Recent zbMATH articles in MSC 68U10 https://www.zbmath.org/atom/cc/68U10 2021-04-16T16:22:00+00:00 Werkzeug CURE: curvature regularization for missing data recovery. https://www.zbmath.org/1456.62127 2021-04-16T16:22:00+00:00 "Dong, Bin" https://www.zbmath.org/authors/?q=ai:dong.bin|dong.bin.1 "Ju, Haocheng" https://www.zbmath.org/authors/?q=ai:ju.haocheng "Lu, Yiping" https://www.zbmath.org/authors/?q=ai:lu.yiping "Shi, Zuoqiang" https://www.zbmath.org/authors/?q=ai:shi.zuoqiang Replication of a binary image on a one-dimensional cellular automaton with linear rules. https://www.zbmath.org/1456.68108 2021-04-16T16:22:00+00:00 "Rao, U. Srinivasa" https://www.zbmath.org/authors/?q=ai:rao.u-srinivasa "Jeganathan, L." https://www.zbmath.org/authors/?q=ai:jeganathan.l Summary: A two-state, one-dimensional cellular automaton (1D CA) with uniform linear rules on an $$(r+1)$$-neighborhood replicates any arbitrary binary image given as an initial configuration. By these linear rules, any cell gets updated by an EX-OR operation of the states of extreme (first and last) cells of its $$(r+1)$$-neighborhood. These linear rules replicate the binary image in two ways on the 1D CA: one is without changing the position of the original binary image at time step $$t=0$$ and the other is by changing the position of the original binary image at time step $$t=0$$. Based on the two ways of replication, we have classified the linear rules into three types. In this paper, we have proven that the binary image of size $$m$$ gets replicated exactly at time step $$2^k$$ of the uniform linear rules on the $$(r+1)$$-neighborhood 1D CA, where $$k$$ is the least positive integer satisfying the inequality $$m/r\le 2^k$$. We have also proved that there are exactly $$(r*2^k-m)$$ cells between the last cell of the binary image and the first cell of the replicated binary image (or the first cell of the binary image and the last cell of the replicated image). Tomographic reconstruction from a few views: a multi-marginal optimal transport approach. https://www.zbmath.org/1456.49035 2021-04-16T16:22:00+00:00 "Abraham, I." https://www.zbmath.org/authors/?q=ai:abraham.isabelle "Abraham, R." https://www.zbmath.org/authors/?q=ai:abraham.romain "Bergounioux, M." https://www.zbmath.org/authors/?q=ai:bergounioux.maitine "Carlier, G." https://www.zbmath.org/authors/?q=ai:carlier.guillaume Summary: In this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented. Marcus-Wyse topological rough sets and their applications. https://www.zbmath.org/1456.68222 2021-04-16T16:22:00+00:00 "Han, Sang-Eon" https://www.zbmath.org/authors/?q=ai:han.sang-eon Summary: The aim of this paper is to establish two new types of rough set structures associated with the Marcus-Wyse (MW, for brevity) topology, such as an M-rough set and an MW-topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in $$\mathbb{Z}^2$$, where $$\mathbb{Z}$$ is the set of integers. These two rough set structures are related to each other via an M-digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC, for short) space $$(U, \mathbf{C})$$ and a subset $$X$$ of $$U$$, we firstly introduce a new neighborhood system on $$U$$ related to $$X$$. Next, we formulate the lower and upper approximations with respect to $$X$$, where all of the sets $$U$$ and $$X(\subseteq U)$$ need not be finite and the covering $$\mathbf{C}$$ is locally finite. Actually, the notion of M-digitization of a 2-dimensional Euclidean space plays an important role in developing an M-rough and MW-topological rough set structures. Further, we prove that M-rough set operators have a duality between them. However, each of MW-topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW-topology. PSO image thresholding on images compressed via fuzzy transforms. https://www.zbmath.org/1456.68224 2021-04-16T16:22:00+00:00 "Martino, Ferdinando Di" https://www.zbmath.org/authors/?q=ai:di-martino.ferdinando "Sessa, Salvatore" https://www.zbmath.org/authors/?q=ai:sessa.salvatore Summary: We present a new multi-level image thresholding method in which a Chaotic Darwinian Particle Swarm Optimization algorithm is applied on images compressed by using Fuzzy Transforms. The method requires a partition of the pixels of the image under several thresholds which are obtained by maximizing a fuzzy entropy. The usage of compressed images produces benefits in terms of execution CPU times. In a pre-processing phase the best compression rate is found by comparing the grey level histograms of the source and compressed images. Comparisons with the classical Darwinian Particle Swarm Optimization multi-level image thresholding algorithm and other meta-heuristic algorithms are presented in terms of quality of the segmented image via PSNR and SSIM. Exact recovery of multichannel sparse blind deconvolution via gradient descent. https://www.zbmath.org/1456.65043 2021-04-16T16:22:00+00:00 "Qu, Qing" https://www.zbmath.org/authors/?q=ai:qu.qing "Li, Xiao" https://www.zbmath.org/authors/?q=ai:li.xiao "Zhu, Zhihui" https://www.zbmath.org/authors/?q=ai:zhu.zhihui Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory. https://www.zbmath.org/1456.68034 2021-04-16T16:22:00+00:00 "Wang, Xingyuan" https://www.zbmath.org/authors/?q=ai:wang.xingyuan "Gao, Suo" https://www.zbmath.org/authors/?q=ai:gao.suo Summary: This paper studies chaotic image encryption technology and an application of matrix semi-tensor product theory, and a Boolean network encryption algorithm for a synchronous update process is proposed. A 2D-LASM chaotic system is used to generate a random key stream. First, a Boolean network is coded, and a Boolean matrix is generated. If necessary, the Boolean network matrix is diffused in one round so that the Boolean matrix can be saved in the form of an image. Then, three random position scramblings are used to scramble the plaintext image. Finally, using a matrix semi-tensor product technique to generate an encrypted image in a second round of diffusion, a new Boolean network can be generated by encoding the encrypted image. In secure communications, users can choose to implement an image encryption transmission or a Boolean network encryption transmission according to their own needs. Compared with other algorithms, this algorithm exhibits good security characteristics. Reconstruction of convex bodies from moments. https://www.zbmath.org/1456.52005 2021-04-16T16:22:00+00:00 "Kousholt, Astrid" https://www.zbmath.org/authors/?q=ai:kousholt.astrid "Schulte, Julia" https://www.zbmath.org/authors/?q=ai:schulte.julia Summary: We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result for convex bodies based on geometric moments. It turns out that the stability result is improved considerably by using another set of moments, namely Legendre moments. We present a reconstruction algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under certain assumptions on the variance of the noise variables. Robust reversible data hiding scheme based on two-layer embedding strategy. https://www.zbmath.org/1456.68223 2021-04-16T16:22:00+00:00 "Kumar, Rajeev" https://www.zbmath.org/authors/?q=ai:kumar.rajeev "Jung, Ki-Hyun" https://www.zbmath.org/authors/?q=ai:jung.ki-hyun Summary: Robust reversible data hiding (RRDH) prevents the hidden secret information from unintentional modifications. This paper presents a novel RRDH scheme based on two-layer embedding with reduced capacity-distortion trade-off. The proposed scheme first decomposes the image into two planes namely higher significant bit (HSB) and least significant bit (LSB) planes and then employs prediction error expansion (PEE) to embed the secret data into the HSB plane. The high correlation of HSB plane helps in achieving high embedding capacity. Further, non-malicious attacks such as Joint Photographic Experts Group (JPEG) compression which usually changes the LSBs, will not cause any disturbance to the main contents of original image and the hidden secret data. The experimental results show that the proposed scheme has superior performance than the previous works. Quantum vision representations and multi-dimensional quantum transforms. https://www.zbmath.org/1456.81146 2021-04-16T16:22:00+00:00 "Li, Hai-Sheng" https://www.zbmath.org/authors/?q=ai:li.haisheng.1|li.haisheng "Song, Shuxiang" https://www.zbmath.org/authors/?q=ai:song.shuxiang "Fan, Ping" https://www.zbmath.org/authors/?q=ai:fan.ping "Peng, Huiling" https://www.zbmath.org/authors/?q=ai:peng.huiling "Xia, Hai-ying" https://www.zbmath.org/authors/?q=ai:xia.haiying "Liang, Yan" https://www.zbmath.org/authors/?q=ai:liang.yan Summary: Quantum vision representation (QVR) is the foundation of quantum vision information processing, which is a possible solution to store and process massive visual data efficiently. In this paper, firstly, quantum image representations are divided into three categories based on different methods of color information storage. Secondly, in order to systematize quantum image representation, we propose five new methods. Thirdly, we develop models of QVR by extending three categories of quantum image representations into corresponding QVRs. Next, we design and implement 1D, 2D, and 3D quantum transforms based on QVR for the first time. Simulation experiments demonstrate that proposed multi-dimensional quantum transforms are effective. In conclusion, this paper develops a model of QVR and provides a feasible scheme for multi-dimensional quantum transforms to be applied in quantum vision information processing. Quaternion weighted spherical Bessel-Fourier moment and its invariant for color image reconstruction and object recognition. https://www.zbmath.org/1456.68225 2021-04-16T16:22:00+00:00 "Yang, Tengfei" https://www.zbmath.org/authors/?q=ai:yang.tengfei "Ma, Jianfeng" https://www.zbmath.org/authors/?q=ai:ma.jianfeng "Miao, Yinbin" https://www.zbmath.org/authors/?q=ai:miao.yinbin "Wang, Xuan" https://www.zbmath.org/authors/?q=ai:wang.xuan "Xiao, Bin" https://www.zbmath.org/authors/?q=ai:xiao.bin "He, Bing" https://www.zbmath.org/authors/?q=ai:he.bing.1|he.bing|he.bing.2|he.bing.4|he.bing.3 "Meng, Qian" https://www.zbmath.org/authors/?q=ai:meng.qian Summary: Moments with capable of representing global features have been widely used in image analysis, pattern recognition and computer vision applications. However, existing image moment theories are still mainly paid close attention to gray-scale images. In this paper, a new quaternion moment termed as Quaternion weighted Spherical Bessel-Fourier Moment (QSBFM) is proposed to address the issue of color image analysis. Moreover, the relationship between QSBFM and the conventional weighted spherical Bessel-Fourier moment has been established so that the computational cost of QSBFM can be efficiently reduced. Furthermore, the natively geometric invariance of QSBFM is presented and discussed in detail. Experimental results show that the proposed QSBFM outperforms frequently-used quaternion moments including quaternion Bessel-Fourier moment, quaternion Radial-Harmonic-Fourier moment, quaternion Chebyshev-Fourier moment and quaternion orthogonal Fourier-Mellin moment in terms of the color image reconstruction capability and invariant recognition accuracy in noise-free, Salt \& Pepper noise and the Gaussian noise conditions.