The problem of estimating a surface shape from its observed reflectance properties still remains a challenging task in computer vision. The presence of global illumination effects such as inter-reflections or cast shadows makes the task particularly difficult for non-convex real-world surfaces. State-of-the-art methods for calibrated photometric stereo address these issues using convolutional neural networks (CNNs) that primarily aim to capture either the spatial context among adjacent pixels or the photometric one formed by illuminating a sample from adjacent directions.In this paper, we bridge these two objectives and introduce an efficient fully-convolutional architecture that can leverage both spatial and photometric context simultaneously. In contrast to existing approaches that rely on standard 2D CNNs and regress directly to surface normals, we argue that using separable 4D convolutions and regressing to 2D Gaussian heat-maps severely reduces the size of the network and leads to more stable predictions.Our experimental results on a real-world photometric stereo benchmark show that the proposed approach outperforms the existing published methods in accuracy. The source code for our method is available at https://github.com/DawyD/UNet-PS-4D.

Abstract Thanks to recent advancements in image processing and deep learning techniques, visual surface inspection in production lines has become an automated process as long as all the defects are visible in a single or a few images. However, it is often necessary to inspect parts under many different illumination conditions to capture all the defects. Training deep networks to perform this task requires large quantities of annotated data, which are rarely available and cumbersome to obtain. To alleviate this problem, we devised an original augmentation approach that, given a small image collection, generates rotated versions of the images while preserving illumination effects, something that random rotations cannot do. We introduce three real multi-illumination datasets, on which we demonstrate the effectiveness of our illumination preserving rotation approach. Training deep neural architectures with our approach delivers a performance increase of up to 51% in terms of AuPRC score over using standard rotations to perform data augmentation.

Despite the substantial progress made in deep learning in recent years, advanced approaches remain computationally intensive. The trade-off between accuracy and computation time and energy limits their use in real-time applications on low power and other resource-constrained systems. In this paper, we tackle this fundamental challenge by introducing a hybrid optical-digital implementation of a convolutional neural network (CNN) based on engineering of the point spread function (PSF) of an optical imaging system. This is done by coding an imaging aperture such that its PSF replicates a large convolution kernel of the first layer of a pre-trained CNN. As the convolution takes place in the optical domain, it has zero cost in terms of energy consumption and has zero latency independent of the kernel size. Experimental results on two datasets demonstrate that our approach yields more than two orders of magnitude reduction in the computational cost while achieving near-state-of-the-art accuracy, or equivalently, better accuracy at the same computational cost.

We propose a novel approach to reconstructing curvilinear tree structures evolving over time, such as road networks in 2D aerial images or neural structures in 3D microscopy stacks acquired in vivo. To enforce temporal consistency, we simultaneously process all images in a sequence, as opposed to reconstructing structures of interest in each image independently. We formulate the problem as a Quadratic Mixed Integer Program and demonstrate the additional robustness that comes from using all available visual clues at once, instead of working frame by frame. Furthermore, when the linear structures undergo local changes over time, our approach automatically detects them.

We propose a novel approach to automatically tracking elliptical cell populations in time-lapse image sequences. Given an initial segmentation, we account for partial occlusions and overlaps by generating an over-complete set of competing detection hypotheses. To this end, we fit ellipses to portions of the initial regions and build a hierarchy of ellipses, which are then treated as cell candidates. We then select temporally consistent ones by solving to optimality an integer program with only one type of flow variables. This eliminates the need for heuristics to handle missed detections due to partial occlusions and complex morphology. We demonstrate the effectiveness of our approach on a range of challenging sequences consisting of clumped cells and show that it outperforms state-of-the-art techniques.

Finding the centerline and estimating the radius of linear structures is a critical first step in many applications, ranging from road delineation in 2D aerial images to modeling blood vessels, lung bronchi, and dendritic arbors in 3D biomedical image stacks. Existing techniques rely either on filters designed to respond to ideal cylindrical structures or on classification techniques. The former tend to become unreliable when the linear structures are very irregular while the latter often has difficulties distinguishing centerline locations from neighboring ones, thus losing accuracy. We solve this problem by reformulating centerline detection in terms of a regression problem. We first train regressors to return the distances to the closest centerline in scale-space, and we apply them to the input images or volumes. The centerlines and the corresponding scale then correspond to the regressors local maxima, which can be easily identified. We show that our method outperforms state-of-the-art techniques for various 2D and 3D datasets. Moreover, our approach is very generic and also performs well on contour detection. We show an improvement above recent contour detection algorithms on the BSDS500 dataset.

We propose a novel approach to automated delineation of curvilinear structures that form complex and potentially loopy networks. By representing the image data as a graph of potential paths, we first show how to weight these paths using discriminatively-trained classifiers that are both robust and generic enough to be applied to very different imaging modalities. We then present an Integer Programming approach to finding the optimal subset of paths, subject to structural and topological constraints that eliminate implausible solutions. Unlike earlier approaches that assume a tree topology for the networks, ours explicitly models the fact that the networks may contain loops, and can reconstruct both cyclic and acyclic ones. We demonstrate the effectiveness of our approach on a variety of challenging datasets including aerial images of road networks and micrographs of neural arbors, and show that it outperforms state-of-the-art techniques.

In this paper, we show that tracking different kinds of interacting objects can be formulated as a network-flow mixed integer program. This is made possible by tracking all objects simultaneously using intertwined flow variables and expressing the fact that one object can appear or disappear at locations where another is in terms of linear flow constraints. Our proposed method is able to track invisible objects whose only evidence is the presence of other objects that contain them. Furthermore, our tracklet-based implementation yields real-time tracking performance. We demonstrate the power of our approach on scenes involving cars and pedestrians, bags being carried and dropped by people, and balls being passed from one player to the next in team sports. In particular, we show that by estimating jointly and globally the trajectories of different types of objects, the presence of the ones which were not initially detected based solely on image evidence can be inferred from the detections of the others.

We propose an approach to reconstructing tree structures that evolve over time in 2D images and 3D image stacks such as neuronal axons or plant branches. Instead of reconstructing structures in each image independently, we do so for all images simultaneously to take advantage of temporal-consistency constraints. We show that this problem can be formulated as a Quadratic Mixed Integer Program and solved efficiently. The outcome of our approach is a framework that provides substantial improvements in reconstructions over traditional single time-instance formulations. Furthermore, an added benefit of our approach is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data.

We propose a novel approach to automated delineation of linear structures that form complex and potentially loopy networks. This is in contrast to earlier approaches that usually assume a tree topology for the networks. At the heart of our method is an Integer Programming formulation that allows us to find the global optimum of an objective function designed to allow cycles but penalize spurious junctions and early terminations. We demonstrate that it outperforms state-of-the-art techniques on a wide range of datasets.

We propose a new approach to detecting irregular curvilinear structures in noisy image stacks. In contrast to earlier approaches that rely on circular models of the cross-sections, ours allows for the arbitrarily-shaped ones that are prevalent in biological imagery. This is achieved by maximizing the image gradient flux along multiple directions and radii, instead of only two with a unique radius as is usually done. This yields a more complex optimization problem for which we propose a computationally efficient solution. We demonstrate the effectiveness of our approach on a wide range of challenging gray scale and color datasets and show that it outperforms existing techniques, especially on very irregular structures.

Although tracing linear structures in 2D images and 3D image stacks has received much attention over the years, full automation remains elusive. In this paper, we formulate the delineation problem as one of solving a Quadratic Mixed Integer Program (Q-MIP) in a graph of potential paths, which can be done optimally up to a very small tolerance. We further propose a novel approach to weighting these paths, which results in a Q-MIP solution that accurately matches the ground truth. We demonstrate that our approach outperforms a state-of-the-art technique based on the k-Minimum Spanning Tree formulation on a 2D dataset of aerial images and a 3D dataset of confocal microscopy stacks.

Multi-object tracking can be achieved by detecting objects in individual frames and then linking detections across frames. Such an approach can be made very robust to the occasional detection failure: If an object is not detected in a frame but is in previous and following ones, a correct trajectory will nevertheless be produced. By contrast, a false-positive detection in a few frames will be ignored. However, when dealing with a multiple target problem, the linking step results in a difficult optimization problem in the space of all possible families of trajectories. This is usually dealt with by sampling or greedy search based on variants of Dynamic Programming which can easily miss the global optimum. In this paper, we show that reformulating that step as a constrained flow optimization results in a convex problem. We take advantage of its particular structure to solve it using the k-shortest paths algorithm, which is very fast. This new approach is far simpler formally and algorithmically than existing techniques and lets us demonstrate excellent performance in two very different contexts.

We present a novel approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, our method builds a set of candidate trees over many different subsets of points likely to belong to the final one and then chooses the best one according to a global objective function. Since we are not systematically trying to span all nodes, our algorithm is able to eliminate noise while retaining the right tree structure. Manually annotated dendrite micrographs and retinal scans are used to evaluate the performance of our method, which is shown to be able to reject noise while retaining the tree structure.

A new region-based frame interpolation algorithm is proposed based on the segmented motion layers with planar perspective motion models. It is shown that performing the motion model interpolation in the homography parameter space is equivalent to interpolating the parameters of the real camera motion, which requires decomposition of the homography matrix, under several practically reasonable assumptions. Based on this reasoning, backward and forward motion models from the interpolation frame(s) to the original frames of the sequence are estimated for each motion layer. Layer support maps at the point(s) of interpolation in time are generated by using these interpolated motion models and the layer maps of the neighboring original frames. Finally, pixel intensities of the interpolation frame are determined by a series of conditions on the layer occlusion relations and the intensities at the transformed locations of the original frames. Experimental results show that the proposed algorithm achieves visually pleasing results without blur or halo effects on dynamic scenes with complex motion.