Hang Liu

Hang Liu, Anna Scaglione, Sean Peisert

Gaussian Mixture Models (GMMs) are widely used statistical models for representing multi-modal data distributions, with numerous applications in data mining, pattern recognition, data simulation, and machine learning. However, recent research has shown that releasing GMM parameters poses significant privacy risks, potentially exposing sensitive information about the underlying data. In this paper, we address the challenge of releasing GMM parameters while ensuring differential privacy (DP) guarantees. Specifically, we focus on the privacy protection of mixture weights, component means, and covariance matrices. We propose to use Kullback-Leibler (KL) divergence as a utility metric to assess the accuracy of the released GMM, as it captures the joint impact of noise perturbation on all the model parameters. To achieve privacy, we introduce a DP mechanism that adds carefully calibrated random perturbations to the GMM parameters. Through theoretical analysis, we quantify the effects of privacy budget allocation and perturbation statistics on the DP guarantee, and derive a tractable expression for evaluating KL divergence. We formulate and solve an optimization problem to minimize the KL divergence between the released and original models, subject to a given $(ε, δ)$-DP constraint. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach achieves strong privacy guarantees while maintaining high utility.

Hang Liu, Hengyu Li, Xiahua Liu et al.

This letter presents a novel method to estimate the relative poses between RGB-D cameras with minimal overlapping fields of view in a panoramic RGB-D camera system. This calibration problem is relevant to applications such as indoor 3D mapping and robot navigation that can benefit from a 360$^\circ$ field of view using RGB-D cameras. The proposed approach relies on descriptor-based patterns to provide well-matched 2D keypoints in the case of a minimal overlapping field of view between cameras. Integrating the matched 2D keypoints with corresponding depth values, a set of 3D matched keypoints are constructed to calibrate multiple RGB-D cameras. Experiments validated the accuracy and efficiency of the proposed calibration approach, both superior to those of existing methods (800 ms vs. 5 seconds; rotation error of 0.56 degrees vs. 1.6 degrees; and translation error of 1.80 cm vs. 2.5 cm.

Hang Liu, Hengyu Li, Jun Luo et al.

Multi-focus image fusion is a technique for obtaining an all-in-focus image in which all objects are in focus to extend the limited depth of field (DoF) of an imaging system. Different from traditional RGB-based methods, this paper presents a new multi-focus image fusion method assisted by depth sensing. In this work, a depth sensor is used together with a color camera to capture images of a scene. A graph-based segmentation algorithm is used to segment the depth map from the depth sensor, and the segmented regions are used to guide a focus algorithm to locate in-focus image blocks from among multi-focus source images to construct the reference all-in-focus image. Five test scenes and six evaluation metrics were used to compare the proposed method and representative state-of-the-art algorithms. Experimental results quantitatively demonstrate that this method outperforms existing methods in both speed and quality (in terms of comprehensive fusion metrics). The generated images can potentially be used as reference all-in-focus images.