Unsupervised Learning of Shape Manifolds

Abstract

Classical shape analysis methods use principal component analysis to reduce the dimensionality of shape spaces. The basic assumption behind these methods is that the subspace corresponding to the major modes of variation for a particular class of shapes is linearised. This may not necessarily be the case in practice. In this paper, we present a novel method for extraction of the intrinsic parameters of multiple shape classes in an unsupervised manner. The proposed method is based on learning the global structure of shape manifolds using diffusion maps. We demonstrate that the method is effective in separating the members of different shape classes after embedding them into a low-dimensional Euclidean space.

Histopathological Image Analysis: A Review

“…Manifold learning has also been shown to be useful for shape-based classification of prostate nuclei [106]. Rajpoot et al [106] employ Diffusion Maps [107] in order to reduce the dimensionality of shape descriptors down to two dimensions and a fast classification algorithm is derived based on a simple thresholding of the diffusion coordinates.…”

Unsupervised Clustering Using Diffusion Maps for Local Shape Modelling

“…Our first experiments use closed contours. The data set was the same data set as in [10], six different shape classes from the Kimia database of object silhouettes.…”

“…Here, we introduce the use of spectral clustering to build a set of linear shape spaces for such analysis (figure 1-(α)). We use the method described in [10] for extracting the intrinsic parameters of multiple shape classes in an unsupervised manner, where the method is based on learning the global structure of the shape manifolds [2].…”

Multi-manifold modeling for head pose estimation

“…Thus, many multi-manifold methods have been proposed [9,10,11]. Multi-subspace methods are also called Hybrid Linear Modeling (HLM: one linear model for each homogeneous subset of data) [12,13].…”