This paper presents a novel Log-Euclidean metric inspired color-to-gray conversion model for faithfully preserving the contrast details of color image, which differs from the traditional Euclidean metric approaches. In the proposed model, motivated by the fact that Log-Euclidean metric has promising invariance properties such as inversion invariant and similarity invariant, we present a Log-Euclidean metric-based maximum function to model the decolorization procedure. The Gaussian-like penalty function consisting of the Log-Euclidean metric between gradients of the input color image and transformed grayscale image is incorporated to better reflect the degree of preserving feature discriminability and color ordering in color-to-gray conversion. A discrete searching algorithm is employed to solve the proposed model with linear parametric and non-negative constraints. Extensive evaluation experiments show that the proposed method outperforms the state-of-the-art methods both quantitatively and qualitatively.

Extensive neurophysiological studies have shown that the receptive field plays a significant role in the human visual system. It has various kinds of properties such as orientation-selectivity, correlativity, etc. Motivated by these structural and functional properties, we propose in this paper a novel local image descriptor namely the Discriminative Transform of Receptive Fields (DTRF). Specifically, Receptive Field Patterns (RFP) are defined around each sample pixel and then divided into two kinds of components: RFP-Surround and RFP-Center. The RFP-Surround serves as the basic feature structure, which is extracted based on Local Annular Discrete Cosine Transform (LADCT) algorithm. The RFP-Center is used to pool these local features to simulate the correlative property of receptive field. Experimental results on the standard Oxford data set demonstrate the superiority of DTR-F over the state-of-the-art descriptors under various types of image transformations such as rotation and scaling changes, viewpoint changes, image blurring, JPEG compression, illumination changes, and image noise.

We present a new fuzzy c-means algorithm for image segmentation by introducing a novel spatially constrained Student's t-distribution and a new regularization term. Firstly, considering that conventional distribution models lack spatial information and the multivariate Student's t-distribution is heavily tailed, we propose a new way to incorporate spatial information between neighboring pixels into the Student's t-distribution based on Markov random field (MRF) in order to enhance robustness. Secondly, the new regularization term, inspired by the geodesic active contour (GAC) with a strong ability in capturing boundary, can preserve the details of edges and further enhance its robustness to noise and outliers by capitalizing on the local context information and edge information. Finally, in comparison to other Markov random fields that are complex and computationally expensive, the parameters are easily optimized with the EM algorithm in our proposed method. The proposed algorithm demonstrates the robustness and effectiveness, compared with other state-of-the-art methods on synthetic and real images.