Energy Based Multi-Model Fitting and Matching Problems

Feature matching and model fitting are fundamental problems in multi-view geometry. They are chicken-&-egg problems: if models are known it is easier to find matches and vice versa. Standard multi-view geometry techniques sequentially solve feature matching and model fitting as two independent problems after making fairly restrictive assumptions. For example, matching methods rely on strong discriminative power of feature descriptors, which fail for stereo images with repetitive textures or wide baseline. Also, model fitting methods assume given feature matches, which are not known a priori. Moreover, when data supports multiple models the fitting problem becomes challenging even with known matches and current methods commonly use heuristics. One of the main contributions of this thesis is a joint formulation of fitting and matching problems. We are first to introduce an objective function combining both matching and multi-model estimation. We also propose an approximation algorithm for the corresponding NP-hard optimization problem using block-coordinate descent with respect to matching and model fitting variables. For fixed models, our method uses min-cost-max-flow based algorithm to solve a generalization of a linear assignment problem with label cost (sparsity constraint). Fixed matching case reduces to multi-model fitting subproblem, which is interesting in its own right. In contrast to standard heuristic approaches, we introduce global objective functions for multi-model fitting using various forms of regularization (spatial smoothness and sparsity) and propose a graph-cut based optimization algorithm, PEaRL. Experimental results show that our proposed mathematical formulations and optimization algorithms improve the accuracy and robustness of model estimation over the state-of-the-art in computer vision

Fast Multi-frame Stereo Scene Flow with Motion Segmentation

We propose a new multi-frame method for efficiently computing scene flow (dense depth and optical flow) and camera ego-motion for a dynamic scene observed from a moving stereo camera rig. Our technique also segments out moving objects from the rigid scene. In our method, we first estimate the disparity map and the 6-DOF camera motion using stereo matching and visual odometry. We then identify regions inconsistent with the estimated camera motion and compute per-pixel optical flow only at these regions. This flow proposal is fused with the camera motion-based flow proposal using fusion moves to obtain the final optical flow and motion segmentation. This unified framework benefits all four tasks - stereo, optical flow, visual odometry and motion segmentation leading to overall higher accuracy and efficiency. Our method is currently ranked third on the KITTI 2015 scene flow benchmark. Furthermore, our CPU implementation runs in 2-3 seconds per frame which is 1-3 orders of magnitude faster than the top six methods. We also report a thorough evaluation on challenging Sintel sequences with fast camera and object motion, where our method consistently outperforms OSF [Menze and Geiger, 2015], which is currently ranked second on the KITTI benchmark.Comment: 15 pages. To appear at IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017). Our results were submitted to KITTI 2015 Stereo Scene Flow Benchmark in November 201

Image Based View Synthesis

This dissertation deals with the image-based approach to synthesize a virtual scene using sparse images or a video sequence without the use of 3D models. In our scenario, a real dynamic or static scene is captured by a set of un-calibrated images from different viewpoints. After automatically recovering the geometric transformations between these images, a series of photo-realistic virtual views can be rendered and a virtual environment covered by these several static cameras can be synthesized. This image-based approach has applications in object recognition, object transfer, video synthesis and video compression. In this dissertation, I have contributed to several sub-problems related to image based view synthesis. Before image-based view synthesis can be performed, images need to be segmented into individual objects. Assuming that a scene can approximately be described by multiple planar regions, I have developed a robust and novel approach to automatically extract a set of affine or projective transformations induced by these regions, correctly detect the occlusion pixels over multiple consecutive frames, and accurately segment the scene into several motion layers. First, a number of seed regions using correspondences in two frames are determined, and the seed regions are expanded and outliers are rejected employing the graph cuts method integrated with level set representation. Next, these initial regions are merged into several initial layers according to the motion similarity. Third, the occlusion order constraints on multiple frames are explored, which guarantee that the occlusion area increases with the temporal order in a short period and effectively maintains segmentation consistency over multiple consecutive frames. Then the correct layer segmentation is obtained by using a graph cuts algorithm, and the occlusions between the overlapping layers are explicitly determined. Several experimental results are demonstrated to show that our approach is effective and robust. Recovering the geometrical transformations among images of a scene is a prerequisite step for image-based view synthesis. I have developed a wide baseline matching algorithm to identify the correspondences between two un-calibrated images, and to further determine the geometric relationship between images, such as epipolar geometry or projective transformation. In our approach, a set of salient features, edge-corners, are detected to provide robust and consistent matching primitives. Then, based on the Singular Value Decomposition (SVD) of an affine matrix, we effectively quantize the search space into two independent subspaces for rotation angle and scaling factor, and then we use a two-stage affine matching algorithm to obtain robust matches between these two frames. The experimental results on a number of wide baseline images strongly demonstrate that our matching method outperforms the state-of-art algorithms even under the significant camera motion, illumination variation, occlusion, and self-similarity. Given the wide baseline matches among images I have developed a novel method for Dynamic view morphing. Dynamic view morphing deals with the scenes containing moving objects in presence of camera motion. The objects can be rigid or non-rigid, each of them can move in any orientation or direction. The proposed method can generate a series of continuous and physically accurate intermediate views from only two reference images without any knowledge about 3D. The procedure consists of three steps: segmentation, morphing and post-warping. Given a boundary connection constraint, the source and target scenes are segmented into several layers for morphing. Based on the decomposition of affine transformation between corresponding points, we uniquely determine a physically correct path for post-warping by the least distortion method. I have successfully generalized the dynamic scene synthesis problem from the simple scene with only rotation to the dynamic scene containing non-rigid objects. My method can handle dynamic rigid or non-rigid objects, including complicated objects such as humans. Finally, I have also developed a novel algorithm for tri-view morphing. This is an efficient image-based method to navigate a scene based on only three wide-baseline un-calibrated images without the explicit use of a 3D model. After automatically recovering corresponding points between each pair of images using our wide baseline matching method, an accurate trifocal plane is extracted from the trifocal tensor implied in these three images. Next, employing a trinocular-stereo algorithm and barycentric blending technique, we generate an arbitrary novel view to navigate the scene in a 2D space. Furthermore, after self-calibration of the cameras, a 3D model can also be correctly augmented into this virtual environment synthesized by the tri-view morphing algorithm. We have applied our view morphing framework to several interesting applications: 4D video synthesis, automatic target recognition, multi-view morphing

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types