Abstract-In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis unctions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power ( 1 55 ), which, while slower than the optimal rate ( 2 ), is much better than ( 1 ) achieved with wavelets, but at similar complexity.

Abstract-The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient space-frequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a rate-distortion sense, both in terms of mean-square error and visual quality, especially in the low-rate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm.

Recent developments in computational photography enabled variation of the optical focus of a plenoptic camera after image exposure, also known as refocusing. Existing ray models in the field simplify the camera's complexity for the purpose of image and depth map enhancement, but fail to satisfyingly predict the distance to which a photograph is refocused. By treating a pair of light rays as a system of linear functions, it will be shown in this paper that its solution yields an intersection indicating the distance to a refocused object plane. Experimental work is conducted with different lenses and focus settings while comparing distance estimates with a stack of refocused photographs for which a blur metric has been devised. Quantitative assessments over a 24 m distance range suggest that predictions deviate by less than 0.35 % in comparison to an optical design software. The proposed refocusing estimator assists in predicting object distances just as in the prototyping stage of plenoptic cameras and will be an essential feature in applications demanding high precision in synthetic focus or where depth map recovery is done by analyzing a stack of refocused photographs.

Abstract-The encoding of both texture and depth maps of multiview images, captured by a set of spatially correlated cameras, is important for any 3-D visual communication system based on depth-image-based rendering (DIBR). In this paper, we address the problem of efficient bit allocation among texture and depth maps of multiview images. More specifically, suppose we are given a coding tool to encode texture and depth maps at the encoder and a view-synthesis tool to construct intermediate views at the decoder using neighboring encoded texture and depth maps. Our goal is to determine how to best select captured views for encoding and distribute available bits among texture and depth maps of selected coded views, such that the visual distortion of desired constructed views is minimized. First, in order to obtain at the encoder a low complexity estimate of the visual quality of a large number of desired synthesized views, we derive a cubic distortion model based on basic DIBR properties, whose parameters are obtained using only a small number of viewpoint samples. Then, we demonstrate that the optimal selection of coded views and quantization levels for corresponding texture and depth maps is equivalent to the shortest path in a specially constructed 3-D trellis. Finally, we show that, using the assumptions of monotonicity in the predictor's quantization level and distance, suboptimal solutions can be efficiently pruned from the feasible space during solution search. Experiments show that our proposed efficient selection of coded views and quantization levels for corresponding texture and depth maps outperforms an alternative scheme using constant quantization levels for all maps (commonly used in video standard implementations) by up to 1.5 dB. Moreover, the complexity of our scheme can be reduced by at least 80% over the full solution search.Index Terms-Bit allocation, depth-image-based rendering, 3-D image coding.