Omnidirectional Light Field Analysis and Reconstruction

Digital photography exists since 1975, when Steven Sasson attempted to build the first digital camera. Since then the concept of digital camera did not evolve much: an optical lens concentrates light rays onto a focal plane where a planar photosensitive array transforms the light intensity into an electric signal. During the last decade a new way of conceiving digital photography emerged: a photography is the acquisition of the entire light ray field in a confined region of space. The main implication of this new concept is that a digital camera does not acquire a 2-D signal anymore, but a 5-D signal in general. Acquiring an image becomes more demanding in terms of memory and processing power; at the same time, it offers the users a new set of possibilities, like choosing dynamically the focal plane and the depth of field of the final digital photo. In this thesis we develop a complete mathematical framework to acquire and then reconstruct the omnidirectional light field around an observer. We also propose the design of a digital light field camera system, which is composed by several pinhole cameras distributed around a sphere. The choice is not casual, as we take inspiration from something already seen in nature: the compound eyes of common terrestrial and flying insects like the house fly. In the first part of the thesis we analyze the optimal sampling conditions that permit an efficient discrete representation of the continuous light field. In other words, we will give an answer to the question: how many cameras and what resolution are needed to have a good representation of the 4-D light field? Since we are dealing with an omnidirectional light field we use a spherical parametrization. The results of our analysis is that we need an irregular (i.e., not rectangular) sampling scheme to represent efficiently the light field. Then, to store the samples we use a graph structure, where each node represents a light ray and the edges encode the topology of the light field. When compared to other existing approaches our scheme has the favorable property of having a number of samples that scales smoothly for a given output resolution. The next step after the acquisition of the light field is to reconstruct a digital picture, which can be seen as a 2-D slice of the 4-D acquired light field. We interpret the reconstruction as a regularized inverse problem defined on the light field graph and obtain a solution based on a diffusion process. The proposed scheme has three main advantages when compared to the classic linear interpolation: it is robust to noise, it is computationally efficient and can be implemented in a distributed fashion. In the second part of the thesis we investigate the problem of extracting geometric information about the scene in the form of a depth map. We show that the depth information is encoded inside the light field derivatives and set up a TV-regularized inverse problem, which efficiently calculates a dense depth map of the scene while respecting the discontinuities at the boundaries of objects. The extracted depth map is used to remove visual and geometrical artifacts from the reconstruction when the light field is under-sampled. In other words, it can be used to help the reconstruction process in challenging situations. Furthermore, when the light field camera is moving temporally, we show how the depth map can be used to estimate the motion parameters between two consecutive acquisitions with a simple and effective algorithm, which does not require the computation nor the matching of features and performs only simple arithmetic operations directly in the pixel space. In the last part of the thesis, we introduce a novel omnidirectional light field camera that we call Panoptic. We obtain it by layering miniature CMOS imagers onto an hemispherical surface, which are then connected to a network of FPGAs. We show that the proposed mathematical framework is well suited to be embedded in hardware by demonstrating a real time reconstruction of an omnidirectional video stream at 25 frames per second.

Distributed Compressed Representation of Correlated Image Sets

Vijayaraghavan Thirumalai

Vision 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.

EPFL2012

DAISY: A Fast Descriptor for Dense Wide Baseline Stereo and Multiview Reconstruction

Engin Tola

Stereo reconstruction is a fundamental problem of computer vision. It has been studied for more than three decades and significant progress has been made in recent years as evidenced by the quality of the models now being produced. This is highly related with the advances in other fields. With the emergence of low cost high-quality cameras, we now live in an era where there is an abundant amount of data for use in reconstruction. The multitude of images with numerous sources of capture arose new interest in the stereo vision community due to new challenges such as being robust to photometric and geometric variability, scalability issues related to number of images and image resolutions. In this thesis, we aim to find efficient, and therefore practical, algorithmic solutions for the two extreme ends of stereo vision problem: first, we consider only two input image case where the cameras are placed far from each other and then we investigate the large scale multi-view reconstruction for ultra-high resolution image sets. Both problems have unique challenges where in the first part we need to handle the large perspective distortions that the image texture undergoes and in the second part we need to design an algorithm that can scale up to ultra-high resolution very large number of image sets using only a single standard computer. For the first problem, we design an efficient dense image descriptor, called DAISY, that is not only robust to photometric transforms like brightness and contrast changes but also robust to perspective effects that view-point changes produce. We use the DAISY descriptor as a photo-consistency measure in an expectation maximization framework with a global graph-cuts optimization algorithm to estimate depth and occlusion maps. We demonstrate very successful results on a variety of data sets some of which have laser scanned ground truths. After the estimation of depth and occlusion maps, we introduce a technique to improve the surface reconstruction in occluded areas by extracting normal cues using simple binary classifiers trained over DAISY-like features. For the large scale ultra-high resolution multi-view stereo problem, we design a very efficient local optimization algorithm instead of the global one developed in the first part of the thesis for the depth estimation framework. The scalability over the number of images is handled by representing the scene with a set of depth maps and the scalability over the image resolution is handled by the use of a local approach for depth map estimation. We demonstrate state-of-the-art quality results for very large sets of very high resolution images computed on a single standard computer at comparatively very short computation times. Overall, we show that the use of a distinctive and robust descriptor to measure photo-consistency allows us to avoid many complex stages other algorithms utilize without sacrificing from the accuracy of the results and thus scale up to large data sets easily.

EPFL2010

Analysis of Multiview Omnidirectional Images in a Spherical Framework

Zafer Arican

With the increasing demand of information for more immersive applications such as Google Street view or 3D movies, the efficient analysis of visual data from cameras has gained more importance. This visual information permits to extract some crucial information in scenes such as similarity for recognition, 3D scene information, textures and patterns of objects. Multi-camera systems provide detailed visual information about a scene with images from different positions and viewing angles. The conventional perspective cameras that are commonly used in these systems however, have limited field of view. Therefore, they require either the deployment of many of these cameras or the capture of many images from different points to extract sufficient details about a scene. It increases the amount of data to be processed and the maintenance costs for such systems. Omnidirectional vision systems overcome this problem due to their 360-degree field of view and have found wide application areas in robotics, surveillance. These systems often use special refractive elements such as fisheye lenses or mirror-lense systems. The resulting images however inherit from the specific geometry of these units. Therefore, the analysis of these images with methods designed for perspective cameras results in degraded performance in omnivision systems. In this thesis, we focus on the analysis of multi-view omnidirectional images for efficient scene information extraction. We propose a novel spherical framework for omnidirectional image processing by exploiting the property that most omnidirectional images can be uniquely mapped on the sphere. We propose solutions for three common multiview image processing problems, namely feature detection, dense depth estimation and super-resolution for omnidirectional images. We first address the feature extraction problem in omnidirectional images. We develop a scale-invariant feature detection method which carefully handles the geometry of the images by performing the scale-space analysis directly on their native manifolds such as the parabola or the sphere. We then propose a new descriptor and a matching criteria that take into account the geometry and also eliminate the need for orientation computation. We also demonstrate that the proposed method can be used to match features in images captured by different types of sensors such as perspective, omnidirectional or spherical cameras. We then propose a dense depth estimation method to extract the 3D scene information from multiple omnidirectional images. We propose a graph-cut method adapted to the geometry of those images to minimize an energy function formulated for the dense depth estimation problem. We also propose a parallel graph-cut method that gives a significant speed improvement without a big penalty in accuracy. We show that the proposed method can be applied to multi-camera depth estimation and depth-based arbitrary view synthesis. Finally, we consider the multi-view omnidirectional images with the transformation of pure rotation. We address the view synthesis problem for these images in the framework of super-resolution. Considering also the inaccuracies in the rotation parameters, we solve an optimization problem that jointly estimates the rotation errors and reconstructs a high resolution omnidirectional image. We then extend the minimization problem with a regularization term for improved reconstruction quality with a reduced number of images. Results with both synthetic and real omnidirectional images suggest that the proposed method is a viable solution for super-resolution with omnidirectional images. Overall, this dissertation addresses three important issues of multiview omnidirectional image analysis and processing in a novel spherical framework. Our feature detection method can be used for the calibration of omnidirectional images as well as the feature matching in mobile and hybrid camera networks. Furthermore, our dense depth estimation method can impact the quality of 3D scene reconstruction and provide efficient solutions for view synthesis and multiview omnidirectional image coding. Finally, our super-resolution algorithm for omnidirectional images can promote the development of efficient acquisition systems for high resolution omnidirectional images

EPFL2010

Distributed Compressed Representation of Correlated Image Sets

Vijayaraghavan Thirumalai

EPFL2012

DAISY: A Fast Descriptor for Dense Wide Baseline Stereo and Multiview Reconstruction

Engin Tola

EPFL2010

Analysis of Multiview Omnidirectional Images in a Spherical Framework

Zafer Arican

EPFL2010