A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms

Single Frame Image super Resolution using Learned Directionlets

In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture directional features and to extract edge information along different directions of a set of available high resolution images .This information is used as the training set for super resolving a low resolution input image and the Directionlet coefficients at finer scales of its high-resolution image are learned locally from this training set and the inverse Directionlet transform recovers the super-resolved high resolution image. The simulation results showed that the proposed approach outperforms standard interpolation techniques like Cubic spline interpolation as well as standard Wavelet-based learning, both visually and in terms of the mean squared error (mse) values. This method gives good result with aliased images also.Comment: 14 pages,6 figure

Signal Decomposition Methods for Reducing Drawbacks of the DWT

Besides many advantages of wavelet transform, it has several drawbacks, e.g. ringing, shift variance, aliasing and lack of directionality. Some of them can be eliminated by using wavelet packet transform, stationary wavelet transform, complex wavelet transform, adaptive directional lifting-based wavelet transform, or adaptive wavelet filter banks that use either L2 or L1 norm. This paper contains an overview of these methods

Blending of Images Using Discrete Wavelet Transform

The project presents multi focus image fusion using discrete wavelet transform with local directional pattern and spatial frequency analysis. Multi focus image fusion in wireless visual sensor networks is a process of blending two or more images to get a new one which has a more accurate description of the scene than the individual source images. In this project, the proposed model utilizes the multi scale decomposition done by discrete wavelet transform for fusing the images in its frequency domain. It decomposes an image into two different components like structural and textural information. It doesn’t down sample the image while transforming into frequency domain. So it preserves the edge texture details while reconstructing image from its frequency domain. It is used to reduce the problems like blocking, ringing artifacts occurs because of DCT and DWT. The low frequency sub-band coefficients are fused by selecting coefficient having maximum spatial frequency. It indicates the overall active level of an image. The high frequency sub-band coefficients are fused by selecting coefficients having maximum LDP code value LDP computes the edge response values in all eight directions at each pixel position and generates a code from the relative strength magnitude. Finally, fused two different frequency sub-bands are inverse transformed to reconstruct fused image. The system performance will be evaluated by using the parameters such as Peak signal to noise ratio, correlation and entrop

Directional Transforms for Video Coding Based on Lifting on Graphs

In this work we describe and optimize a general scheme based on lifting transforms on graphs for video coding. A graph is constructed to represent the video signal. Each pixel becomes a node in the graph and links between nodes represent similarity between them. Therefore, spatial neighbors and temporal motion-related pixels can be linked, while nonsimilar pixels (e.g., pixels across an edge) may not be. Then, a lifting-based transform, in which filterin operations are performed using linked nodes, is applied to this graph, leading to a 3-dimensional (spatio-temporal) directional transform which can be viewed as an extension of wavelet transforms for video. The design of the proposed scheme requires four main steps: (i) graph construction, (ii) graph splitting, (iii) filte design, and (iv) extension of the transform to different levels of decomposition. We focus on the optimization of these steps in order to obtain an effective transform for video coding. Furthermore, based on this scheme, we propose a coefficien reordering method and an entropy coder leading to a complete video encoder that achieves better coding performance than a motion compensated temporal filterin wavelet-based encoder and a simple encoder derived from H.264/AVC that makes use of similar tools as our proposed encoder (reference software JM15.1 configu ed to use 1 reference frame, no subpixel motion estimation, 16 × 16 inter and 4 × 4 intra modes).This work was supported in part by NSF under grant CCF-1018977 and by Spanish Ministry of Economy and Competitiveness under grants TEC2014-53390-P and TEC2014-52289-R.Publicad

State of the art in 2D content representation and compression

Livrable D1.3 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D3.1 du projet

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications