Showing papers on "Image gradient published in 2013"

Semi-dense Visual Odometry for a Monocular Camera

Abstract: We propose a fundamentally novel approach to real-time visual odometry for a monocular camera. It allows to benefit from the simplicity and accuracy of dense tracking - which does not depend on visual features - while running in real-time on a CPU. The key idea is to continuously estimate a semi-dense inverse depth map for the current frame, which in turn is used to track the motion of the camera using dense image alignment. More specifically, we estimate the depth of all pixels which have a non-negligible image gradient. Each estimate is represented as a Gaussian probability distribution over the inverse depth. We propagate this information over time, and update it with new measurements as new images arrive. In terms of tracking accuracy and computational speed, the proposed method compares favorably to both state-of-the-art dense and feature-based visual odometry and SLAM algorithms. As our method runs in real-time on a CPU, it is of large practical value for robotics and augmented reality applications.

Robust Document Image Binarization Technique for Degraded Document Images

Abstract: Segmentation of text from badly degraded document images is a very challenging task due to the high inter/intra-variation between the document background and the foreground text of different document images. In this paper, we propose a novel document image binarization technique that addresses these issues by using adaptive image contrast. The adaptive image contrast is a combination of the local image contrast and the local image gradient that is tolerant to text and background variation caused by different types of document degradations. In the proposed technique, an adaptive contrast map is first constructed for an input degraded document image. The contrast map is then binarized and combined with Canny's edge map to identify the text stroke edge pixels. The document text is further segmented by a local threshold that is estimated based on the intensities of detected text stroke edge pixels within a local window. The proposed method is simple, robust, and involves minimum parameter tuning. It has been tested on three public datasets that are used in the recent document image binarization contest (DIBCO) 2009 & 2011 and handwritten-DIBCO 2010 and achieves accuracies of 93.5%, 87.8%, and 92.03%, respectively, that are significantly higher than or close to that of the best-performing methods reported in the three contests. Experiments on the Bickley diary dataset that consists of several challenging bad quality document images also show the superior performance of our proposed method, compared with other techniques.

Joint Geodesic Upsampling of Depth Images

Abstract: We propose an algorithm utilizing geodesic distances to upsample a low resolution depth image using a registered high resolution color image. Specifically, it computes depth for each pixel in the high resolution image using geodesic paths to the pixels whose depths are known from the low resolution one. Though this is closely related to the all-pair-shortest-path problem which has O(n2 log n) complexity, we develop a novel approximation algorithm whose complexity grows linearly with the image size and achieve realtime performance. We compare our algorithm with the state of the art on the benchmark dataset and show that our approach provides more accurate depth upsampling with fewer artifacts. In addition, we show that the proposed algorithm is well suited for upsampling depth images using binary edge maps, an important sensor fusion application.

Scene Text Localization and Recognition with Oriented Stroke Detection

Abstract: An unconstrained end-to-end text localization and recognition method is presented. The method introduces a novel approach for character detection and recognition which combines the advantages of sliding-window and connected component methods. Characters are detected and recognized as image regions which contain strokes of specific orientations in a specific relative position, where the strokes are efficiently detected by convolving the image gradient field with a set of oriented bar filters. Additionally, a novel character representation efficiently calculated from the values obtained in the stroke detection phase is introduced. The representation is robust to shift at the stroke level, which makes it less sensitive to intra-class variations and the noise induced by normalizing character size and positioning. The effectiveness of the representation is demonstrated by the results achieved in the classification of real-world characters using an euclidian nearest-neighbor classifier trained on synthetic data in a plain form. The method was evaluated on a standard dataset, where it achieves state-of-the-art results in both text localization and recognition.

Exposing Digital Image Forgeries by Illumination Color Classification

Abstract: For decades, photographs have been used to document space-time events and they have often served as evidence in courts. Although photographers are able to create composites of analog pictures, this process is very time consuming and requires expert knowledge. Today, however, powerful digital image editing software makes image modifications straightforward. This undermines our trust in photographs and, in particular, questions pictures as evidence for real-world events. In this paper, we analyze one of the most common forms of photographic manipulation, known as image composition or splicing. We propose a forgery detection method that exploits subtle inconsistencies in the color of the illumination of images. Our approach is machine-learning-based and requires minimal user interaction. The technique is applicable to images containing two or more people and requires no expert interaction for the tampering decision. To achieve this, we incorporate information from physics- and statistical-based illuminant estimators on image regions of similar material. From these illuminant estimates, we extract texture- and edge-based features which are then provided to a machine-learning approach for automatic decision-making. The classification performance using an SVM meta-fusion classifier is promising. It yields detection rates of 86% on a new benchmark dataset consisting of 200 images, and 83% on 50 images that were collected from the Internet.

Color retinal image enhancement using CLAHE

Abstract: Common method in image enhancement that's often use is histogram equalization, due to this method is simple and has low computation load. In this research, we use Contrast Limited Adaptive Histogram Equalization (CLAHE) to enhance the color retinal image. To reduce this noise effect in color retinal image due to the acquisition process, we need to enhance this image. Color retinal image has unique characteristic than other image, that is, this image has important in green (G) channel. Image enhancement has important contribution in ophthalmology. In this paper, we propose new enhancement method using CLAHE in G channel to improve the color retinal image quality. The enhancement process conduct in G channel is appropriate to enhance the color retinal image quality.

Structured Face Hallucination

Abstract: The goal of face hallucination is to generate high-resolution images with fidelity from low-resolution ones. In contrast to existing methods based on patch similarity or holistic constraints in the image space, we propose to exploit local image structures for face hallucination. Each face image is represented in terms of facial components, contours and smooth regions. The image structure is maintained via matching gradients in the reconstructed high-resolution output. For facial components, we align input images to generate accurate exemplars and transfer the high-frequency details for preserving structural consistency. For contours, we learn statistical priors to generate salient structures in the high-resolution images. A patch matching method is utilized on the smooth regions where the image gradients are preserved. Experimental results demonstrate that the proposed algorithm generates hallucinated face images with favorable quality and adaptability.

Sobel Edge Detection Algorithm

Abstract: Edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. Sobel which is a popular edge detection algorithm is considered in this work. There exists a function, edge.m which is in the image toolbox. In the edge function, the Sobel method uses the derivative approximation to find edges. Therefore, it returns edges at those points where the gradient of the considered image is maximum. The Sobel operator performs a 2-D spatial gradient measurement on images. It uses a pair of horizontal and vertical gradient matrices whose dimensions are 3×3 for edge detection operations. It will also demonstrate how to build a Sobel detector function of 5 ×5 dimension in matlab to find edges.

Edge-Directed Single-Image Super-Resolution Via Adaptive Gradient Magnitude Self-Interpolation

Abstract: Super-resolution from a single image plays an important role in many computer vision systems. However, it is still a challenging task, especially in preserving local edge structures. To construct high-resolution images while preserving the sharp edges, an effective edge-directed super-resolution method is presented in this paper. An adaptive self-interpolation algorithm is first proposed to estimate a sharp high-resolution gradient field directly from the input low-resolution image. The obtained high-resolution gradient is then regarded as a gradient constraint or an edge-preserving constraint to reconstruct the high-resolution image. Extensive results have shown both qualitatively and quantitatively that the proposed method can produce convincing super-resolution images containing complex and sharp features, as compared with the other state-of-the-art super-resolution algorithms.

Local Edge-Preserving Multiscale Decomposition for High Dynamic Range Image Tone Mapping

Abstract: A novel filter is proposed for edge-preserving decomposition of an image. It is different from previous filters in its locally adaptive property. The filtered image contains local means everywhere and preserves local salient edges. Comparisons are made between our filtered result and the results of three other methods. A detailed analysis is also made on the behavior of the filter. A multiscale decomposition with this filter is proposed for manipulating a high dynamic range image, which has three detail layers and one base layer. The multiscale decomposition with the filter addresses three assumptions: 1) the base layer preserves local means everywhere; 2) every scale's salient edges are relatively large gradients in a local window; and 3) all of the nonzero gradient information belongs to the detail layer. An effective function is also proposed for compressing the detail layers. The reproduced image gives a good visualization. Experimental results on real images demonstrate that our algorithm is especially effective at preserving or enhancing local details.

Introduction to Digital Image Processing

Abstract: CONTINUOUS IMAGE CHARACTERIZATION Continuous Image Mathematical Characterization Image Representation Two-Dimensional Systems Two-Dimensional Fourier Transform Image Stochastic Characterization Psychophysical Vision Properties Light Perception Eye Physiology Visual Phenomena Monochrome Vision Model Color Vision Model Photometry and Colorimetry Photometry Color Matching Colorimetry Concepts Color Spaces DIGITAL IMAGE CHARACTERIZATION Image Sampling and Reconstruction Image Sampling and Reconstruction Concepts Monochrome Image Sampling Systems Monochrome Image Reconstruction Systems Color Image Sampling Systems Image Quantization Scalar Quantization Processing Quantized Variables Monochrome and Color Image Quantization DISCRETE TWO-DIMENSIONAL LINEAR PROCESSING Discrete Image Mathematical Characterization Vector-Space Image Representation Generalized Two-Dimensional Linear Operator Image Statistical Characterization Image Probability Density Models Linear Operator Statistical Representation Superposition and Convolution Finite-Area Superposition and Convolution Sampled Image Superposition and Convolution Circulant Superposition and Convolution Superposition and Convolution Operator Relationships Unitary and Wavelet Transforms General Unitary Transforms Fourier Transform, Cosine, Sine, and Hartley Transforms Hadamard, Haar, and Daubechies Transforms Karhunen-Loeve Transform Wavelet Transforms Linear Processing Techniques Transform Domain Transform Domain Superposition Fast Fourier Transform Convolution Fourier Transform Filtering IMAGE IMPROVEMENT Image Enhancement Contrast Manipulation Histogram Modification Noise Cleaning Edge Crispening Color Image Enhancement Multispectral Image Enhancement Image Restoration Image Restoration Models Sensor and Display Point Nonlinearity Correction Continuous Image Spatial Filtering Restoration Pseudoinverse Spatial Image Restoration Statistical Estimation Spatial Image Restoration Multi-Plane Image Restoration Geometrical Image Modification Basic Geometrical Methods Spatial Warping Geometrical Image Resampling IMAGE ANALYSIS Morphological Image Processing Binary Image Connectivity Binary Image Hit or Miss Transformations Binary Image Shrinking, Thinning, Skeletonizing, and Thickening Binary Image Generalized Dilation and Erosion Binary Image Close and Open Operations Gray Scale Image Morphological Operations Edge Detection Edge, Line, and Spot Models First-Order Derivative Edge Detection Second-Order Derivative Edge Detection Edge-Fitting Edge Detection Luminance Edge Detector Performance Color Edge Detection Line and Spot Detection Image Feature Extraction Image Features Evaluation Amplitude Features Transform Coefficient Features Texture Characterization Texture Features Scale-Invariant Features Image Segmentation Amplitude Segmentation Clustering Segmentation Region Segmentation Boundary Segmentation Texture Segmentation Segment Labeling Shape Analysis Topological Attributes Distance, Perimeter, and Area Measurements Spatial Moments Shape Orientation Descriptors Fourier Descriptors Thinning and Skeletonizing Image Detection and Registration Template Matching Matched Filtering of Continuous Images Image Registration IMAGE AND VIDEO COMPRESSION Point Processing Image Compression Pulse Code Modulation Coding of Monochrome Images Statistical Coding of Monochrome Images Predictive Coding of Monochrome Images Point Processing Color Image Coding JPEG Lossless Image Coding Spatial Processing Image Compression Run Coding of Monochrome Images Interpolation Coding of Monochrome Images Unitary Transform Coding of Monochrome Images Wavelet Coding of Monochrome Images Spatial Processing Color Image Coding JPEG Baseline Image Coding Standard JPEG2000 Image Coding Standard Video Compression Spatial Video Coding Techniques Spatial/Temporal Video Coding Techniques MPEG - 1 Video Coding Standard MPEG - 2 Video Coding Standard MPEG - 4 Video Coding Standards Appendices Annexes Bibliography Index Exercises appear at the end of each chapter.

Image processing method and device, and program

Abstract: In image processing of multi-viewpoint image data including image data captured with different focal lengths, an image of high quality, distance information with high precision, etc., are obtained by utilizing image data with different angles of view (focal lengths). An image processing device for generating combined image data using multi-viewpoint image data including image data acquired with different focal lengths, includes a resolution converting unit configured to perform resolution conversion for at least part of image data in multi-viewpoint image data in accordance with a focal length to be output and an image combining unit configured to generate combined image data with the focal length to be output using the resolution-converted image data.

Landmark Image Super-Resolution by Retrieving Web Images

Abstract: This paper proposes a new super-resolution (SR) scheme for landmark images by retrieving correlated web images. Using correlated web images significantly improves the exemplar-based SR. Given a low-resolution (LR) image, we extract local descriptors from its up-sampled version and bundle the descriptors according to their spatial relationship to retrieve correlated high-resolution (HR) images from the web. Though similar in content, the retrieved images are usually taken with different illumination, focal lengths, and shot perspectives, resulting in uncertainty for the HR detail approximation. To solve this problem, we first propose aligning these images to the up-sampled LR image through a global registration, which identifies the corresponding regions in these images and reduces the mismatching. Second, we propose a structure-aware matching criterion and adaptive block sizes to improve the mapping accuracy between LR and HR patches. Finally, these matched HR patches are blended together by solving an energy minimization problem to recover the desired HR image. Experimental results demonstrate that our SR scheme achieves significant improvement compared with four state-of-the-art schemes in terms of both subjective and objective qualities.

Cross-Field Joint Image Restoration via Scale Map

Abstract: Color, infrared, and flash images captured in different fields can be employed to effectively eliminate noise and other visual artifacts. We propose a two-image restoration framework considering input images in different fields, for example, one noisy color image and one dark-flashed near infrared image. The major issue in such a framework is to handle structure divergence and find commonly usable edges and smooth transition for visually compelling image reconstruction. We introduce a scale map as a competent representation to explicitly model derivative-level confidence and propose new functions and a numerical solver to effectively infer it following new structural observations. Our method is general and shows a principled way for cross-field restoration.

Texture Enhanced Image Denoising via Gradient Histogram Preservation

Abstract: Image denoising is a classical yet fundamental problem in low level vision, as well as an ideal test bed to evaluate various statistical image modeling methods. One of the most challenging problems in image denoising is how to preserve the fine scale texture structures while removing noise. Various natural image priors, such as gradient based prior, nonlocal self-similarity prior, and sparsity prior, have been extensively exploited for noise removal. The denoising algorithms based on these priors, however, tend to smooth the detailed image textures, degrading the image visual quality. To address this problem, in this paper we propose a texture enhanced image denoising (TEID) method by enforcing the gradient distribution of the denoised image to be close to the estimated gradient distribution of the original image. A novel gradient histogram preservation (GHP) algorithm is developed to enhance the texture structures while removing noise. Our experimental results demonstrate that the proposed GHP based TEID can well preserve the texture features of the denoised images, making them look more natural.

Single Image Super-resolution With Detail Enhancement Based on Local Fractal Analysis of Gradient

Abstract: In this paper, we propose a single image super-resolution and enhancement algorithm using local fractal analysis If we treat the pixels of a natural image as a fractal set, the image gradient can then be regarded as a measure of the fractal set According to the scale invariance (a special case of bi-Lipschitz invariance) feature of fractal dimension, we will be able to estimate the gradient of a high-resolution image from that of a low-resolution one Moreover, the high-resolution image can be further enhanced by preserving the local fractal length of gradient during the up-sampling process We show that a regularization term based on the scale invariance of fractal dimension and length can be effective in recovering details of the high-resolution image Analysis is provided on the relation and difference among the proposed approach and some other state of the art interpolation methods Experimental results show that the proposed method has superior super-resolution and enhancement results as compared to other competitors

Systems and methods for initializing motion tracking of human hands

Abstract: Systems and methods for initializing motion tracking of human hands are disclosed. One embodiment includes a processor; a reference camera; and memory containing: a hand tracking application; and a plurality of edge feature templates that are rotated and scaled versions of a base template. The hand tracking application configures the processor to: determine whether any pixels in a frame of video are part of a human hand, where a part of a human hand is identified by searching the frame of video data for a grouping of pixels that have image gradient orientations that match the edge features of one of the plurality of edge feature templates; track the motion of the part of the human hand visible in a sequence of frames of video; confirm that the tracked motion corresponds to an initialization gesture; and commence tracking the human hand as part of a gesture based interactive session.

An Improved Canny Edge Detection Algorithm

Abstract: Traditional Canny edge detection algorithm uses a global threshold selection method, when large changes are in the background of the image and the target gray, global threshold method may lose some local edge information. For this problem, this paper therefore proposes an adaptive dynamic threshold improved Canny edge detection algorithm. The method uses image gradient variance as the criterion of the image block according to the four forks tree principle, then uses the Otsu method to get the corresponding sub-block threshold value for each sub-block, and obtains threshold value matrix by interpolation, finally, gets image edge with improved edge connected algorithm. Experimental results show that, the algorithm not only has good anti-noise performance, but also better detection accuracy.

Active contour model combining region and edge information

Abstract: A novel active contour model is proposed by combining region and edge information. Its level set formulation consists of the edge-related term, the region-based term and the regularization term. The edge-related term is derived from the image gradient, and facilitates the contours evolving into object boundaries. The region-based term is constructed using both local and global statistical information, and related to the direction and velocity of the contour propagation. The last term ensures stable evolution of the contours. Finally, a Gaussian convolution is used to regularize the level set function. In addition, a new quantitative metric named modified root mean squared error is defined, which can be used to evaluate the final contour more accurately. Experimental results show that the proposed method is efficient and robust, and can segment homogenous images and inhomogenous images with the initial contour being set freely.

Method and apparatus for bi-layer segmentation

Abstract: A method and an apparatus for bi-layer segmentation of an image or a sequence of images are described. A classifier is derived based on depth data of the image and another classifier is derived based on color data of the image. The image is then segmented by maximizing a weighted sum of matching scores derived from the classifiers based on depth data and color data of the image. The classifier based on color data of the image is derived using color sampling subsequent to generating an initial segmentation of the image.

Imaging systems with clear filter pixels

Abstract: An image sensor may have an array of image sensor pixels arranged in color filter unit cells each having one red image pixel that generates red image signals, one blue image pixel that generate blue image signals, and two clear image sensor pixels that generate white image signals. The image sensor may be coupled to processing circuitry that performs filtering operations on the red, blue, and white image signals to increase noise correlations in the image signals that reduce noise amplification when applying a color correction matrix to the image signals. The processing circuitry may extract a green image signal from the white image signal. The processing circuitry may compute a scaling value that includes a linear combination of the red, blue, white and green image signals. The scaling value may be applied to the red, blue, and green image signals to produce corrected image signals having improved image quality.

Image edge detection algorithm based on improved Canny operator

Abstract: The traditional Canny operator does not have the adaptive ability in the selection of the variance of the Gaussian filtering. Filtering requires human intervention, and the selection of the variance of Gaussian filtering affects the edge preserving and denoising effect. An improved edge detection algorithm is proposed in this paper. The Gaussian filtering is replaced with the morphological filtering. Experimental results show that the improved Canny operator can filter the salt & pepper noise effectively, improve the accuracy of edge detection, and achieve an ideal effect of edge detection. The experiment results show that the objective evaluation and visual effect are good.

Defect detection for tire laser shearography image using curvelet transform based edge detector

Abstract: In this work, we approach the analysis and segmentation of tire laser shearography image by combining curvelet transform and Canny edge detection to detect defects in tire surface. We rely on the feature of curvelet that edge features can be represented with larger coefficients in sub-highest frequency band thus we modify curvelet coefficients to enhance image edges before further edge detection operations. Only the most important coefficients that contribute to rebuild edges are selected to reconstruct the image while most small coefficients are cut off. This would result in a reconstructed image more convenient for edge detection and the time complexity is reduced on the other hand. Furthermore, the eight-neighborhood bilinear interpolation non-maximum suppression method is introduced to improve the performance of Canny edge detection. Our detection results are evaluated on test laser shearography images using the proposed scheme and compare favorably to the state-of-the-art methods.

A Spatial Clustering Method With Edge Weighting for Image Segmentation

Abstract: As one of the best image clustering methods, fuzzy local information C-means is often used for image segmentation. The effects of noise are avoided by utilizing the spatial relationship among pixels, but it often generates boundary zones for the mix pixels around the edges. This letter presents an image spatial clustering method, called fuzzy C-means with edge and local information (FELICM), which reduces the edge degradation by introducing the weights of pixels within local neighbor windows. The edges are extracted at first by Canny edge detection. During detection, two adaptive thresholds obtained by multi-Otsu method are used. Then, different weights are set according to whether the window center and the local neighbors are separated by an edge or not. Pixels, together with different weighted local neighbors, are clustered iteratively, until the final clustering result is obtained. The method can be directly applied to the image without any filter preprocessing, and the experimental results over remote sensing images show that FELICM not only effectively solves the problem of isolated and random distribution of pixels inside regions but also obtains high edge accuracies.

Content Based Image Retrieval using Discrete Wavelet Transform and Edge Histogram Descriptor

Abstract: This paper describes an efficient algorithm for Content Based Image Retrieval (CBIR) based on Discrete Wavelet Transform (DWT) and Edge Histogram Descriptor (EHD) feature of MPEG-7. The proposed algorithm is explained for image retrieval based on shape and texture features only not on the basis of color information. Here input image is first decomposed into wavelet coefficients. These wavelet coefficients give mainly horizontal, vertical and diagonal features in the image. After wavelet transform, Edge Histogram Descriptor is then used on selected wavelet coefficients to gather the information of dominant edge orientations. The combination of DWT and EHD techniques increases the performance of image retrieval system for shape and texture based search. The performance of various wavelets is also compared to find the suitability of particular wavelet function for image retrieval. The proposed algorithm is trained and tested for Wang image database. The results of retrieval are expressed in terms of Precision and Recall and compared with various other proposed schemes to show the superiority of our scheme.

Systems and methods for tracking human hands by performing parts based template matching using images from multiple viewpoints

Abstract: Systems and methods for tracking human hands by performing parts based template matching using images captured from multiple viewpoints are described. One embodiment of the invention includes a processor, a reference camera, an alternate view camera, and memory containing: a hand tracking application; and a plurality of edge feature templates that are rotated and scaled versions of a finger template that includes an edge features template. In addition, the hand tracking application configures the processor to: detect at least one candidate finger in a reference frame, where each candidate finger is a grouping of pixels identified by searching the reference frame for a grouping of pixels that have image gradient orientations that match one of the plurality of edge feature templates; and verify the correct detection of a candidate finger in the reference frame by locating a grouping of pixels in an alternate view frame that correspond to the candidate finger.

Region-based multi-focus image fusion using the local spatial frequency

Abstract: In image fusion domain, generic pixel-based image fusion methods are sensitive to imperfections of source images, and it therefore has much influence on the quality of the fusion results. Focusing on this problem, a region-based multi-focus image fusion scheme is proposed based on the local spatial frequency (LSF) in this paper. Firstly, calculate LSF for each pixel of source images, and a segmentation of the average image is introduced to segment the source images. From the segmented image, a shared region representation is obtained to label the source images. The identification of important features in shared region representation, region spatial frequency (RSF), is used to guide the fusion process. The experimental results show that the proposed scheme works well in multi-focus image fusion, and it outperforms comparison methods in terms of visual and objective evaluations.

Single-Image Vignetting Correction from Gradient Distribution Symmetries

Abstract: We present novel techniques for single-image vignetting correction based on symmetries of two forms of image gradients: semicircular tangential gradients (SCTG) and radial gradients (RG). For a given image pixel, an SCTG is an image gradient along the tangential direction of a circle centered at the presumed optical center and passing through the pixel. An RG is an image gradient along the radial direction with respect to the optical center. We observe that the symmetry properties of SCTG and RG distributions are closely related to the vignetting in the image. Based on these symmetry properties, we develop an automatic optical center estimation algorithm by minimizing the asymmetry of SCTG distributions, and also present two methods for vignetting estimation based on minimizing the asymmetry of RG distributions. In comparison to prior approaches to single-image vignetting correction, our methods do not rely on image segmentation and they produce more accurate results. Experiments show our techniques to work well for a wide range of images while achieving a speed-up of 3-5 times compared to a state-of-the-art method.

A unifying retinex model based on non-local differential operators

Abstract: In this paper, we present a unifying framework for retinex that is able to reproduce many of the existing retinex implementations within a single model. The fundamental assumption, as shared with many retinex models, is that the observed image is a multiplication between the illumination and the true underlying reflectance of the object. Starting from Morel’s 2010 PDE model for retinex, where illumination is supposed to vary smoothly and where the reflectance is thus recovered from a hard-thresholded Laplacian of the observed image in a Poisson equation, we define our retinex model in similar but more general two steps. First, look for a filtered gradient that is the solution of an optimization problem consisting of two terms: The first term is a sparsity prior of the reflectance, such as the TV or H1 norm, while the second term is a quadratic fidelity prior of the reflectance gradient with respect to the observed image gradients. In a second step, since this filtered gradient almost certainly is not a consistent image gradient, we then look for a reflectance whose actual gradient comes close. Beyond unifying existing models, we are able to derive entirely novel retinex formulations by using more interesting non-local versions for the sparsity and fidelity prior. Hence we define within a single framework new retinex instances particularly suited for texture-preserving shadow removal, cartoon-texture decomposition, color and hyperspectral image enhancement.