Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of one smoothing operator is usually fixed and thus cannot meet the various requirements of different applications. In this paper, a non-convex non-smooth optimization framework is proposed to achieve diverse smoothing natures where even contradictive smoothing behaviors can be achieved. To this end, we first introduce the truncated Huber penalty function which has seldom been used in image smoothing. A robust framework is then proposed. When combined with the strong flexibility of the truncated Huber penalty function, our framework is capable of a range of applications and can outperform the state-of-the-art approaches in several tasks. In addition, an efficient numerical solution is provided and its convergence is theoretically guaranteed even the optimization framework is non-convex and non-smooth. The effectiveness and superior performance of our approach are validated through comprehensive experimental results in a range of applications.
In terms of structure-preserving smoothing, Zhang et al. @cite_28 proposed to smooth structures of different scales with a rolling guidance filter (RGF). Cho et al. @cite_27 modified the original BLF with local patch-based analysis of texture features and obtained a bilateral texture filter (BTF) for image texture removal. Karacan et al. @cite_7 proposed to smooth image textures by making use of region covariances that captured local structure and textural information. Xu et al. @cite_8 adopted the relative total variation (RTV) as a prior to regularize the texture smoothing procedure. Chen et al. @cite_10 proved that the TV- @math model @cite_10 @cite_43 could smooth images in a scale-aware manner, and it is thus ideal for structure-preserving smoothing such as image texture removal @cite_1 @cite_33 .
@cite_33 @cite_7 @cite_8 @cite_28 @cite_1 @cite_43 @cite_27 @cite_10
2057203222 2078718577 2231495490 2165154777 2109075629 1998999283
Recent years have witnessed the emergence of new image smoothing techniques which have provided new insights and raised new questions about the nature of this well-studied problem. Specifically, these models separate a given image into its structure and texture layers by utilizing non-gradient based definitions for edges or special measures that distinguish edges from oscillations. In this study, we propose an alternative yet simple image smoothing approach which depends on covariance matrices of simple image features, aka the region covariances. The use of second order statistics as a patch descriptor allows us to implicitly capture local structure and texture information and makes our approach particularly effective for structure extraction from texture. Our experimental results have shown that the proposed approach leads to better image decompositions as compared to the state-of-the-art methods and preserves prominent edges and shading well. Moreover, we also demonstrate the applicability of our approach on some image editing and manipulation tasks such as image abstraction, texture and detail enhancement, image composition, inverse halftoning and seam carving. It is ubiquitous that meaningful structures are formed by or appear over textured surfaces. Extracting them under the complication of texture patterns, which could be regular, near-regular, or irregular, is very challenging, but of great practical importance. We propose new inherent variation and relative total variation measures, which capture the essential difference of these two types of visual forms, and develop an efficient optimization system to extract main structures. The new variation measures are validated on millions of sample patches. Our approach finds a number of new applications to manipulate, render, and reuse the immense number of "structure with texture" images and drawings that were traditionally difficult to be edited properly. Images contain many levels of important structures and edges. Compared to masses of research to make filters edge preserving, finding scale-aware local operations was seldom addressed in a practical way, albeit similarly vital in image processing and computer vision. We propose a new framework to filter images with the complete control of detail smoothing under a scale measure. It is based on a rolling guidance implemented in an iterative manner that converges quickly. Our method is simple in implementation, easy to understand, fully extensible to accommodate various data operations, and fast to produce results. Our implementation achieves realtime performance and produces artifact-free results in separating different scale structures. This filter also introduces several inspiring properties different from previous edge-preserving ones. Surrogate maximization (or minimization) (SM) algorithms are a family of algorithm that can be regarded as a generalization of expectation-maximization (EM) algorithms. There are three major approaches to the construction of surrogate function, all relying on the convexity of some function. In this paper, we solve the boosting problem by proposing SM algorithms for the corresponding optimization problem. Specifically, for AdaBoost, we derive an SM algorithm that can be shown to be identical to the algorithm proposed by (2002) based on Bregman distance. More importantly, for LogitBoost (or logistic boosting), we use several methods to construct different surrogate functions which result in different SM algorithms. By combining multiple methods, we are able to derive an SM algorithm that is also the same as an algorithm derived by (2002). Our approach based on SM algorithms is much simpler and convergence results follow naturally. This paper presents a novel structure-preserving image decomposition operator called bilateral texture filter. As a simple modification of the original bilateral filter [Tomasi and Manduchi 1998], it performs local patch-based analysis of texture features and incorporates its results into the range filter kernel. The central idea to ensure proper texture structure separation is based on patch shift that captures the texture information from the most representative texture patch clear of prominent structure edges. Our method outperforms the original bilateral filter in removing texture while preserving main image structures, at the cost of some added computation. It inherits well-known advantages of the bilateral filter, such as simplicity, local nature, ease of implementation, scalability, and adaptability to other application scenarios. The total variation--based image denoising model of Rudin, Osher, and Fatemi [Phys. D, 60, (1992), pp. 259--268] has been generalized and modified in many ways in the literature; one of these modifications is to use the L1 -norm as the fidelity term. We study the interesting consequences of this modification, especially from the point of view of geometric properties of its solutions. It turns out to have interesting new implications for data-driven scale selection and multiscale image decomposition.