Removing the geometric distortion and space-time-varying blur caused by atmospheric turbulence from a given image sequence remains a challenge. Since geometric distortion and blur are two different kinds of distortions and interact with each other in the process of image restoration, it is difficult to extract the features that are useful to the restoration process when the images experience multiple distortions. In this article, we propose a new scheme based on geometric distortion and blur representation. The blur invariants and maximum gradient are used to represent the geometric distortion and sharpness of an image frame, respectively. The proposed scheme consists of three parts. First, two fast frame selection algorithms based on independent evaluations of the sharpness and geometric distortion are proposed to subsample a sharp subsequence and obtain a reference image. Next, to suppress the geometric distortion, a moment-blur-invariant-based method is presented to estimate the deformation vector between two degraded frames, and the selected sharp frames are registered to the reference image. Finally, a blind deconvolution method is applied to deblur the fused image, generating a final restoration result. Various experimental results show that the proposed method can effectively alleviate distortion and blur, as well as significantly improve the visual quality of real atmospheric turbulence-degraded images.

Superpixel segmentation partitions an image into perceptually coherent segments of similar size, namely, superpixels. It is becoming a fundamental preprocessing step for various computer vision tasks because superpixels significantly reduce the number of inputs and provide a meaningful representation for feature extraction. We present a pixel-related Gaussian mixture model (GMM) to segment images into superpixels. GMM is a weighted sum of Gaussian functions, each one corresponding to a superpixel, to describe the density of each pixel represented by a random variable. Different from previously proposed GMMs, our weights are constant, and Gaussian functions in the sums are subsets of all the Gaussian functions, resulting in segments of similar size and an algorithm of linear complexity with respect to the number of pixels. In addition to the linear complexity, our algorithm is inherently parallel and allows fast execution on multicore systems. During the expectation-maximization iterations of estimating the unknown parameters in the Gaussian functions, we impose two lower bounds to truncate the eigenvalues of the covariance matrices, which enables the proposed algorithm to control the regularity of superpixels. Experiments on a wellknown segmentation dataset show that our method can efficiently produce superpixels that adhere to object boundaries better than the current state-of-the-art methods.

This paper initially develops the discrete-point sampling operator's concept, model, and parameters that we have previously proposed, and makes its belt-shaped regions in a discrete-point sampling map more salient and appropriate for centerline extraction. The cross-sectional features of these belt-shaped regions are then analyzed and seven types of feature points are defined to facilitate descriptions of such features. Based on these feature points, a three-level detection system is proposed, including feature points, line segments, and centerlines, to extract centerlines from the belt-shaped regions. Eight basic types of centerlines and five types of relationships among the centerlines are defined by computational geometry algorithms, and Gestalt laws are used to cluster them into groupings. If some prior information about a desired shape is available, retrieval grouping may be carried out by a discrete-point sampling map, the purpose of which is to find centerlines by best matching with prior information. Discrete-point sampling effectually overcomes the influences of interference from noise, textures, and uneven illumination, and greatly reduces the difficulty of centerline extraction. Centerline clustered groupings and retrieval grouping can offer a strong anti-interference ability with nonlinear deformations such as articulation and occlusion. This method can extract large-scale complex shapes combined of lines and planes from complex images. The wheel location results of noise test and other shape extraction experiments show that our method has a strong capability to persist with nonlinear deformations.

This paper presents a novel fast algorithm for digital convolutions. It is able to compute arbitrary-length convolutions more efficiently via transforming the convolution into a first-order moment. Although many additions are required, the proposed algorithm has some advantages such as the avoidance of multiplications, simple computation structure, and only integer additions. These advantages contribute to this algorithm being so easy that it can compute convolutions rapidly. Based on the proposed algorithm a very simple and scalable systolic array without multipliers and ROM has been developed leading to more efficient VLSI implementation of convolutions.

When the scale-invariant feature transform (SIFT) is adopted in the registration of remote sensing images, a lot of incorrect matches of keypoints will appear owing to the significant difference in the image intensity between remote sensing images compared to visible images. Scale–orientation joint restriction criteria are proposed to achieve robust feature matching for keypoints in remote sensing images. Moreover, the feature descriptor of each keypoint is also refined to overcome the difference in the gradient intensity and orientation between remote image pairs. Experimental results for multidate, multispectral, and multisensor remote images indicate that the proposed method improves the match performance compared to intensity- and SIFT-based methods in terms of correct-match rate and aligning accuracy.

Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time.

This paper presents a novel approach to compute discrete sine transforms (DSTs). By using a modular mapping, DSTs are approximated by the sum of a finite sequence of discrete moments. Hence, by extending our earlier technique in computing moments with an adder network only, DSTs can also be implemented easily by a systolic array primarily involving additions. The method can be applied to multidimensional DSTs as well as their inverses.