Q. M. J. Wu

Affine Legendre Moment Invariants for Image Watermarking Robust to Geometric Distortions

Geometric distortions are generally simple and effective attacks for many watermarking methods. They can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark. In this paper, we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of our approach stands on a set of affine invariants we derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. We also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction. Experimental results show that the proposed watermarking scheme is robust to a wide range of attacks: geometric distortion, filtering, compression, and additive noise.

An Extension of the Standard Mixture Model for Image Segmentation

Standard Gaussian mixture modeling (GMM) is a well-known method for image segmentation. However, the pixels themselves are considered independent of each other, making the segmentation result sensitive to noise. To reduce the sensitivity of the segmented result with respect to noise, Markov random field (MRF) models provide a powerful way to account for spatial dependences between image pixels. However, their main drawback is that they are computationally expensive to implement, and require large numbers of parameters. Based on these considerations, we propose an extension of the standard GMM for image segmentation, which utilizes a novel approach to incorporate the spatial relationships between neighboring pixels into the standard GMM. The proposed model is easy to implement and compared with MRF models, requires lesser number of parameters. We also propose a new method to estimate the model parameters in order to minimize the higher bound on the data negative log-likelihood, based on the gradient method. Experimental results obtained on noisy synthetic and real world grayscale images demonstrate the robustness, accuracy and effectiveness of the proposed model in image segmentation, as compared to other methods based on standard GMM and MRF models.

Gaussian-Mixture-Model-Based Spatial Neighborhood Relationships for Pixel Labeling Problem

In this paper, we present a new algorithm for pixel labeling and image segmentation based on the standard Gaussian mixture model (GMM). Unlike the standard GMM where pixels themselves are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account, the proposed method incorporates this spatial relationship into the standard GMM. Moreover, the proposed model requires fewer parameters compared with the models based on Markov random fields. In order to estimate model parameters from observations, instead of utilizing an expectation-maximization algorithm, we employ gradient method to minimize a higher bound on the data negative log-likelihood. The performance of the proposed model is compared with methods based on both standard GMM and Markov random fields, demonstrating the robustness, accuracy, and effectiveness of our method.

A Nonsymmetric Mixture Model for Unsupervised Image Segmentation

Finite mixture models with symmetric distribution have been widely used for many computer vision and pattern recognition problems. However, in many applications, the distribution of the data has a non-Gaussian and nonsymmetric form. This paper presents a new nonsymmetric mixture model for image segmentation. The advantage of our method is that it is simple, easy to implement, and intuitively appealing. In this paper, each label is modeled with multiple D-dimensional Students t-distribution, which is heavily tailed and more robust than Gaussian distribution. Expectation-maximization algorithm is adopted to estimate model parameters and to maximize the lower bound on the data log-likelihood from observations. Numerical experiments on various data types are conducted. The performance of the proposed model is compared with that of other mixture models, demonstrating the robustness, accuracy, and effectiveness of our method.

A Robust Fuzzy Algorithm Based on Student's t-Distribution and Mean Template for Image Segmentation Application

Fuzzy c-means (FCM) with spatial constraints has been considered as an effective algorithm for image segmentation. Students t-distribution has come to be regarded as an alternative to Gaussian distribution, as it is heavily tailed and more robust for outliers. In this letter, we propose a new algorithm to incorporate the merits of these two approaches. The advantages of our method are as follows: First, we incorporate the local spatial information and pixel intensity value by considering the labeling of an image pixel influenced by the labels in its immediate neighborhood. Second, we introduce additional parameter a to control the extent of this influence. The larger a indicates heavier extent of influence in the neighborhoods. Finally, we utilize a mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. Compared with HMRF, our method is simple, easy and fast to implement. Experimental results on synthetic and real images demonstrate the improved robustness and effectiveness of our approach.

Perspective 3-D Euclidean Reconstruction With Varying Camera Parameters

The paper addresses the problem of 3-D Euclidean structure and motion recovery from video sequences based on perspective factorization. It is well known that projective depth recovery and camera calibration are two essential and difficult steps in metric reconstruction. We focus on the difficulties and propose two new algorithms to improve the performance of perspective factorization. First, we propose to initialize the projective depths via a projective structure reconstructed from two views with large camera movement, and optimize the depths iteratively by minimizing reprojection residues. The algorithm is more accurate than previous methods and converges quickly. Second, we propose a self-calibration method based on the Kruppa constraint to deal with more general camera model. The Euclidean structure can be recovered from factorization of the normalized tracking matrix. Extensive experiments on synthetic data and real sequences are performed to validate the proposed method and good improvements are observed.

Data Partition Learning With Multiple Extreme Learning Machines

As demonstrated earlier, the learning accuracy of the single-layer-feedforward-network (SLFN) is generally far lower than expected, which has been a major bottleneck for many applications. In fact, for some large real problems, it is accepted that after tremendous learning time (within finite epochs), the network output error of SLFN will stop or reduce increasingly slowly. This report offers an extreme learning machine (ELM)-based learning method, referred to as the parent-offspring progressive learning method. The proposed method works by separating the data points into various parts, and then multiple ELMs learn and identify the clustered parts separately. The key advantages of the proposed algorithms as compared to the traditional supervised methods are twofold. First, it extends the ELM learning method from a single neural network to a multinetwork learning system, as the proposed multiELM method can approximate any target continuous function and classify disjointed regions. Second, the proposed method tends to deliver a similar or much better generalization performance than other learning methods. All the methods proposed in this paper are tested on both artificial and real datasets.

Adaptive Variable Block-Size Early Motion Estimation Termination Algorithm for H.264/AVC Video Coding Standard

The variable block-size motion estimation (ME) process is the H.264/AVC encoders most time-consuming function. This letter proposes to reduce the complexity of the ME process with an early termination algorithm that features an adaptive threshold based on the statistical characteristics of rate-distortion (RD) cost regarding current block and previously processed blocks and modes. In this method, most motion searches can be stopped early, with a large number of search points saved. A region-based search is also suggested to further reduce the computation required for full search ME. A search point reduction scheme for the fast motion estimation of H.264/AVC is also introduced, and the experimental results illustrate how the proposed method reduces ME times for full search and fast motion estimation by about 77 and 31%, respectively, despite the insignificant degradation of RD performance.

Incorporating Mean Template Into Finite Mixture Model for Image Segmentation

The well-known finite mixture model (FMM) has been regarded as a useful tool for image segmentation application. However, the pixels in FMM are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account. These limitations make the FMM more sensitive to noise. In this brief, we propose a simple and effective method to make the traditional FMM more robust to noise with the help of a mean template. FMM can be considered a linear combination of prior and conditional probability from the expression of its mathematical formula. We calculate these probabilities with two mean templates: a weighted arithmetic mean template and a weighted geometric mean template. Thus, in our model, the prior probability (or conditional probability) of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the local spatial and intensity information for eliminating the noise. Finally, our algorithm is general enough and can be extended to any other FMM-based models to achieve super performance. Experimental results demonstrate the improved robustness and effectiveness of our approach.

An Efficient Algorithm for Focus Measure Computation in Constant Time

This letter presents an efficient algorithm for focus measure computation, in constant time, to estimate depth map using image sequences acquired at varying focus. Two major factors that complicate focus measure computation include neighborhood support and gradient detection for oriented intensity variations. We present a distinct focus measure based on steerable filters that is invariant to neighborhood size and accomplishes fast depth map estimation at a considerably faster speed compared to other well-documented methods. Steerable filters represent architecture to synthesize filters of arbitrary orientation using a linear combination of basis filters. Such synthesis is helpful to analytically determine the filter output as a function of orientation. Steerable filters remove inherent limitations of traditional gradient detection techniques which perform inadequately for oriented intensity variations and low textured regions.