Evaluating Initialization Methods for Discriminative and Fast-Converging HGMM Point Clouds

Abstract

Discriminative data representations for point cloud data are critical for computer vision applications. Recently, the Hierarchical Gaussian Mixture Model (HGMM) has become a popular representation due to its compactness and real-time execution. However, HGMM still lacks a well-designed and robust initialization criterion. Ad-hoc initializations for HGMM can lead to a low discriminative clustering capability, slow convergence, and loss of scale-invariance. To adopt the optimal initialization scheme, we evaluate four potential candidates: K-Means++, Fuzzy C-Means (FCM), uniform, and random initialization across a few synthetic and measured datasets. Our experiments involve comparing the quality of HGMM point cloud reconstruction based on different initialization methods. The reconstruction quality is evaluated by the peak signal-to-noise ratio (PSNR). Our experiments show that clustering-based initialization methods can result in higher-quality HGMMs because of i) faster convergence of the Expectation-Maximization (EM) optimization, ii) better scaleinvariance across differently sized datasets, and iii) greater stability for different initial scales of covariance matrices of the HGMM.