While fuzzy c-means is a popular soft-clustering method, its effectiveness is largely limited to spherical clusters. By applying kernel tricks, the kernel fuzzy c-means algorithm attempts to address this problem by mapping data with nonlinear relationships to appropriate feature spaces. Kernel combination, or selection, is crucial for effective kernel clustering. Unfortunately, for most applications, it is uneasy to find the right combination. We propose a multiple kernel fuzzy c-means (MKFC) algorithm that extends the fuzzy c-means algorithm with a multiple kernel-learning setting. By incorporating multiple kernels and automatically adjusting the kernel weights, MKFC is more immune to ineffective kernels and irrelevant features. This makes the choice of kernels less crucial. In addition, we show multiple kernel k-means to be a special case of MKFC. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed MKFC algorithm.

This paper proposes a new Bayesian framework for solving the matting problem, i.e. extracting a foreground element from a background image by estimating an opacity for each pixel of the foreground element. Our approach models both the foreground and background color distributions with spatially-varying sets of Gaussians, and assumes a fractional blending of the foreground and background colors to produce the final output. It then uses a maximum-likelihood criterion to estimate the optimal opacity, foreground and background simultaneously. In addition to providing a principled approach to the matting problem, our algorithm effectively handles objects with intricate boundaries, such as hair strands and fur, and provides an improvement over existing techniques for these difficult cases.

We propose a content-aware stereoscopic image display adaptation method which simultaneously resizes a binocular image to the target resolution and adapts its depth to the comfort zone of the display while preserving the perceived shapes of prominent objects. This method does not require depth information or dense correspondences. Given the specification of the target display and a sparse set of correspondences, our method efficiently deforms the input stereoscopic images for display adaptation by solving a least-squares energy minimization problem. This can be used to adjust stereoscopic images to fit displays with different real estates, aspect ratios and comfort zones. In addition, with slight modifications to the energy function, our method allows users to interactively adjust the sizes, locations and depths of the selected objects, giving users aesthetic control for depth perception. User studies show that the method is effective at editing depth and reducing occurrences of diplopia and distortions.

We apply Stein's Unbiased Risk Estimator (SURE) to adaptive sampling and reconstruction to reduce noise in Monte Carlo rendering. SURE is a general unbiased estimator for mean squared error (MSE) in statistics. With SURE, we are able to estimate error for an arbitrary reconstruction kernel, enabling us to use more effective kernels rather than being restricted to the symmetric ones used in previous work. It also allows us to allocate more samples to areas with higher estimated MSE. Adaptive sampling and reconstruction can therefore be processed within an optimization framework. We also propose an efficient and memory-friendly approach to reduce the impact of noisy geometry features where there is depth of field or motion blur. Experiments show that our method produces images with less noise and crisper details than previous methods.

Spectral clustering makes use of spectral-graph structure of an affinity matrix to partition data into disjoint meaningful groups. Because of its elegance, efficiency and good performance, spectral clustering has become one of the most popular clustering methods. Traditional spectral clustering assumes a single affinity matrix. However, in many applications, there could be multiple potentially useful features and thereby multiple affinity matrices. To apply spectral clustering for these cases, a possible way is to aggregate the affinity matrices into a single one. Unfortunately, affinity measures constructed from different features could have different characteristics. Careless aggregation might make even worse clustering performance. This paper proposes an affinity aggregation spectral clustering (AASC) algorithm which extends spectral clustering to a setting with multiple affinities available. AASC seeks for an optimal combination of affinity matrices so that it is more immune to ineffective affinities and irrelevant features. This enables the construction of similarity or distance-metric measures for clustering less crucial. Experiments show that AASC is effective in simultaneous clustering and feature fusion, thus enhancing the performance of spectral clustering by employing multiple affinities.