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Image-based oil painting stylisation is a popular non-realistic drawing research area. A multi-scale visual layered stylisation algorithm is proposed, simulating the artist's process from coarse to fine. Results show the brush flow is determined by the Voronoi sequence and tangent direction, combined with brush shape and height field for texture mapping. This algorithm closely mimics real oil painting and enhances hierarchical picture sense, highlighting features and details.

The paper proposes the numerical schemes applied in the macrophage segmentation process on a quadtree grid, generated adaptively with respect to intensity of the data. Because the data are sparse and, in general, distinctly rectangular images, to generate the mesh the library ‘p4est’ (parallel forest) has been selected. The library offers tools to connect multiple trees into a ‘forest’ (‘4est’), enabling parallel processing (‘p4est’). The segmentation methods used canbe solvedwith PDEs commonly used in image processing, the linear heat equation and the modified SUBSURF model, for which we proposed explicit and semi-implicit schemes based on the finite volume space discretisation. The choice of numerical algorithms is adapted to the way the grid elements are iterated in the environment of the library. In this paper we focus on a single quadtree. From the numerical point of view, the extension to the forest is straightforward. Description of the library’s principles with respect to the grid generation, its elements iteration, refining, coarsening and balancing the grid with the help of so-called callback functions and parallelism can be found in more detail, e.g., in [7], [8].

Due to their ability to handle discontinuous images while having a well-understood behavior, regularizations with total variation (TV) and total generalized variation (TGV) are some of the best-known methods in image denoising. However, like other variational models including a fidelity term, they crucially depend on the choice of their tuning parameters. A remedy is to choose these automatically through multilevel approaches, for example by optimizing performance on noisy/clean image pairs. In this work, we consider such methods with space-dependent parameters which are piecewise constant on dyadic grids, with the grid itself being part of the minimization. We prove existence of minimizers for fixed discontinuous parameters under mild assumptions on the data, which lead to existence of finite optimal partitions. We further establish that these assumptions are equivalent to the commonly used box constraints on the parameters. On the numerical side, we consider a simple subdivision scheme for optimal partitions built on top of any other bilevel optimization method for scalar parameters, and demonstrate its improved performance on some representative test images when compared with constant optimized parameters.

With the rapid development of the times, new tools are constantly appearing in visual communication design, such as the use of image packaging in visual communication. In order to speed up the transmission speed of visual images, ensure the integrity of visual images, and solve the transmission effect during visual communication. In this paper, based on the modern information fusion context, the object visualization image virtual packaging for model construction, the introduction of MOEA/D algorithm, the decomposition technique to decompose the MOP problem into a series of subproblems to solve, the use of weight vectors to obtain the neighbors of each subproblem, followed by the calculation of neighbor subproblems, the division of individuals into segments to obtain the child individuals. Finally, the fitness of each offspring individual was calculated and cut to give the final level of each factor. The final calculation of the proportion of images in different media communication from the MOEA/D algorithm leads to the strategy of using image virtual packaging in visual communication design. The experimental results showed that by means of multiple control groups, the experimental group achieved a 30% correct rate for Q3 and Q9 quiz questions, and the experimental group had a significantly greater correct rate than the control group. Therefore, more design concepts and design thinking can be explored through the study and analysis of image virtualization to help the use of image virtual packaging in visual communication design work.

To study convexity properties of digital planar objects, the minimum perimeter polygon (MPP) was defined in the 1970 s in articles by Sklansky, Chazin, Hansen, Kibler, and Kim, where pixels were identified with polygonal tiles in mosaics, and two algorithms (1972, 1976) were proposed to determine the MPP vertices. These algorithms are based on constructing and iteratively restricting visibility cones, the MPP vertices result as special vertices of the tiles. The present paper proposes a novel MPP algorithm for objects given as regular complexes in rectangular mosaics, which are edge-adjacency-connected sets of tiles that have neither end tiles nor holes and whose boundaries not necessarily are simple. The new algorithm takes as input the canonical boundary path, we also propose a boundary tracing algorithm to obtain this path. We review the two classic MPP algorithms for rectangular tiles and a simplified adaptation for square tiles that is recommended in widely used modern textbooks on digital image analysis (2018, 2020) to produce approximations of simple digital 4-contours. We show that all these algorithms fail and that their mathematical basis is flawed, we correct the errors to develop the new MPP algorithm. Our MPP algorithm is illustrated using examples and its correctness is proved. Under our assumptions, the MPP coincides with the relative convex hull of a set A with respect to a polygon B ⊃ A , where A is not necessarily a polygon, not even connected.

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including rotations requires sampling the whole space of rotations, repeating the computation of the correlation each time.This article develops an alternative mathematical theory to handle efficiently, at the same time, rotations and translations. Our proposal has a reduced computational complexity because it does not require to repeatedly sample the space of rotations. To do so, we integrate the information relative to all rotated versions of the template into a unique symmetric tensor template -which is computed only once per template-. Afterward, we demonstrate that the correlation between the image to be processed with the independent tensor components of the tensorial template contains enough information to recover template instance positions and rotations. Our proposed method has the potential to speed up conventional template matching computations by a factor of several magnitude orders for the case of 3D images.

In this paper, we propose a novel curvature-guided saturation-value total variation model for color image restoration. Specifically, we incorporate the curvature prior into the traditional variational model to guide the evolution in the direction that maintains the curvature information. Theoretically, we investigate the properties of the proposed model and give a detailed discussion based on the mathematical foundation about the existence of the solution. Numerically, we formulate an effective and efficient algorithm to solve the proposed minimization problem based on the framework of alternating direction method of multipliers. Numerical examples are presented to demonstrate that the performance of the proposed model is better than that of other testing methods for several testing color images.

The Non-Local Means (NLM) algorithm is a fundamental denoising technique widely utilized in various domains of image processing. However, further research is essential to gain a comprehensive understanding of its capabilities and limitations. This includes determining the types of noise it can effectively remove, choosing an appropriate kernel, and assessing its convergence behavior. In this study, we optimize the NLM algorithm for all variations of independent and identically distributed (i.i.d.) variance-stabilized noise and conduct a thorough examination of its convergence behavior. We introduce the concept of the optimal oracle NLM, which minimizes the upper bound of pointwise L 1 or L 2 risk. We demonstrate that the optimal oracle weights comprise triangular kernels with point-adaptive bandwidth, contrasting with the commonly used Gaussian kernel, which has a fixed bandwidth. The computable optimal weighted NLM is derived from this oracle filter by replacing the similarity function with an estimator based on the similarity patch. We present theorems demonstrating that both the oracle filter and the computable filter achieve optimal convergence rates under minimal regularity conditions. Finally, we conduct numerical experiments to validate the performance, accuracy, and convergence of L 1 and L 2 risk minimization for NLM. These convergence theorems provide a theoretical foundation for further advancing the study of the NLM algorithm and its practical applications.

This paper introduces a novel local intensity fitting energy model for segmenting noisy and intensity inhomogeneous images. A notable feature of the proposed model is its ability to simultaneously segment the image while obtaining a denoised and inhomogeneity-corrected result. The model integrates a local clustering criterion function with a denoising mechanism, in which the total energy functional comprises three key components: a local fitting energy on the denoised image, which generates a local force to attract the segmentation contour towards the expected object boundary; an edge detector-dependent smoothing term to denoise the source image, and a length regularization ensuring precise wrapping of the segmentation contour around the target object. In addition, we employ an efficient iterative convolution-thresholding method to solve the associated energy minimization problem, ensuring energy decay at each iteration. We demonstrate the efficacy and efficiency of our proposed variational image segmentation model through numerical experiments conducted on both synthetic and real images.

We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal volume algorithms to improve the computational efficiency of matrix cross approximation. The proposed algorithms are shown to have theoretical guarantees of convergence. Finally, we present two applications: image compression and the least squares approximation of continuous functions. Our numerical results at the end of the paper demonstrate the effective performance of our approach.