Topological Fidelity and Image Thresholding: A Persistent Homology Approach

We develop a method based on persistent homology to analyze topological structure in noisy digital images. The method returns threshold(s) for image segmentation to represent inherent topological structure as well as estimates of topological quantities in the form of Betti numbers. Two motivating data sets are scans of binary alloys and firn, the intermediate stage between snow and ice.     

No-Reference Image Quality Assessment for Image Auto-Denoising

This paper proposes two new non-reference image quality metrics that can be adopted by the state-of-the-art image/video denoising algorithms for auto-denoising. The first metric is proposed based on the assumption that the noise should be independent of the original image. A direct measurement of this dependence is, however, impractical due to the relatively low accuracy of existing denoising method. The proposed metric thus tackles the homogeneous regions and highly-structured regions separately. Nevertheless, this metric is only stable when the noise level is relatively low. Most denoising algorithms reduce noise by (weighted) averaging repeated noisy measurements. As a result, another metric is proposed for high-level noise based on the fact that more noisy measurements will be required when the noise level increases. The number of measurements before converging is thus related to the quality of noisy images. Our patch-matching based metric proposes to iteratively find and add noisy image measurements for averaging until there is no visible difference between two successively averaged images. Both metrics are evaluated on LIVE2 (Sheikh et al. in LIVE image quality assessment database release 2: 2013) and TID2013 (Ponomarenko et al. in Color image database tid2013: Peculiarities and preliminary results: 2005) data sets using standard Spearman and Kendall rank-order correlation coefficients (ROCC), showing that they subjectively outperforms current state-of-the-art no-reference metrics. Quantitative evaluation w.r.t. different level of synthetic noisy images also demonstrates consistently higher performance over state-of-the-art non-reference metrics when used for image denoising.     

Meaningful visual secret sharing based on error diffusion and random grids

Random grid (RG) is an efficient method of eliminating the drawback of pixel expansion problem in visual secret sharing (VSS). Error diffusion (ED) technique is a brilliant method that improves the diffusion performance in an image by reducing the pattern noise and removing boundary and ’blackhole’ effects. In this paper, a novel meaningful RG-ED-based VSS, which encodes the (k, n) threshold into meaningful shadow images, is proposed at the price of not-clear recovered images. In addition, the novel scheme realizes the (k, n) threshold, avoids the design of complex codebook and averts the pixel expansion problem. Furthermore, the proposed RG-ED-based VSS inherits conventional benefits of VSS without the need of cryptographic efforts to decode the secret. Compared with other schemes reported in the literature, the present scheme has the benefits mentioned above, at the price of possible degrading of recovered images’ quality.     

Efficient batch similarity join processing of social images based on arbitrary features

In this paper, we identify and solve a multi-join optimization problem for Arbitrary Feature-based social image Similarity JOINs(AFS-JOIN). Given two collections(i.e., R and S) of social images that carry both visual, spatial and textual(i.e., tag) information, the multiple joins based on arbitrary features retrieves the pairs of images that are visually, textually similar or spatially close from different users. To address this problem, in this paper, we have proposed three methods to facilitate the multi-join processing: 1) two baseline approaches(i.e., a naïve join approach and a maximal threshold(MT)-based), and 2) a Batch Similarity Join(BSJ) method. For the BSJ method, given m users’ join requests, they are first conversed and grouped into m″ clusters which correspond to m″ join boxes, where m > m″. To speedup the BSJ processing, a feature distance space is first partitioned into some cubes based on four segmentation schemes; the image pairs falling in the cubes are indexed by the cube tree index; thus BSJ processing is transformed into the searching of the image pairs falling in some affected cubes for m″ AFS-JOINs with the aid of the index. An extensive experimental evaluation using real and synthetic datasets shows that our proposed BSJ technique outperforms the state-of-the-art solutions.     

Removal of impulse noise in color images based on convolutional neural network

A new denoising framework based on deep convolutional neural network for suppressing impulse noise in color images is proposed in this paper. The proposed framework consists of two modules: noise detection and image reconstruction, both of which are implemented by a deep convolutional neural network. First, a noise classifier network is trained to detect random-valued impulse noise in a color image, which not only can detect the noisy color vector pixels but also can further identify the corrupted channels of each noisy color pixel. Then, a sparse clean color image is computed by replacing the values of noisy channels with 0 and keeping other noise-free channels unchanged. Finally, the sparse clean color image is fed to another denoiser network to reconstruct the denoised image. Experimental results show that the proposed denoiser outperforms other state-of-the-art methods clearly in both performance measure and visual evaluation.     

Machine learning and directional switching median-based filter for highly corrupted images

In this paper, two-stage machine learning-based noise detection scheme has been proposed for identification of salt-and- pepper impulse noise which gives excellent detection results for highly corrupted images. In the first stage, a window of size $3\times 3$ is taken from image and some other features of this window are used as input to neural network. This scheme has distinction of having very low missed detection (MD) and false positives rates. In the second stage, decision tree-based algorithm (J48) is applied on some well-known statistical parameters to generate rules for noise detection. These noise detection methods give promising results for identification of noise from highly corrupted images. A modified version of switching median filter (directional weighted switching median filter) is proposed for noise removal. Performance of noise detector is measured using MD and false alarm FA. Filtering results are compared with state-of-the-art noise removal techniques in terms of peak signal-to-noise ratio and structural similarity index measure. Extensive experiments are performed to show that the proposed technique gives better results than state-of-the-art noise detection and filtering methods.     

On the optimal choice of quality metric in image compression: a soft computing approach

Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image ? is, in general, different from the original image I. There exist many different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I,?) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L ^p metrics d(I,?)=∫|I(x)??(x)| ^p dx are the best, and that the optimal value of p can be selected depending on the expected relative size r of the informative part of the image.     

一种针对彩色图像随机值脉冲噪声的矢量滤波方法

为了去除彩色图像随机值脉冲噪声,提出了一种新的矢量滤波方法。该方法对图像的平滑区域和边缘区域的滤波工作分开进行,平滑区域滤波方法将窗口分成多个区域,然后基于矢量中值和平滑区域像素的特征检测出平滑区域的信号,边缘区域的滤波是在已知信号的基础上对非信号进行矢量中值滤波。仿真实验结果表明,该方法能够有效地去除彩色图像的随机值脉冲噪声,尤其当噪声密度较高时,去噪效果明显优于传统的矢量中值滤波。     

<Emphasis Type="Italic">υ</Emphasis>-Support vector machine based on discriminant sparse neighborhood preserving embedding

In this paper, we mainly focus on two issues (1) SVM is very sensitive to noise. (2) The solution of SVM does not take into consideration of the intrinsic structure and the discriminant information of the data. To address these two problems, we first propose an integration model to integrate both the local manifold structure and the local discriminant information into ?₁ graph embedding. Then we add the integration model into the objection function of υ-support vector machine. Therefore, a discriminant sparse neighborhood preserving embedding υ-support vector machine (υ-DSNPESVM) method is proposed. The theoretical analysis demonstrates that υ-DSNPESVM is a reasonable maximum margin classifier and can obtain a very lower generalization error upper bound by minimizing the integration model and the upper bound of margin error. Moreover, in the nonlinear case, we construct the kernel sparse representation-based ?₁ graph for υ-DSNPESVM, which is more conducive to improve the classification accuracy than ?₁ graph constructed in the original space. Experimental results on real datasets show the effectiveness of the proposed υ-DSNPESVM method.     

Noise Level Estimation in High-Dimensional Linear Models

We consider the problem of estimating the noise level σ² in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ?ⁿ is a standard discrete white Gaussian noise and β ∈ ?^p an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate ||Y ? Xβ||²/n.     

Efficient <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> norm based sparse subspace clustering via smooth IRLS and ADMM

Recently, sparse subspace clustering, as a subspace learning technique, has been successfully applied to several computer vision applications, e.g. face clustering and motion segmentation. The main idea of sparse subspace clustering is to learn an effective sparse representation that are used to construct an affinity matrix for spectral clustering. While most of existing sparse subspace clustering algorithms and its extensions seek the forms of convex relaxation, the use of non-convex and non-smooth l _q (0 < q < 1) norm has demonstrated better recovery performance. In this paper we propose an l _q norm based Sparse Subspace Clustering method (lqSSC), which is motivated by the recent work that l _q norm can enhance the sparsity and make better approximation to l ₀ than l ₁. However, the optimization of l _q norm with multiple constraints is much difficult. To solve this non-convex problem, we make use of the Alternating Direction Method of Multipliers (ADMM) for solving the l _q norm optimization, updating the variables in an alternating minimization way. ADMM splits the unconstrained optimization into multiple terms, such that the l _q norm term can be solved via Smooth Iterative Reweighted Least Square (SIRLS), which converges with guarantee. Different from traditional IRLS algorithms, the proposed algorithm is based on gradient descent with adaptive weight, making it well suit for general sparse subspace clustering problem. Experiments on computer vision tasks (synthetic data, face clustering and motion segmentation) demonstrate that the proposed approach achieves considerable improvement of clustering accuracy than the convex based subspace clustering methods.     

On the Advice Complexity of the k-server Problem Under Sparse Metrics

We consider the k-Server problem under the advice model of computation when the underlying metric space is sparse. On one side, we introduce Θ(1)-competitive algorithms for a wide range of sparse graphs. These algorithms require advice of (almost) linear size. We show that for graphs of size N and treewidth α, there is an online algorithm that receives O (n(log α + log log N))^* bits of advice and optimally serves any sequence of length n. We also prove that if a graph admits a system of μ collective tree (q, r)-spanners, then there is a (q + r)-competitive algorithm which requires O (n(log μ + log log N)) bits of advice. Among other results, this gives a 3-competitive algorithm for planar graphs, when provided with O (n log log N) bits of advice. On the other side, we prove that advice of size Ω(n) is required to obtain a 1-competitive algorithm for sequences of length n even for the 2-server problem on a path metric of size N ≥ 3. Through another lower bound argument, we show that at least \(\frac {n}{2}(\log \alpha - 1.22)\) bits of advice is required to obtain an optimal solution for metric spaces of treewidth α, where 4 ≤ α < 2k.     

HSR: <Emphasis Type="Italic">L</Emphasis><Subscript>1/2</Subscript>-regularized sparse representation for fast face recognition using hierarchical feature selection

In this paper, we propose a novel method for fast face recognition called L _1/2-regularized sparse representation using hierarchical feature selection. By employing hierarchical feature selection, we can compress the scale and dimension of global dictionary, which directly contributes to the decrease of computational cost in sparse representation that our approach is strongly rooted in. It consists of Gabor wavelets and extreme learning machine auto-encoder (ELM-AE) hierarchically. For Gabor wavelets’ part, local features can be extracted at multiple scales and orientations to form Gabor-feature-based image, which in turn improves the recognition rate. Besides, in the presence of occluded face image, the scale of Gabor-feature-based global dictionary can be compressed accordingly because redundancies exist in Gabor-feature-based occlusion dictionary. For ELM-AE part, the dimension of Gabor-feature-based global dictionary can be compressed because high-dimensional face images can be rapidly represented by low-dimensional feature. By introducing L _1/2 regularization, our approach can produce sparser and more robust representation compared to L ₁-regularized sparse representation-based classification (SRC), which also contributes to the decrease of the computational cost in sparse representation. In comparison with related work such as SRC and Gabor-feature-based SRC, experimental results on a variety of face databases demonstrate the great advantage of our method for computational cost. Moreover, we also achieve approximate or even better recognition rate.     

Nonparametric estimation of signal amplitude in white Gaussian noise

We assume that a transmitted signal is of the form S(t)f(t), where f(t) is a known function vanishing at some points of the observation interval and S(t) is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity ?. For this model, we construct an estimator for S(t) which is optimal with respect to the rate of convergence of the risk to zero as ? → 0.     

Meaningful (2, infinity) secret image sharing scheme based on flipping operations

In this paper, a new method to construct a secret image sharing (SIS) scheme is proposed, where a secret image is shared into several shares by a perfect secure way without any knowledge of cryptography. A basic algorithm implemented by flipping operations with probability for constructing a meaningful (2, 2) SIS scheme is first proposed. Neither codebook tailor-made requirement nor pixel expansion is required in the proposed scheme. Additionally, the meaningful shares by the proposed scheme can be directly generated without any extra data hiding process. During the decrypting procedure, the secret image is visually revealed by performing XOR operations on two meaningful shares. In the following stage, a meaningful (2, infinity) SIS scheme is extended underlying the basic algorithm, where the number of shares can be extended anytime. Further, no matter how large the number of the extended shares is, the visual qualities of both the meaningful share and revealed secret image remain unchanged. Finally, sufficient number of formal proofs are provided to validate the correctness of the proposed schemes, whose superiority is also demonstrated by the experimental results.     

Locally Adaptive Frames in the Roto-Translation Group and Their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations \(U:\mathbb {R}^{d} \rtimes S^{d-1} \rightarrow \mathbb {R}\) defined on the extended space of positions and orientations, which we relate to data on the roto-translation group SE(d), \(d=2,3\). This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in SE(d). These curve fits minimize first- or second-order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on SE(d). We include these gauge frames in differential invariants and crossing-preserving PDE-flows acting on extended data representation U and we show their advantage compared to the standard left-invariant frame on SE(d). Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores.     

Symmetric Masks for In-fill Pixel Interpolation on Discrete <Emphasis Type="Italic">p</Emphasis>:<Emphasis Type="Italic">q</Emphasis> Lattices

A 2D p:q lattice contains image intensity entries at pixels located at regular, staggered intervals that are spaced p rows and q columns apart. Zero values appear at all other intermediate grid locations. We consider here the construction, for any given p:q, of convolution masks to smoothly and uniformly interpolate values across all of the intermediate grid positions. The conventional pixel-filling approach is to allocate intensities proportional to the fractional area that each grid pixel occupies inside the boundaries formed by the p:q lines. However, these area-based masks have asymmetric boundaries, flat interior values and may be odd or even in size. Where edges, lines or points are in-filled, area-based p:q masks imprint intensity patterns that recall p:q because the shape of those masks is asymmetric and depends on p:q. We aim to remove these “memory” artefacts by building symmetric p:q masks. We show here that smoother, symmetric versions of such convolution masks exist. The coefficients of the masks constructed here have simple integer values whose distribution is derived purely from symmetry considerations. We have application for these symmetric interpolation masks as part of a precise image rotation algorithm which disguises the rotation angle, as well as to smooth back-projected values when performing discrete tomographic image reconstruction.     

Compressing three-dimensional sparse arrays using inter- and intra-task parallelization strategies on Intel Xeon and Xeon Phi

Array operations are useful in a lot of scientific codes. In recent years, several applications, such as the geological analysis and the medical images processing, are processed using array operations for three-dimensional (abbreviate to “3D”) sparse arrays. Due to the huge computation time, it is necessary to compress 3D sparse arrays and use parallel computing technologies to speed up sparse array operations. How to compress the sparse arrays efficiently is an important task for practical applications. Hence, in this paper, two strategies, inter- and intra-task parallelization (abbreviate to “ETP” and “RTP”), are presented to compress 3D sparse arrays, respectively. Each strategy was designed and implemented on Intel Xeon and Xeon Phi, respectively. From experimental results, the ETP strategy achieves 17.5\(\times \) and 18.2\(\times \) speedup ratios based on Intel Xeon E5-2670 v2 and Intel Xeon Phi SE10X, respectively; 4.5\(\times \) and 4.5\(\times \) speedup ratios for the RTP strategy based on these two environments, respectively.     

Using dynamic pixel value mapping method to construct visible and reversible image watermarking scheme

A reversible and visible image watermarking scheme extracts a visibly embedded binary watermark image and recovers the original cover image. This paper presents a reversible and visible image watermarking scheme that embeds visible watermarks into a part of the cover image, called the embedded region R, and embeds required binary strings into the whole image through the conventional difference-expansion method. The size of the embedded visible watermark is determined by the coefficient k; a large k value leads to a large embedded region for the visible watermark. The embedded region R is first segmented to non-overlapped k×k blocks, and each block is related to one bit of the watermark image. For those blocks that are related to the logo bits of the watermark image, these k×k blocks are adjusted by the proposed dynamic pixel value mapping method for highly visual detection. The binary bit string S, composed of the binary watermark image and LSB bits of the logo watermark bits’ corresponding k×k blocks, is embedded into the cover image using the conventional difference-expansion method. Experimental results show that the watermark is clearly embedded into the embedded region R and that the distortion of the reversible embedding is limited.     

An orthogonal analysis method for decoupling the nozzle geometrical parameters of microthrusters

This paper proposes an orthogonal analysis method for decoupling the multiple nozzle geometrical parameters of microthrusters, thus an reconfigured design can be implemented to generate a proper thrust. In this method, the effects of various nozzle geometrical parameters, including throat width W _t , half convergence angle θ _in , half divergence angle θ _out , exit-to-throat section ratio W _e /W _t and throat radius of the curvature R _t /W _t , on the performance of microthrusters are sorted by range analysis. Analysis results show that throat width seriously affects thrust because range value of 67.53 mN is extremely larger than the range value of other geometry parameters. For average specific impulse (ASI), the range value of exit-to-throat section ratio W _e /W _t and half divergence angle θ _out are 4.82 s and 3.72 s, respectively. Half convergence angle with the range value of 0.39 s and throat radius with 0.32 s have less influence on ASI compared with exit-to-throat section ratio and half divergence angle. When increasing the half convergence angle from 10° to 40° and throat radius of the curvature from 3 to 9, average specific impulse initially decreases and then increases. A MEMS solid propellant thruster (MSPT) with the reconfigured geometrical parameters of nozzle is fabricated to verify the feasibility of the proposed method. The thrust of the microthruster can reach 25 mN. Power is estimated to be 0.84 W. This work provides design guideline to reasonably configure geometry parameters of microthruster.