Multiscale 3D Feature Extraction and Matching

Partial 3D shape matching refers to the process of computing a similarity measure between partial regions of 3D objects. This remains a difficult challenge without \emph{a priori} knowledge of the scale of the input objects, as well as their rotation and translation. This paper focuses on the problem of partial shape matching among 3D objects of unknown scale. We consider the problem of face detection on arbitrary 3D surfaces and introduce a multiscale surface representation for feature extraction and matching. This work is motivated by the scale-space theory for images. Scale-space based techniques have proven very successful for dealing with noise and scale changes in matching applications for 2D images. However, efficient and practical scale-space representations for 3D surfaces are lacking. Our proposed scale-space representation is defined in terms of the evolution of surface curvatures according to the heat equation. This representation is shown to be insensitive to noise, computationally efficient, and capable of automatic scale selection. Examples in face detection and surface registration are given.