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Publication# Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

Pascal Frossard, Vijayaraghavan Thirumalai

*Institute of Electrical and Electronics Engineers, *2012

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Résumé

The distributed representation of correlated images is an important challenge in applications such as multi-view imaging in camera networks or low complexity video coding. This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements, which are used for estimation of the correlation between images at decoder. We propose a geometry-based correlation model in order to describe the correlation between pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. These prominent visual features are estimated with a sparse approximation of a reference image by a dictionary of geometric basis functions. The corresponding features in the other images are then identified from the compressed measurements. The correlation model is given by the relative geometric transformations between corresponding features. We thus formulate a regularized optimization problem for the estimation of correspondences where the local transformations between images form a consistent motion or disparity map. Then, we propose an efficient joint reconstruction algorithm that decodes the compressed images such that they stay consistent with the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in video sequences or multi-view data. In addition, the proposed reconstruction strategy provides effective decoding performance that compares advantageously to distributed coding schemes based on disparity or motion learning and to independent coding solution based on JPEG-2000.

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Pascal Frossard, Vijayaraghavan Thirumalai

The distributed representation of correlated images is an important challenge in applications such as multi-view imaging in camera networks or low complexity video coding. This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or the positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements, which are used for estimation of the correlation between images at decoder. We propose a geometry-based correlation model in order to describe the correlation between pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. These prominent visual features are estimated with a sparse approximation of a reference image by a dictionary of geometric basis functions. The corresponding features in the other images are then identified from the compressed measurements. The correlation model is given by the relative geometric transformations between corresponding features. We thus formulate a regularized optimization problem for the estimation of correspondences where the local transformations between images form a consistent motion or disparity map. Then, we propose an efficient joint reconstruction algorithm that decodes the compressed images such that they stay consistent with the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in video sequences or multi-view data. In addition, the proposed reconstruction strategy provides effective decoding performance that compares advantageously to distributed coding schemes based on disparity or motion learning and to independent coding solution based on JPEG-2000.

2010Vision sensor networks and video cameras find widespread usage in several applications that rely on effective representation of scenes or analysis of 3D information. These systems usually acquire multiple images of the same 3D scene from different viewpoints or at different time instants. Therefore, these images are generally correlated through displacement of scene objects. Efficient compression techniques have to exploit this correlation in order to efficiently communicate the 3D scene information. Instead of joint encoding that requires communication between the cameras, in this thesis we concentrate on distributed representation, where the captured images are encoded independently, but decoded jointly to exploit the correlation between images. One of the most important and challenging tasks relies in estimation of the underlying correlation from the compressed correlated images for effective reconstruction or analysis in the joint decoder. This thesis focuses on developing efficient correlation estimation algorithms and joint representation of multiple correlated images captured by various sensing methodologies, e.g., planar, omnidirectional and compressive sensing (CS) sensors. The geometry of the 2D visual representation and the acquisition complexity vary for each sensor type. Therefore, we need to carefully consider the specific geometric nature of the captured images while developing distributed representation algorithms. In this thesis we propose robust algorithms in different scene analysis and reconstruction scenarios. We first concentrate on the distributed representation of omnidirectional images captured by catadioptric sensors. The omnidirectional images are captured from different viewpoints and encoded independently with a balanced rate distribution among the different cameras. They are mapped on the sphere which captures the plenoptic function in its radial form without Euclidean discrepancies. We propose a transform-based distributed coding algorithm, where the spherical images initially undergo a multi-resolution decomposition. The visual information is then split into two correlated partitions. The encoder transmits one partition after entropy coding, as well as the syndrome bits resulting from the Slepian-Wolf encoding of the other partition. The joint decoder estimates a disparity image to take benefit of the correlation between views and uses the syndrome bits to decode the missing information. Such a strategy proves to be beneficial with respect to the independent processing of images and shows only a small performance loss compared to the joint encoding of different views. The encoding complexity in the previous approach is non-negligible due to the visual information processing based on Slepian-Wolf coding and its associated rate parameter estimation. We therefore discard the Slepian-Wolf encoding and propose a distributed coding solution, where the correlated images are encoded independently using transform-based coding solutions (e.g., SPIHT). The central decoder now builds a correlation model from the compressed images, which is used to jointly decode a pair of images. Experimental results demonstrate that the proposed distributed coding solution improves the rate-distortion performance of the separate coding results for both planar and omnidirectional images. However, this improvement is significant only at medium to high bit rates. We therefore propose a rate allocation scheme that identifies and transmits the necessary visual information from each image to improve the correlation estimation accuracy at low bit rate. Experimental results show that for a given bit budget the proposed encoding scheme permits to compute an accurate correlation estimation comparing to the one obtained with SPIHT, JPEG 2000 or JPEG coding schemes. We show however that the improvement in the correlation estimation comes at the price of penalizing the image reconstruction quality; therefore there exists an interesting trade-off between the accurate correlation estimation and image reconstruction as encoding optimization objectives are different in both cases. Next, we further simplify the encoding complexity by replacing the classical imaging sensors with the simple CS sensors, that directly acquire the compressed images in the form of quantized linear measurements. We now concentrate on the particular problem, where one image is selected as the reference and it is used as a side information for the correlation estimation. We propose a geometry-based model to describe the correlation between the visual information in a pair of images. The joint decoder first captures the most prominent visual features in the reconstructed reference image using geometric functions. Since the images are correlated, these features are likely to be present in the other images too, possibly with geometric transformations. Hence, we propose to estimate the correlation model with a regularized optimization problem that locates these features in the compressed images. The regularization terms enforce smoothness of the transformation field, and consistency between the estimated images and the quantized measurements. Experimental results show that the proposed scheme is able to efficiently estimate the correlation between images for several multi-view and video datasets. The proposed scheme is finally shown to outperform DSC schemes based on unsupervised disparity (or motion) learning, as well as independent coding solutions based on JPEG 2000. We then extend the previous scenario to a symmetric decoding problem, where we are interested to estimate the correlation model directly from the quantized linear measurements without explicitly reconstructing the reference images. We first show that the motion field that represents the main source of correlation between images can be described as a linear operator. We further derive a linear relationship between the correlated measurements in the compressed domain. We then derive a regularized cost function to estimate the correlation model directly in the compressed domain using graph-based optimization algorithms. Experimental results show that the proposed scheme estimates an accurate correlation model among images in both multi-view and video imaging scenarios. We then propose a robust data fidelity term that improves the quality of the correlation estimation when the measurements are quantized. Finally, we show by experiments that the proposed compressed correlation estimation scheme is able to compete the solution of a scheme that estimates a correlation model from the reconstructed images without the complexity of image reconstruction. Finally, we study the benefit of using the correlation information while jointly reconstructing the images from the compressed linear measurements. We consider both the asymmetric and symmetric scenarios described previously. We propose joint reconstruction methodologies based on a constrained optimization problem which is solved using effective proximal splitting methods. The constraints included in our framework enforce the reconstructed images to satisfy both the correlation and the quantized measurements consistency objectives. Experimental results demonstrate that the proposed joint reconstruction scheme improves the quality of the decoded images, when compared to a scheme where the images are handled independently. In this thesis we build efficient distributed scene representation algorithms for the multiple correlated images captured in planar, omnidirectional and CS cameras. The coding rate in our symmetric distributed coding solution stays balanced between the encoders and stays close to the joint encoding solutions. Our novel algorithms lead to effective correlation estimation in different sensing and coding scenarios. In addition, we provide innovative solutions for robust correlation estimation from highly compressed images in simple sensing frameworks. Our CS-based joint reconstruction frameworks effectively exploit the inter-view correlation, that permits to achieve high compression gains compared to state-of-the-art independent and distributed coding solutions.

Pascal Frossard, Vijayaraghavan Thirumalai

This paper proposes a joint reconstruction algorithm for compressed correlated images that are given under the form of linear measurements. We first propose a geometry based model in order to describe the correlation between visual information in pairs of images, which is mostly driven by the translational motion of objects or vision sensors. We consider the particular problem where one image is selected as the reference image and it is used as the side information for decoding the compressed correlated images. These compressed images are built on random measurements that are further quantized and entropy coded. The joint decoder first captures the most prominent visual features in the reference image using geometric basis functions. Since images are correlated, these features are likely to be present in the compressed images too, possibly with some small transformation. Hence, the reconstruction of the compressed image is based on a regularized optimization problem that estimates these features in the compressed images. The regularization term further enforces the consistency between the reconstructed images and the quantized measurements. Experimental results show that the proposed scheme is able to efficiently estimate the correlation between images. It further leads to good reconstruction performance. The proposed scheme is finally shown to outperform DSC schemes based on unsupervised disparity or motion learning as well as independent coding solutions based on JPEG-2000 from a rate-distortion perspective.

2010