Nonlinear Image Decomposition Research Articles

Model-Based Deep Network for Single Image Deraining

For current learning-based single image deraining methods, deraining networks are usually designed based on a simplified linear additive rain model, which may not only cause unreal synthetic rainy images for both training and testing datasets, but also adversely affect the applicability and generality of corresponding networks. In this paper, we use the screen blend model of Photoshop as the nonlinear rainy image decomposition model. Based on this model, we design a novel channel attention U-DenseNet for rain detection and a residual dense block for rain removal. The detection sub-network not only adjusts channel-wise feature responses by our novel channel attention block to pay more attention to learn the rain map, but also combines the context information with the precise localization by the U-DenseNet to promote pixel-wise estimation accuracy. After rain detection, we use the nonlinear model to get a coarse rain-free image, and then introduce a deraining refinement subnetwork consisted of the residual dense block to obtain a fine rain-free image. For training our network, we apply the nonlinear rain model to synthesize a benchmark dataset called as RITD. It contains 3200 triplets of rainy images, rain maps, and clean background images. Our extensive quantitative and qualitative experimental results show that our method outperforms several state-of-the-art methods on both synthetic and real images.

4-8 CFAモザイク画像の非線形画像分解とその応用(第4部門 画像・映像処理1)

4-8 CFAモザイク画像の非線形画像分解とその応用(第4部門 画像・映像処理1)

Constant time texture filtering

We present a novel texture-filtering method which can effectively separate the main image structures from textures even with high variations. Our nonlinear image decomposition is based on a variant of the weighted-median filter which incorporates structure and texture information into the guidance image. To guarantee effective texture filtering, the guidance image not only contains prominent structure edges of the input, but also reduces the contrast in texture regions. We develop a constant time algorithm for the generation of guidance image by formulating the calculation of local extrema as a histogram volume aggregation problem. The local nature of the algorithm enables an efficient parallel GPU implementation. In addition, we demonstrate the effectiveness of our texture-filtering method in the context of detail enhancement, JPEG artifact removal, inverse halftoning, image segmentation, edge detection, and image stylization.

Superresolved labeling nanoscopy based on temporally flickering nanoparticles and the K-factor image deshadowing.

Localization microscopy provides valuable insights into cellular structures and is a rapidly developing field. The precision is mainly limited by additive noise and the requirement for single molecule imaging that dictates a low density of activated emitters in the field of view. In this paper we present a technique aimed for noise reduction and improved localization accuracy. The method has two steps; the first is the imaging of gold nanoparticles that labels targets of interest inside biological cells using a lock-in technique that enables the separation of the signal from the wide spread spectral noise. The second step is the application of the K-factor nonlinear image decomposition algorithm on the obtained image, which improves the localization accuracy that can reach 5nm and enables the localization of overlapping particles at minimal distances that are closer by 65% than conventional methods.

Improved localization accuracy in stochastic super-resolution fluorescence microscopy by K-factor image deshadowing

Localization of a single fluorescent particle with sub-diffraction-limit accuracy is a key merit in localization microscopy. Existing methods such as photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) achieve localization accuracies of single emitters that can reach an order of magnitude lower than the conventional resolving capabilities of optical microscopy. However, these techniques require a sparse distribution of simultaneously activated fluorophores in the field of view, resulting in larger time needed for the construction of the full image. In this paper we present the use of a nonlinear image decomposition algorithm termed K-factor, which reduces an image into a nonlinear set of contrast-ordered decompositions whose joint product reassembles the original image. The K-factor technique, when implemented on raw data prior to localization, can improve the localization accuracy of standard existing methods, and also enable the localization of overlapping particles, allowing the use of increased fluorophore activation density, and thereby increased data collection speed. Numerical simulations of fluorescence data with random probe positions, and especially at high densities of activated fluorophores, demonstrate an improvement of up to 85% in the localization precision compared to single fitting techniques. Implementing the proposed concept on experimental data of cellular structures yielded a 37% improvement in resolution for the same super-resolution image acquisition time, and a decrease of 42% in the collection time of super-resolution data with the same resolution.

Noise reduction using multiscale bilateral decomposition for digital color images

In this paper, we propose a noise reduction algorithm for digital color images using a nonlinear image decomposition approach. Most existing noise reduction methods do not adequately consider spatial correlation of color noise in digital color images. Color noise components in color images captured by digital cameras are observed as irregular grains with various sizes and shapes, which are spatially randomly distributed. We use a modified multiscale bilateral decomposition to effectively separate signal and mixed-type noise components, in which a noisy input image is decomposed into a base layer and several detail layers. A base layer contains strong edges, and most of noise components are contained in detail layers. Noise components in detail layers are reduced by an adaptive thresholding function. We obtain a denoised image by combining a base layer and noise-reduced detail layers. Experimental results show the effectiveness of the proposed algorithm, in terms of both the peak signal-to-noise ratio and visual quality.

Intrinsic nonlinear multiscale image decomposition: A 2 D empirical mode decomposition-like tool

Many works have been achieved for analyzing images with a multiscale approach. In this paper, an intrinsic and nonlinear multiscale image decomposition is proposed, based on partial differential equations (PDEs) and the image frequency contents. Our model is inspired from the 2 D empirical mode decomposition (EMD) for which a theoretical study is quite nonexistent, mainly because the algorithm is based on heuristic and ad hoc elements making its mathematical study hard. This work has three main advantages. Firstly, we prove that the 2 D sifting process iterations are consistent with the resolution of a nonlinear PDE, by considering continuous morphological operators to build local upper and lower envelopes of the image extrema. In addition to the fact that now differential calculus can be performed on envelopes, the introduction of such morphological filters eliminates the interpolation dependency that also terribly suffers the method. Also, contrary to former 2 D empirical modes, precise mathematical definition for a class of functions are now introduced thanks to the nonlinear PDE derived from the consistency result, and their characterization on the basis of Meyer spaces. Secondly, an intrinsic multiscale image decomposition is introduced based on the image frequency contents; the proposed approach almost captures the essence and philosophy of the 2 D EMD and is linked to the well known Absolutely Minimizing Lipschitz Extension model. Lastly, the proposed multiscale decomposition allows a reconstruction of images. The filterbank capability of the new multiscale decomposition algorithm is shown both on synthetic and real images, and results show that our proposed approach improves a lot on the 2 D EMD. Moreover, the complexity of the proposed multiscale decomposition is very reduced compared to the 2 D EMD by avoiding the surface interpolation approach, which is the core of all 2 D EMD algorithms and is very time consuming. For that purpose also, our work will then be a great benefit; especially, in higher dimension spaces.

STRUCTURALLY ADAPTIVE MATHEMATICAL MORPHOLOGY BASED ON NONLINEAR SCALE-SPACE DECOMPOSITIONS

Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the present approach is to work on a nonlinear multi-scale image decomposition, and then to adapt intrinsically the size of the operator to the local scale of the structures. The properties of the derived operators are investigated and their practical performances are compared with respect to standard morphological operators using natural image examples.

Image-Processing Approach Based on Nonlinear Image-Decomposition

It is a very important and intriguing problem in digital image-processing to decompose an input image into intuitively convincible image-components such as a structure component and a texture component, which is an inherently nonlinear problem. Recently, several numerical schemes to solve the nonlinear image-decomposition problem have been proposed. The use of the nonlinear image-decomposition as a pre-process of several image-processing tasks will possibly pave the way to solve difficult problems posed by the classic approach of digital image-processing. Since the new image-processing approach via the nonlinear image-decomposition treats each separated component with a processing method suitable to it, the approach will successfully attain target items seemingly contrary to each other, for instance invisibility of ringing artifacts and sharpness of edges and textures, which have not attained simultaneously by the classic image-processing approach. This paper reviews quite recently developed state-of-the-art schemes of the nonlinear image-decomposition, and introduces some examples of the decomposition-and-processing approach.

6-3 ディジタルカメラ信号依存性雑音の非線形画像分解による特徴付けと除去(第6部門 映像処理・CG)

6-3 ディジタルカメラ信号依存性雑音の非線形画像分解による特徴付けと除去(第6部門 映像処理・CG)

Nonlinear image decomposition for multiresolution edge detection using gray-level edge maps

Edge detection remains an important low-level vision problem. Most edge detection methods operate on an image at a single resolution. Edges within an image, however, generally occur at various resolutions, or scales, and represent transitions of different degrees, or gradient levels. Thus, single-resolution edge detection methods that output binary edge maps do not always yield satisfactory results. We develop a multiresolution (MR) edge detection method based on nonlinear image decomposition that produces gray-level edge maps. Unlike linear decomposition methods that tend to blur image features, nonlinear methods can be designed that yield greater control over the scale of structures preserved by the decomposition. The proposed decomposition method utilizes rank-order-based filtering, which preserves visually important cues, such as edges, while eliminating structures smaller than a minimum constraint. The images produced by the decomposition have progressively lower resolution, or more precisely, contain structures of progressively increasing scale. The resulting sequence of images is subject to an edge detection process that incorporates edge strength to yield gray-level edge maps. These edge maps are restricted to form a stacking edge map pyramid. In this formulation, the base edge map contains edges at all scales, while edge pruning, based on edge scale, is performed at subsequent levels. Thus, moving up in the pyramid yields edge maps with fewer small-scale, or detail, edges. The motivation behind this algorithm comes from tactile imaging, an important problem in facilitating access to visual information for blind people. The proposed scheme is suited for such applications because it provides more control over detail (edge scale) level and is compatible with how the mind perceives information, beginning with course information and progressively increasing the detail level. Simulation results are presented on synthetic signals, electron micrographs, and images. A comparison of results with Park's linear decomposition algorithm demonstrate the advantages of the proposed method.

A Study of Pyramidal Techniques for Image Representation and Compression

We review and compare a number of linear and nonlinear pyramidal image decomposition techniques which are based on the approach proposed by Burt and Adelson ( IEEE Trans. Comm. 31, 1983, 532-540). We argue that the design of a proper Burt-Adelson type pyramidal decomposition technique is directly related to the design of an optimal (nonlinear in general) image predictor. However, determining such a predictor is not possible in general. We propose four prediction constraints, which uniquely identify the "optimal" predictor as being a morphological opening. This choice naturally leads to one of the morphological image decomposition algorithms proposed by Heijmans and Toet ( Comput. Vision Graphics Image Process. Image Understanding, 54, 1991, 384-400). By using an experimental analysis, based on a collection of four images with a broad spectrum of structural detail, we are able to study the behavior of six pyramidal image representation and compression techniques, and demonstrate the superiority (in terms of compression performance and computational simplicity) of the Heijmans-Toet algorithm.