This article presents a novel variational model based on fuzzy clustering and total variation regularization for superpixel segmentation. Compared with the classical hard-labeled methodologies, our approach gives soft results via the fuzzy membership function, and moreover, the use of total variation provides additional information that can enhance the superpixel regularity, which in turn improves the segmentation performance. To efficiently minimize the energy functional of the proposed model, we adopt an alternating direction method of multipliers with the modified Chambolle’s fast duality projection algorithm. Our algorithm can generate regular and compact superpixels with high segmentation accuracy, satisfactory boundary adherence, and low computational cost. Comparative experimental results with the current state-of-the-art approaches reveal the superior performance of the proposed method.

Principal Component Analysis (PCA) is one of the most widely used tools for the representation of high-dimensional data. Many different versions have been proposed to enhance the robustness of the model. Most of these ideas are not median based formulation, which is always a robust estimator in statistics. In this paper, we attempt to design a new median based PCA model based on k-medians clustering, for which each principal component is always the spatial median of the projected space. We prove that the proposed method converges. We also compare the proposed method with several state-of-the-art methods including ℓ1-PCA, RPCA and RPCA-OM. Experimental results show that the proposed k-medians clustering based PCA performs the best in many cases.

Inverse lithography technology formulates the photomask synthesis as an inverse mathematical problem. To solve this, we propose a variational functional and develop a robust computational algorithm, where the proposed functional takes into account the process variations and incorporates several regularization terms that can control the mask complexity. We establish the existence of the minimizer of the functional, and in order to optimize it effectively, we adopt an alternating minimization procedure with Chambolle's fast duality projection algorithm. Experimental results show that our proposed algorithm is effective in synthesizing high quality photomasks as compared with existing methods.

This paper presents a multiphase fuzzy region competition model that takes into account spatial and frequency information for image segmentation. In the proposed energy functional, each region is represented by a fuzzy membership function and a data fidelity term that measures the conformity of spatial and frequency data within each region to (generalized) gaussian densities whose parameters are determined jointly with the segmentation process. Compared with the classical region competition model, our approach gives soft segmentation results via the fuzzy membership functions, and moreover, the use of frequency data provides additional region information that can improve the overall segmentation result. To efficiently solve the minimization of the energy functional, we adopt an alternate minimization procedure and make use of Chambolle's fast duality projection algorithm. We apply the proposed method to synthetic and natural textures as well as real-world natural images. Experimental results show that our proposed method has very promising segmentation performance compared with the current state-of-the-art approaches.

The modeling of image data by a general parametric family of statistical distributions plays an important role in many applications. In this paper, we propose to adopt the three-parameter generalized Gamma density (GGammaD) for modeling wavelet detail subband histograms and for texture image retrieval. The advantage of GGammaD over the existing generalized Gaussian density (GGD) is that it provides more flexibility to control the shape of model which is critical for practical histogram-based applications. To measure the discrepancy between GGammaDs, we use the symmetrized Kullback-Leibler distance (SKLD) and derive a closed form for the SKLD between GGammaDs. Such a distance can be computed directly and effectively via the model parameters, making our proposed scheme particularly suitable for image retrieval systems with large image database. Experimental results on the well-known databases reveal the superior performance of our proposed method compared with the current existing approaches.

In this correspondence, we propose a novel, efficient, and effective Refined Histogram (RH) for modeling the wavelet subband detail coefficients and present a new image signature based on the RH model for supervised texture classification. Our RH makes use of a step function with exponentially increasing intervals to model the histogram of detail coefficients, and the concatenation of the RH model parameters for all wavelet subbands forms the so-called RH signature. To justify the usefulness of the RH signature, we discuss and investigate some of its statistical properties. These properties would clarify the sufficiency of the signature to characterize the wavelet subband information. In addition, we shall also present an efficient RH signature extraction algorithm based on the coefficient-counting technique, which helps to speed up the overall classification system performance. We apply the RH signature to texture classification using the well-known databases. Experimental results show that our proposed RH signature in conjunction with the use of symmetrized Kullback-Leibler divergence gives a satisfactory classification performance compared with the current state-of-the-art methods.

The modeling of wavelet subband histograms via the product Bernoulli distributions (PBD) has received a lot of interest and the PBD model has been applied successfully in texture image retrieval. In order to fully understand the usefulness and effectiveness of the PBD model and its associated signature, namely, the bit-plane probability (BP) signature on image processing applications, we discuss and investigate some of their statistical properties. These properties would help to clarify the sufficiency of the BP signature to characterize wavelet subbands, which, in turn, justifies its use in real time applications. We apply the BP signature on supervised texture classification problem and experimental results suggest that the weighted L(1)-norm (rather than the standard L (1)-norm) should be used for the BP signature. Comparative classification experiments show that our method outperforms the current state-of-the-art Generalized Gaussian Density approaches.

This paper presents a novel, effective, and efficient characterization of wavelet subbands by bit-plane extractions. Each bit plane is associated with a probability that represents the frequency of 1-bit occurrence, and the concatenation of all the bit-plane probabilities forms our new image signature. Such a signature can be extracted directly from the code-block code-stream, rather than from the de-quantized wavelet coefficients, making our method particularly adaptable for image retrieval in the compression domain such as JPEG2000 format images. Our signatures have smaller storage requirement and lower computational complexity, and yet, experimental results on texture image retrieval show that our proposed signatures are much more cost effective to current state-of-the-art methods including the generalized Gaussian density signatures and histogram signatures.