Sparse modeling of landmark and texture variability using the orthomax criterion

Abstract

In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach.

Sparse Decomposition and Modeling of Anatomical Shape Variation

“…There exist a few interesting alternatives to SPCA to construct sparse representations of anatomy, most notably independent component analysis (ICA) [31] and varimax rotated principal components [30]. Some experiments using these bases have been carried out, with results similar to those of SPCA.…”

“…Examples of other statistical decomposition techniques used in shape analysis are factor analysis [29], varimax rotated principal components [30], and independent component analysis [31]. The latter two typically produce approximately sparse representations but lack the flexibility of most SPCA implementations.…”

Hierarchical 3D diffusion wavelet shape priors

“…The orthomax criterion [24] allows to obtain a simple and compact hierarchical representation through a rotation of the model parameter system. We explore the varimax version [15] for optimizing sparsity corresponding to new variables being associated to localized variation modes.…”

Localized Shape Variations for Classifying Wall Motion in Echocardiograms

“…Orthomax rotations were applied to the PCA shape models to produce models with localized spatial variations [7], [9]. Orthomax rotations are reparameterizations of the PCA space producing a simple basis.…”

“…Recently, Stegmann et al [7] suggested a method using orthomax rotations, which seems particularly attractive due to its computational feasibility in high-dimensional spaces. The applicability for localized classification was mentioned in that paper, but has not yet been investigated.…”