Automatic understanding of human health and disease has a huge need for prevention, management, and treatment. This understanding, from low-level image processing to advanced analysis, is evolving. So, Zhang et al. Alfaroalmagro et al. The results show that the digital image processing technology can quickly and accurately identify insect holes, junctions, and decay defects. The unique wood texture pattern can be extracted by digital image processing technology.

Finally, the application prospect of digital image processing technology in wood science is expounded, which can create great commercial value in wood defect automatic detection, category identification, and esthetic research. Based on the application characteristics of digital image processing process, Grant et al.

The image processing technology is introduced into the teaching. Image processing and recognition technology is an important product of the information age; its main function is to use computer to process a large amount of physical information can effectively save manpower. Image processing and recognition technology has been widely used in many fields in China and has made important contributions to the development of society. Robertson et al. Traditional virtual role reconstruction method can reconstruct role, but the efficiency of virtual role reconstruction is poor.

Therefore, Brezis et al. Key nodes are reconstructed using 3D images to capture and mark standard points for virtual role reconstruction. The edge operator of 3D virtual character image is determined, and the reconstructed contour area is divided to highlight the effect of reconstruction background. The rendering process of 3D virtual character image is optimized to reduce the virtual shadow effect of texture mapping on reconstructed image.

In order to increase the texture ratio of the reconstructed image and realize the reconstruction of virtual characters, the contrast of image effect is carried out. The simulation results show that the improved virtual role reconstruction method has a good 3D reconstruction effect. The rapid development of computer science, cloud computing, Internet of things, and mobile Internet have become the symbol of the times. The rapid development of these software technologies has challenged the reliability and hardware performance of self-verification.

The performance requirements for hardware ultimately fall on the reliability of hardware integrated circuits. However, in the course of hardware development, verification of the correctness and reliability of integrated chips has been a bottleneck. The verification method based on simulation is widely used in the field of verification, which has irreparable shortcomings, that is, it can only prove that the system is wrong, but it can not prove the correctness of the system design. In software, the verification of reliability is still in the stage of no specific specification.

Therefore, it is meaningful to verify the reliability of software or hardware. In the past two decades, the semi-tensor product STP of matrices has attracted more and more attention in control theory and engineering. Niazian et al. First, we review some preliminary results about the STP method. Secondly, some applications of STP in engineering are reviewed, including gene regulation, power system, wireless communication, smart grid, information security, internal combustion engine, and vehicle control.

Finally, some potential applications of the STP method are predicted. The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k -tensor and let t be an l tensor. Tensor rank is sub-multiplicative under the tensor product.

We revisit the connection between restrictions and degenerations. A result of their study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specifically, if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t is not multiplicative under taking a sufficiently hight tensor product power.

Nonmultiplicativity of the tensor Kronecker product has been known since the work of Strassen. It remains an open question whether border rank and asymptotic rank are multiplicative under the tensor product. Interestingly, lower bounds on border rank obtained from generalized flattenings including Young flattenings multiply under the tensor.

Taha et al.

### Core Algorithms

Firstly, the label evolution equation of colored Petri nets is established by using the semiconductor product of matrix. Then, we define the concept of controllability and the control label adjacency matrix of colored Petri nets. A sufficient and necessary condition for the reachability and controllability of colored Petri nets is given based on the label evolution equation and the control label adjacency matrix.

An algorithm to verify the reachability of colored Petri nets is presented, and the computational complexity of the algorithm is analyzed. Finally, an example is given to illustrate the validity of the proposed theory. The significance of this study is to apply the model Petri net method based on matrix half product to colored Petri nets. This is a convenient way to verify whether one tag can be reached from another and to find all trigger sequences between any two reachable tags.

In addition, this method lays a foundation for the analysis of other properties of colored Petri nets. Firstly, the properties of the state transfer matrix of granular cascade FSR are studied. Then, we put forward their sufficient and necessary non-odd heterosexual conditions.

Next, the valley-like cascaded FSR is regarded as a Boolean control network BCN and further provides sufficient conditions for its nonsingularity. Finally, two examples are provided to illustrate the results obtained by the method. Precise angle measurement and transmission techniques have been widely used in precision measurement, aerospace, military, biomedicine, and other equipment based on polarized light and magneto-optic modulation.

The method has the advantages of no rigid connection, long distance transmission, and high precision. However, the azimuth information measurement method needs to assist the complex servo tracking system according to the orthogonal extinction principle of the polarization prism, and the measurement time is longer, which reduces the reliability and the sensitivity of the system. In order to improve the measurement accuracy and rapid response of the system, a fast spatial angular measurement method is proposed by using the Wollaston prism polarization beam splitter, and the azimuth angle is calculated directly according to the two kinds of light intensity.

By using magneto-optic modulation technology, the measuring time can be shortened and the accuracy can be improved. The fast spatial angle measurement system needs to realize the measurement function in a certain translation range, which requires the beam to have a certain coverage area in the receiving unit. However, the system is limited by the size and volume of the equipment; we can only choose to expand the incident beam.

Therefore, when the beam is incident to the receiving unit, some incident angles and azimuths, that is, non-perpendicular incidence, will be generated. However, the polarization of the non-perpendicular incident light will change and there will be polarization aberration, which will lead to measurement error. Ramalakshmi and Kompala [ 9 ] proposed that the beam passes through the polarization prism in a certain range of azimuth and incidence angle and uses the polarized light tracking method and the boundary conditions of the electromagnetic field to study and simulate the polarization variation and distribution of the beam.

The change of azimuth and angle can be simulated by the translation of the receiving unit, and the azimuth can be indirectly measured by using the self-collimating theodolite and the right-angle prism. The influence of polarization aberration on angle measurement system and the correctness of theoretical analysis are verified by comparing the measured azimuth angles under the conditions of translation and centering.

According to the comparison between the experimental data and the simulation results, the existing problems are pointed out, and the corresponding improvement measures are put forward. The results of this work have a certain significance for guiding the optimization of the system structure and the further improvement of the system performance. The specific expression needs to be designed according to the specific application of image processing.

For the application of the denoising method of partial differential equation image discussed in this paper, the designed F function needs to remove noise and preserve the image edge, texture, detail, and other functions. To achieve the desired processing effect, different denoising models according to the F design can be divided into linear diffusion, nonlinear diffusion, anisotropic diffusion, and the like [ 10 ].

In this paper, a de-noising method combining self-serpent model and P-M model is introduced. P-M model uses the function inversely proportional to the gradient as the diffusion coefficient and controls the size of the diffusion coefficient according to the gradient modulus value of different regions of the image. However, the image edge is blurred by diffusing the detail information. The self-snake model has the property of directional diffusion with edge stopping function and impulse filter which can better keep edge sharpness.

It lays a good foundation for further image processing. For the denoising model, it is ideal to keep the original edge information of the denoised image and eliminate the noise. Therefore, it is necessary to know clearly the controlling factors of diffusion in each direction during the diffusion process [ 11 ]. The diffusion term of the above mixed model is analyzed below. According to Formula 10 , the diffusion behavior of the whole diffusion process in different regions of the image is analyzed. The noise is such that the diffusion coefficient W satisfies a constant greater than zero, while the direction of the vertical edge desirably has a diffusion coefficient as small as possible.

When it is negative, it contributes to the sharpening of the edge, and the diffusion coefficient G satisfies this requirement. Tensor cut apart is to segment tensor product along a certain order of tensor product. The following figure is a third-order tensor cut apart diagram, as shown in Fig. The third-order tensor is divided into four blocks. When dividing the tensor, it is equally divided as much as possible, so that the size of each small tensor block is similar.

Let T be an N -order tensor, 1 Assuming that it is divided into n blocks along a certain order, the number of divided blocks can be expressed by the following formula, see Eqs. After dividing the tensor with the map function, each tensor block of the segmentation is divided into workers. How to combine the last calculated result with the newly arrived data to reduce the calculation amount is a problem that needs to be solved currently [ 13 ].

When the data increases along a certain order of the tensor, take the third-order tensor as an example, as shown in Fig. In the tensor segmentation, it is analyzed how to divide the modular expansion matrix into the modular expansion matrix that constitutes the original tensor. Here, the new tensor expansion matrix is also added to the original tensor expansion matrix by approximation.

In the incremental HOSVD process, the original tensor and the new tensor are first expanded, the order of the two is extended to be consistent, and then the extended original tensor is HOSVD to obtain the left matrix and the core tensor Fig. The expanded new tensor is expanded according to the model, and the expanded matrix is subjected to iterative high-order singular value decomposition using the recursive matrix HOSVD algorithm.

The updated tensor of the matrix and the original matrix using the iterative matrix HOSVD algorithm is used. Fusion is performed to obtain an approximate tensor that can replace the original tensor. Hartmann apertures are small aperture apertures arranged in meters. After passing through the Hartmann aperture, the parallel light emitted by the expanded collimation system is divided into a number of fine beams with different incident heights, which are directed towards the measured lens 6, and the resulting image is a speckle with a meter zigzag distribution.

Each fine beam of light can be equivalent to a ray passing through the centroid of the spot. The volume is a very nice extension to the material and a worthwhile read. The presentation is very algorithmic and expects hands-on experimentation with presented notions and algorithms, every chapter ends with exercises …. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

Computer Science Image Processing. Presents a critical selection of algorithms, illustrated explanations and concise mathematical derivations, for readers to gain a deeper understanding of the topic Encourages the reader to actively construct and experiment with the algorithms to develop their knowledge about how to use these methods in the real world see more benefits.

Buy eBook. Buy Softcover. FAQ Policy. About this Textbook This easy-to-follow textbook is the second of three volumes which provide a modern, algorithmic introduction to digital image processing, designed to be used both by learners desiring a firm foundation on which to build, and practitioners in search of critical analysis and concrete implementations of the most important techniques. Woods and Steven L. David L.

Hall and Sonya A. Jorge E. Kaczynski and K. Mischaikow and M. Mozek, "Computational Homology", Springer.

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## Digital Image Processing: An Algorithmic Introduction Using Java

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## Academic Press Library in Signal Processing, Volume 1 - 1st Edition

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