then used in a practical calibration algorithm, those results do not trivially generalize to the center-of-mass of a radially symmetric intensity distribution. This paper introduces the generalized result of feature location bias with respect to perspective distortion and applies it to several specific radially symmetric intensity distributions. The impact on calibration is then evaluated. Finally, an initial study is conducted comparing calibration results obtained using center-of-mass to those obtained with an ellipse detector. Results demonstrate that feature localization error, over a range of increasingly large projective distortions, can be stabilized at less than a tenth of a pixel versus errors that can grow to larger than a pixel in the uncorrected case.