Ganesh Sundaramoorthi

Sudeepta Mondal, Ganesh Sundaramoorthi

We propose a simple, efficient, and accurate method for detecting out-of-distribution (OOD) data for trained neural networks. We propose a novel descriptor, HAct - activation histograms, for OOD detection, that is, probability distributions (approximated by histograms) of output values of neural network layers under the influence of incoming data. We formulate an OOD detector based on HAct descriptors. We demonstrate that HAct is significantly more accurate than state-of-the-art in OOD detection on multiple image classification benchmarks. For instance, our approach achieves a true positive rate (TPR) of 95% with only 0.03% false-positives using Resnet-50 on standard OOD benchmarks, outperforming previous state-of-the-art by 20.67% in the false positive rate (at the same TPR of 95%). The computational efficiency and the ease of implementation makes HAct suitable for online implementation in monitoring deployed neural networks in practice at scale.

Sudeepta Mondal, Zhuolin Jiang, Ganesh Sundaramoorthi

We present a theory for the construction of out-of-distribution (OOD) detection features for neural networks. We introduce random features for OOD through a novel information-theoretic loss functional consisting of two terms, the first based on the KL divergence separates resulting in-distribution (ID) and OOD feature distributions and the second term is the Information Bottleneck, which favors compressed features that retain the OOD information. We formulate a variational procedure to optimize the loss and obtain OOD features. Based on assumptions on OOD distributions, one can recover properties of existing OOD features, i.e., shaping functions. Furthermore, we show that our theory can predict a new shaping function that out-performs existing ones on OOD benchmarks. Our theory provides a general framework for constructing a variety of new features with clear explainability.

Dong Lao, Peihao Zhu, Peter Wonka et al.

We consider the problem of filling in missing spatio-temporal regions of a video. We provide a novel flow-based solution by introducing a generative model of images in relation to the scene (without missing regions) and mappings from the scene to images. We use the model to jointly infer the scene template, a 2D representation of the scene, and the mappings. This ensures consistency of the frame-to-frame flows generated to the underlying scene, reducing geometric distortions in flow based inpainting. The template is mapped to the missing regions in the video by a new L2-L1 interpolation scheme, creating crisp inpaintings and reducing common blur and distortion artifacts. We show on two benchmark datasets that our approach out-performs state-of-the-art quantitatively and in user studies.

Naeemullah Khan, Angira Sharma, Ganesh Sundaramoorthi et al.

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural for segmentation, where descriptors should describe regions (e.g., of objects) that have diverse shape. We formulate these descriptors through the Poisson partial differential equation (PDE), which can be used to generalize convolution to arbitrary regions. We stack multiple PDE layers to generalize a deep CNN to arbitrary regions, and apply it to segmentation. We show that ST-DNN are covariant to translations and rotations and robust to domain deformations, natural for segmentation, which existing CNN based methods lack. ST-DNN are 3-4 orders of magnitude smaller then CNNs used for segmentation. We show that they exceed segmentation performance compared to state-of-the-art CNN-based descriptors using 2-3 orders smaller training sets on the texture segmentation problem.

Dong Lao, Peihao Zhu, Peter Wonka et al.

We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic gradients, can be used in conjunction with any optimizer, and has only a linear overhead (in the number of parameters) compared to computation of the stochastic gradient. The method works by computing the gradient of the loss function with respect to output-channel directed re-weighted L2 or Sobolev metrics, which has the effect of smoothing components of the gradient across a certain direction of the parameter tensor. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental. We present the continuum theory of such gradients, its discretization, and application to deep networks. Experiments on benchmark datasets, several networks and baseline optimizers show that optimizers can be improved in generalization error by simply computing the stochastic gradient with respect to output-channel directed metrics.

Yanchao Yang, Dong Lao, Ganesh Sundaramoorthi et al.

We introduce two criteria to regularize the optimization involved in learning a classifier in a domain where no annotated data are available, leveraging annotated data in a different domain, a problem known as unsupervised domain adaptation. We focus on the task of semantic segmentation, where annotated synthetic data are aplenty, but annotating real data is laborious. The first criterion, inspired by visual psychophysics, is that the map between the two image domains be phase-preserving. This restricts the set of possible learned maps, while enabling enough flexibility to transfer semantic information. The second criterion aims to leverage ecological statistics, or regularities in the scene which are manifest in any image of it, regardless of the characteristics of the illuminant or the imaging sensor. It is implemented using a deep neural network that scores the likelihood of each possible segmentation given a single un-annotated image. Incorporating these two priors in a standard domain adaptation framework improves performance across the board in the most common unsupervised domain adaptation benchmarks for semantic segmentation.

Ganesh Sundaramoorthi, Timothy E. Wang

We address the problem that state-of-the-art Convolution Neural Networks (CNN) classifiers are not invariant to small shifts. The problem can be solved by the removal of sub-sampling operations such as stride and max pooling, but at a cost of severely degraded training and test efficiency. We present a novel usage of Gaussian-Hermite basis to efficiently approximate arbitrary filters within the CNN framework to obtain translation invariance. This is shown to be invariant to small shifts, and preserves the efficiency of training. Further, to improve efficiency in memory usage as well as computational speed, we show that it is still possible to sub-sample with this approach and retain a weaker form of invariance that we call \emph{translation insensitivity}, which leads to stability with respect to shifts. We prove these claims analytically and empirically. Our analytic methods further provide a framework for understanding any architecture in terms of translation insensitivity, and provide guiding principles for design.

Dong Lao, Ganesh Sundaramoorthi

We consider the problem of detecting objects, as they come into view, from videos in an online fashion. We provide the first real-time solution that is guaranteed to minimize the delay, i.e., the time between when the object comes in view and the declared detection time, subject to acceptable levels of detection accuracy. The method leverages modern CNN-based object detectors that operate on a single frame, to aggregate detection results over frames to provide reliable detection at a rate, specified by the user, in guaranteed minimal delay. To do this, we formulate the problem as a Quickest Detection problem, which provides the aforementioned guarantees. We derive our algorithms from this theory. We show in experiments, that with an overhead of just 50 fps, we can increase the number of correct detections and decrease the overall computational cost compared to running a modern single-frame detector.

Minas Benyamin, Jeff Calder, Ganesh Sundaramoorthi et al.

We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDE's. While the resulting family of PDE's and numerical schemes are quite general, we give special attention to their application for regularized inversion problems, with particular illustrative examples on some popular image processing applications. The method is a generalization of momentum, or accelerated, gradient descent to the PDE setting. For elliptic problems, the descent equations are a nonlinear damped wave equation, instead of a diffusion equation, and the acceleration is realized as an improvement in the CFL condition from $Δt\sim Δx^{2}$ (for diffusion) to $Δt\sim Δx$ (for wave equations). We work out several explicit as well as a semi-implicit numerical schemes, together with their necessary stability constraints, and include recursive update formulations which allow minimal-effort adaptation of existing gradient descent PDE codes into the accelerated PDE framework. We explore these schemes more carefully for a broad class of regularized inversion applications, with special attention to quadratic, Beltrami, and Total Variation regularization, where the accelerated PDE takes the form of a nonlinear wave equation. Experimental examples demonstrate the application of these schemes for image denoising, deblurring, and inpainting, including comparisons against Primal Dual, Split Bregman, and ADMM algorithms.

Marei Algarni, Ganesh Sundaramoorthi

We present SurfCut, an algorithm for extracting a smooth, simple surface with an unknown 3D curve boundary from a noisy 3D image and a seed point. Our method is built on the novel observation that certain ridge curves of a function defined on a front propagated using the Fast Marching algorithm lie on the surface. Our method extracts and cuts these ridges to form the surface boundary. Our surface extraction algorithm is built on the novel observation that the surface lies in a valley of the distance from Fast Marching. We show that the resulting surface is a collection of minimal paths. Using the framework of cubical complexes and Morse theory, we design algorithms to extract these critical structures robustly. Experiments on three 3D datasets show the robustness of our method, and that it achieves higher accuracy with lower computational cost than state-of-the-art.

Dong Lao, Ganesh Sundaramoorthi

We present a general framework and method for simultaneous detection and segmentation of an object in a video that moves (or comes into view of the camera) at some unknown time in the video. The method is an online approach based on motion segmentation, and it operates under dynamic backgrounds caused by a moving camera or moving nuisances. The goal of the method is to detect and segment the object as soon as it moves. Due to stochastic variability in the video and unreliability of the motion signal, several frames are needed to reliably detect the object. The method is designed to detect and segment with minimum delay subject to a constraint on the false alarm rate. The method is derived as a problem of Quickest Change Detection. Experiments on a dataset show the effectiveness of our method in minimizing detection delay subject to false alarm constraints.

Ganesh Sundaramoorthi, Naeemullah Khan, Byung-Woo Hong

We formulate a general energy and method for segmentation that is designed to have preference for segmenting the coarse structure over the fine structure of the data, without smoothing across boundaries of regions. The energy is formulated by considering data terms at a continuum of scales from the scale space computed from the Heat Equation within regions, and integrating these terms over all time. We show that the energy may be approximately optimized without solving for the entire scale space, but rather solving time-independent linear equations at the native scale of the image, making the method computationally feasible. We provide a multi-region scheme, and apply our method to motion segmentation. Experiments on a benchmark dataset shows that our method is less sensitive to clutter or other undesirable fine-scale structure, and leads to better performance in motion segmentation.

Omar Arif, Ganesh Sundaramoorthi, Byung-Woo Hong et al.

In this paper, we propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures via a new deformation estimation scheme that is motivated by physical constraints of fluid motion. The method employs within structure motion estimation (so that differing motions among different structures are not mixed) while simultaneously satisfying the physical constraint in fluid motion that at the interface between a fluid and a medium, the normal component of the fluid's motion must match the normal component of the motion of the medium. We show how to estimate the motion according to the previous considerations in a variational framework, and in particular, show that these conditions lead to PDEs with boundary conditions at the interface that resemble Robin boundary conditions and induce coupling between structures. We illustrate the use of this motion estimation scheme in propagating a segmentation across frames and show that it leads to more accurate segmentation than traditional motion estimation that does not make use of physical constraints. Further, the method is naturally suited to interactive segmentation methods, which are prominently used in practice in commercial applications for cardiac analysis, where typically a segmentation from the previous frame is used to predict a segmentation in the next frame. We show that our propagation scheme reduces the amount of user interaction by predicting more accurate segmentations than commonly used and recent interactive commercial techniques.

Yanchao Yang, Ganesh Sundaramoorthi

We present a method to track the precise shape of an object in video based on new modeling and optimization on a new Riemannian manifold of parameterized regions. Joint dynamic shape and appearance models, in which a template of the object is propagated to match the object shape and radiance in the next frame, are advantageous over methods employing global image statistics in cases of complex object radiance and cluttered background. In cases of 3D object motion and viewpoint change, self-occlusions and dis-occlusions of the object are prominent, and current methods employing joint shape and appearance models are unable to adapt to new shape and appearance information, leading to inaccurate shape detection. In this work, we model self-occlusions and dis-occlusions in a joint shape and appearance tracking framework. Self-occlusions and the warp to propagate the template are coupled, thus a joint problem is formulated. We derive a coarse-to-fine optimization scheme, advantageous in object tracking, that initially perturbs the template by coarse perturbations before transitioning to finer-scale perturbations, traversing all scales, seamlessly and automatically. The scheme is a gradient descent on a novel infinite-dimensional Riemannian manifold that we introduce. The manifold consists of planar parameterized regions, and the metric that we introduce is a novel Sobolev-type metric defined on infinitesimal vector fields on regions. The metric has the property of resulting in a gradient descent that automatically favors coarse-scale deformations (when they reduce the energy) before moving to finer-scale deformations. Experiments on video exhibiting occlusion/dis-occlusion, complex radiance and background show that occlusion/dis-occlusion modeling leads to superior shape accuracy compared to recent methods employing joint shape/appearance models or employing global statistics.