Total Variation Blind Deconvolution: The Devil Is in the Details

In this paper we study the problem of blind deconvolution. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient priors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating energy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. However, experimentally one can observe that Chan and Wong's algorithm converges to the desired solution even when initialized with the no-blur one. We provide both analysis and experiments to resolve this paradoxical conundrum. We find that both claims are right. The key to understanding how this is possible lies in the details of Chan and Wong's implementation and in how seemingly harmless choices result in dramatic effects. Our analysis reveals that the delayed scaling (normalization) in the iterative step of the blur kernel is fundamental to the convergence of the algorithm. This then results in a procedure that eludes the no-blur solution, despite it being a global minimum of the original energy. We introduce an adaptation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

Fully automatic segmentation of AP pelvis X-rays via random forest regression with efficient feature selection and hierarchical sparse shape composition

In clinical practice, traditional X-ray radiography is widely used, and knowledge of landmarks and contours in anteroposterior (AP) pelvis X-rays is invaluable for computer aided diagnosis, hip surgery planning and image-guided interventions. This paper presents a fully automatic approach for landmark detection and shape segmentation of both pelvis and femur in conventional AP X-ray images. Our approach is based on the framework of landmark detection via Random Forest (RF) regression and shape regularization via hierarchical sparse shape composition. We propose a visual feature FL-HoG (Flexible- Level Histogram of Oriented Gradients) and a feature selection algorithm based on trace radio optimization to improve the robustness and the efficacy of RF-based landmark detection. The landmark detection result is then used in a hierarchical sparse shape composition framework for shape regularization. Finally, the extracted shape contour is fine-tuned by a post-processing step based on low level image features. The experimental results demonstrate that our feature selection algorithm reduces the feature dimension in a factor of 40 and improves both training and test efficiency. Further experiments conducted on 436 clinical AP pelvis X-rays show that our approach achieves an average point-to-curve error around 1.2 mm for femur and 1.9 mm for pelvis.

Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.

Dish Detection and Segmentation for Dietary Assessment on Smartphones

Diet-related chronic diseases severely affect personal and global health. However, managing or treating these diseases currently requires long training and high personal involvement to succeed. Computer vision systems could assist with the assessment of diet by detecting and recognizing different foods and their portions in images. We propose novel methods for detecting a dish in an image and segmenting its contents with and without user interaction. All methods were evaluated on a database of over 1600 manually annotated images. The dish detection scored an average of 99% accuracy with a .2s/image run time, while the automatic and semi-automatic dish segmentation methods reached average accuracies of 88% and 91% respectively, with an average run time of .5s/image, outperforming competing solutions.

A Logarithmic Image Prior for Blind Deconvolution

Blind Deconvolution consists in the estimation of a sharp image and a blur kernel from an observed blurry image. Because the blur model admits several solutions it is necessary to devise an image prior that favors the true blur kernel and sharp image. Many successful image priors enforce the sparsity of the sharp image gradients. Ideally the L0 “norm” is the best choice for promoting sparsity, but because it is computationally intractable, some methods have used a logarithmic approximation. In this work we also study a logarithmic image prior. We show empirically how well the prior suits the blind deconvolution problem. Our analysis confirms experimentally the hypothesis that a prior should not necessarily model natural image statistics to correctly estimate the blur kernel. Furthermore, we show that a simple Maximum a Posteriori formulation is enough to achieve state of the art results. To minimize such formulation we devise two iterative minimization algorithms that cope with the non-convexity of the logarithmic prior: one obtained via the primal-dual approach and one via majorization-minimization.

Building the View Graph of a Category by Exploiting Image Realism

We propose a weakly supervised method to arrange images of a given category based on the relative pose between the camera and the object in the scene. Relative poses are points on a sphere centered at the object in a given canonical pose, which we call object viewpoints. Our method builds a graph on this sphere by assigning images with similar viewpoint to the same node and by connecting nodes if they are related by a small rotation. The key idea is to exploit a large unlabeled dataset to validate the likelihood of dominant 3D planes of the object geometry. A number of 3D plane hypotheses are evaluated by applying small 3D rotations to each hypothesis and by measuring how well the deformed images match other images in the dataset. Correct hypotheses will result in deformed images that correspond to plausible views of the object, and thus will likely match well other images in the same category. The identified 3D planes are then used to compute affinities between images related by a change of viewpoint. We then use the affinities to build a view graph via a greedy method and the maximum spanning tree.

Bilayer Blind Deconvolution with the Light Field Camera

In this paper we propose a solution to blind deconvolution of a scene with two layers (foreground/background). We show that the reconstruction of the support of these two layers from a single image of a conventional camera is not possible. As a solution we propose to use a light field camera. We demonstrate that a single light field image captured with a Lytro camera can be successfully deblurred. More specifically, we consider the case of space-varying motion blur, where the blur magnitude depends on the depth changes in the scene. Our method employs a layered model that handles occlusions and partial transparencies due to both motion blur and out of focus blur of the plenoptic camera. We reconstruct each layer support, the corresponding sharp textures, and motion blurs via an optimization scheme. The performance of our algorithm is demonstrated on synthetic as well as real light field images.

Computer Aided Surgery for Percutaneous Nephrolithotomy: Clinical Requirement Analysis and System Design

Percutaneous nephrolithotomy (PCNL) for the treatment of renal stones and other related renal diseases has proved its efficacy and has stood the test of time compared with open surgical methods and extracorporal shock wave lithotripsy. However, access to the collecting system of the kidney is not easy because the available intra-operative image modalities only provide a two dimensional view of the surgical scenario. With this lack of visual information, several punctures are often necessary which, increases the risk of renal bleeding, splanchnic, vascular or pulmonary injury, or damage to the collecting system which sometimes makes the continuation of the procedure impossible. In order to address this problem, this paper proposes a workflow for introduction of a stereotactic needle guidance system for PCNL procedures. An analysis of the imposed clinical requirements, and a instrument guidance approach to provide the physician with a more intuitive planning and visual guidance to access the collecting system of the kidney are presented.

Real-Time Multimodal Retinal Image Registration for a Computer Assisted Laser Photocoagulation System

An algorithm for the real-time registration of a retinal video sequence captured with a scanning digital ophthalmoscope (SDO) to a retinal composite image is presented. This method is designed for a computer-assisted retinal laser photocoagulation system to compensate for retinal motion and hence enhance the accuracy, speed, and patient safety of retinal laser treatments. The procedure combines intensity and feature-based registration techniques. For the registration of an individual frame, the translational frame-to-frame motion between preceding and current frame is detected by normalized cross correlation. Next, vessel points on the current video frame are identified and an initial transformation estimate is constructed from the calculated translation vector and the quadratic registration matrix of the previous frame. The vessel points are then iteratively matched to the segmented vessel centerline of the composite image to refine the initial transformation and register the video frame to the composite image. Criteria for image quality and algorithm convergence are introduced, which assess the exclusion of single frames from the registration process and enable a loss of tracking signal if necessary. The algorithm was successfully applied to ten different video sequences recorded from patients. It revealed an average accuracy of 2.47 ± 2.0 pixels (∼23.2 ± 18.8 μm) for 2764 evaluated video frames and demonstrated that it meets the clinical requirements.