Model-based hierarchical clustering with Bregman divergences and Fishers mixture model: application to depth image analysis

Abstract

International audienceModel-based clustering is a method that clusters data with an assumption of a statistical model structure. In this paper, we propose a novel model-based hierarchical clustering method for a finite statistical mixture model based on the Fisher distribution. The main foci of the proposed method are: (a) provide efficient solution to estimate the parameters of a Fisher mixture model (FMM); (b) generate a hierarchy of FMMs and (c) select the optimal model. To this aim, we develop a Bregman soft clustering method for FMM. Our model estimation strategy exploits Bregman divergence and hierarchical agglomerative clustering. Whereas, our model selection strategy comprises a parsimony-based approach and an evaluation graph-based approach. We empirically validate our proposed method by applying it on simulated data. Next, we apply the method on real data to perform depth image analysis. We demonstrate that the proposed clustering method can be used as a potential tool for unsupervised depth image analysis

Joint Color-Spatial-Directional Clustering and Region Merging (JCSD-RM) for Unsupervised RGB-D Image Segmentation

“…This work exploits our earlier work on image analysis using directional distribution [15], [16], [27]. Moreover, it provides an extension of our recent work on RGB-D segmentation [39] by including additional details and newer contributions, such as:…”

“…However, from a recent study [16], we observe that: (a) the use of surface normals solely is not 1. In order to cluster surface normal, we proposed two methods: one based on the Fisher distribution in [15] and another based on the Watson distribution in [16]. In this paper, we exploit both of them within a common framework.…”

“…sphere, i.e., in S 2 . Based on this observation, we consider the multivariate Gaussian [29] distribution for the color and 3D features and the directional 4 (Fisher or Watson) [14], [15], [16] distribution for surface normals. Mathematically, such a model with k components has the following form: Figure 2 illustrates the workflow of the proposed RGB-D segmentation method that consists of two sub-tasks: (1) clustering heterogeneous (color, 3D and Normal) data and (2) merging regions.…”

“…It follows a generative model-based approach for these features in which they are issued independently (naïve Bayes [12], [13] assumption) from a finite mixture of certain probability distributions. The model considers the Gaussian distribution [2] for color and 3D features and the directional (Fisher or Watson) distribution [14], [15], [16] for surface normals. We use the directional distribution because: (a) it provides adequate statistics to explain the planar property of regions and (b) it helps us to develop a simple and effective region merging method.…”

“…In the context of image analysis and segmentation these models have been employed with the Gaussian distribution for clustering the color image pixels [1], [23], [24], [25], [26]. Recently, these models have been exploited to analyze 3D images by clustering the surface normals with a mixture of directional distributions [15], [16], [27]. These clusters are obtained by using the Expectation Maximization (EM) algorithm that performs Maximum Likelihood Estimate (MLE) of the model parameters [2], [28], [29].…”