Q-MAF Shape Decomposition

Abstract

Abstract. This paper address the problems of generating a low dimensional representation of the shape variation present in a set of shapes represented by a number of landmark points. First, we will present alternatives to the featured Least-Squares Procrustes alignment based on the L∞-norm and the L1-norm. Second, we will define a new shape decomposition based on the Maximum Autocorrelation Factor (MAF) analysis, and investigate and compare its properties to the Principal Components Analysis (PCA). It is shown that Molgedey-Schuster algorithm for Independent Component Analysis (ICA) is equivalent to the MAF analysis. The shape MAF analysis utilises the natural order of landmark points along shape contours.

Probabilistic Generative Modelling

“…Switzer suggests that we estimate Σ ∆ for a shift in lag 1. Blind source separation by independent components analysis using the Molgedey-Schuster (MS-ICA) algorithm [12] is equivalent to MAF [3]. The purpose of this algorithm is to separate independent signals from linear mixings.…”

A Noise Robust Statistical Texture Model

“…When maximising autocorrelation the MNF analysis qualifies as an Independent Components Analysis (ICA) similar to the Molgedy-Schuster algorithm [14], see [5]. A comparative study of the PC and MNF can be found in [15,16].…”

“…One example is the Active Appearance Models (AAMs) [1,2]. Applications of AAMs include recovery and variation analysis of anatomical structures in medical images, such as magnetic resonance images (MRIs) [3], radiographs [4,5] and ultrasound images [6].…”

“…The ancestor of AAMs, the Active Shape Models [9] have previously been extended by means of a variant of MNF in the analysis of shapes, see [5]. Here, we extend this work to pixel intensities, henceforth denoted texture.…”

Statistical 2D and 3D Shape Analysis Using Non-Euclidean Metrics

“…Because imaged phenomena often exhibit some sort of spatial coherence spatial autocorrelation is often a better optimality criterion than variance. We have previously adapted the MAF transform for analysis of tangent space shape coordinates [3]. In [4] the noise adjusted PCA or the minimum noise fraction (MNF) transformations were used for decomposition of multispectral satellite images.…”