arXiv subjects

Srikumar Ramalingam

Publications and source records attributed to Srikumar Ramalingam.

At least 37 records · Page 2Linked to original sources

arXiv2020

Mapping of Sparse 3D Data using Alternating Projection

We propose a novel technique to register sparse 3D scans in the absence of texture. While existing methods such as KinectFusion or Iterative Closest Points (ICP) heavily rely on dense point clouds, this task is particularly challenging under sparse conditions without RGB data. Sparse texture-less data does not come with high-quality boundary signal, and this prohibits the use of correspondences from corners, junctions, or boundary lines. Moreover, in the case of sparse data, it is incorrect to assume that the same point will be captured in two consecutive scans. We take a different approach and first re-parameterize the point-cloud using a large number of line segments. In this re-parameterized data, there exists a large number of line intersection (and not correspondence) constraints that allow us to solve the registration task. We propose the use of a two-step alternating projection algorithm by formulating the registration as the simultaneous satisfaction of intersection and rigidity constraints. The proposed approach outperforms other top-scoring algorithms on both Kinect and LiDAR datasets. In Kinect, we can use 100X downsampled sparse data and still outperform competing methods operating on full-resolution data.

cs.CV↗

arXiv2020

3DRegNet: A Deep Neural Network for 3D Point Registration

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

cs.CV↗

arXiv2020

Lossless Compression of Deep Neural Networks

Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work, we introduce an algorithm that removes units and layers of a neural network while not changing the output that is produced, which thus implies a lossless compression. This algorithm, which we denote as LEO (Lossless Expressiveness Optimization), relies on Mixed-Integer Linear Programming (MILP) to identify Rectified Linear Units (ReLUs) with linear behavior over the input domain. By using L1 regularization to induce such behavior, we can benefit from training over a larger architecture than we would later use in the environment where the trained neural network is deployed.

cs.LG↗

arXiv2019

Empirical Bounds on Linear Regions of Deep Rectifier Networks

We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However, enumerating these regions is prohibitive and the known analytical bounds are identical for networks with same dimensions. In this work, we approximate the number of linear regions through empirical bounds based on features of the trained network and probabilistic inference. Our first contribution is a method to sample the activation patterns defined by ReLUs using universal hash functions. This method is based on a Mixed-Integer Linear Programming (MILP) formulation of the network and an algorithm for probabilistic lower bounds of MILP solution sets that we call MIPBound, which is considerably faster than exact counting and reaches values in similar orders of magnitude. Our second contribution is a tighter activation-based bound for the maximum number of linear regions, which is particularly stronger in networks with narrow layers. Combined, these bounds yield a fast proxy for the number of linear regions of a deep neural network.

cs.LG↗

arXiv2019

Learning Strict Identity Mappings in Deep Residual Networks

A family of super deep networks, referred to as residual networks or ResNet, achieved record-beating performance in various visual tasks such as image recognition, object detection, and semantic segmentation. The ability to train very deep networks naturally pushed the researchers to use enormous resources to achieve the best performance. Consequently, in many applications super deep residual networks were employed for just a marginal improvement in performance. In this paper, we propose epsilon-ResNet that allows us to automatically discard redundant layers, which produces responses that are smaller than a threshold epsilon, with a marginal or no loss in performance. The epsilon-ResNet architecture can be achieved using a few additional rectified linear units in the original ResNet. Our method does not use any additional variables nor numerous trials like other hyper-parameter optimization techniques. The layer selection is achieved using a single training process and the evaluation is performed on CIFAR-10, CIFAR-100, SVHN, and ImageNet datasets. In some instances, we achieve about 80% reduction in the number of parameters.

cs.CV↗

arXiv2019

Can generalised relative pose estimation solve sparse 3D registration?

Popular 3D scan registration projects, such as Stanford digital Michelangelo or KinectFusion, exploit the high-resolution sensor data for scan alignment. It is particularly challenging to solve the registration of sparse 3D scans in the absence of RGB components. In this case, we can not establish point correspondences since the same 3D point cannot be captured in two successive scans. In contrast to correspondence based methods, we take a different viewpoint and formulate the sparse 3D registration problem based on the constraints from the intersection of line segments from adjacent scans. We obtain the line segments by modeling every horizontal and vertical scan-line as piece-wise linear segments. We propose a new alternating projection algorithm for solving the scan alignment problem using line intersection constraints. We develop two new minimal solvers for scan alignment in the presence of plane correspondences: 1) 3 line intersections and 1 plane correspondence, and 2) 1 line intersection and 2 plane correspondences. We outperform other competing methods on Kinect and LiDAR datasets.

cs.CV↗

arXiv2019

Equivalent and Approximate Transformations of Deep Neural Networks

Two networks are equivalent if they produce the same output for any given input. In this paper, we study the possibility of transforming a deep neural network to another network with a different number of units or layers, which can be either equivalent, a local exact approximation, or a global linear approximation of the original network. On the practical side, we show that certain rectified linear units (ReLUs) can be safely removed from a network if they are always active or inactive for any valid input. If we only need an equivalent network for a smaller domain, then more units can be removed and some layers collapsed. On the theoretical side, we constructively show that for any feed-forward ReLU network, there exists a global linear approximation to a 2-hidden-layer shallow network with a fixed number of units. This result is a balance between the increasing number of units for arbitrary approximation with a single layer and the known upper bound of $\lceil log(n_0+1)\rceil +1$ layers for exact representation, where $n_0$ is the input dimension. While the transformed network may require an exponential number of units to capture the activation patterns of the original network, we show that it can be made substantially smaller by only accounting for the patterns that define linear regions. Based on experiments with ReLU networks on the MNIST dataset, we found that $l_1$-regularization and adversarial training reduces the number of linear regions significantly as the number of stable units increases due to weight sparsity. Therefore, we can also intentionally train ReLU networks to allow for effective loss-less compression and approximation.

cs.LG↗

arXiv2019

Minimal Solvers for Mini-Loop Closures in 3D Multi-Scan Alignment

3D scan registration is a classical, yet a highly useful problem in the context of 3D sensors such as Kinect and Velodyne. While there are several existing methods, the techniques are usually incremental where adjacent scans are registered first to obtain the initial poses, followed by motion averaging and bundle-adjustment refinement. In this paper, we take a different approach and develop minimal solvers for jointly computing the initial poses of cameras in small loops such as 3-, 4-, and 5-cycles. Note that the classical registration of 2 scans can be done using a minimum of 3 point matches to compute 6 degrees of relative motion. On the other hand, to jointly compute the 3D registrations in n-cycles, we take 2 point matches between the first n-1 consecutive pairs (i.e., Scan 1 & Scan 2, ... , and Scan n-1 & Scan n) and 1 or 2 point matches between Scan 1 and Scan n. Overall, we use 5, 7, and 10 point matches for 3-, 4-, and 5-cycles, and recover 12, 18, and 24 degrees of transformation variables, respectively. Using simulations and real-data we show that the 3D registration using mini n-cycles are computationally efficient, and can provide alternate and better initial poses compared to standard pairwise methods.

cs.CV↗

arXiv2018

Simultaneous Edge Alignment and Learning

Edge detection is among the most fundamental vision problems for its role in perceptual grouping and its wide applications. Recent advances in representation learning have led to considerable improvements in this area. Many state of the art edge detection models are learned with fully convolutional networks (FCNs). However, FCN-based edge learning tends to be vulnerable to misaligned labels due to the delicate structure of edges. While such problem was considered in evaluation benchmarks, similar issue has not been explicitly addressed in general edge learning. In this paper, we show that label misalignment can cause considerably degraded edge learning quality, and address this issue by proposing a simultaneous edge alignment and learning framework. To this end, we formulate a probabilistic model where edge alignment is treated as latent variable optimization, and is learned end-to-end during network training. Experiments show several applications of this work, including improved edge detection with state of the art performance, and automatic refinement of noisy annotations.

cs.CV↗

arXiv2018

Novel Single View Constraints for Manhattan 3D Line Reconstruction

This paper proposes a novel and exact method to reconstruct line-based 3D structure from a single image using Manhattan world assumption. This problem is a distinctly unsolved problem because there can be multiple 3D reconstructions from a single image. Thus, we are often forced to look for priors like Manhattan world assumption and common scene structures. In addition to the standard orthogonality, perspective projection, and parallelism constraints, we investigate a few novel constraints based on the physical realizability of the 3D scene structure. We treat the line segments in the image to be part of a graph similar to straws and connectors game, where the goal is to back-project the line segments in 3D space and while ensuring that some of these 3D line segments connect with each other (i.e., truly intersect in 3D space) to form the 3D structure. We consider three sets of novel constraints while solving the reconstruction: (1) constraints on a series of Manhattan line intersections that form cycles, but are not all physically realizable, (2) constraints on true and false intersections in the case of nearby lines lying on the same Manhattan plane, and (3) constraints from the intersections on boundary and non-boundary line segments. The reconstruction is achieved using mixed integer linear programming (MILP), and we show compelling results on real images. Along with this paper, we will release a challenging Single View Line Reconstruction dataset with ground truth 3D line models for research purposes.

cs.CV↗

arXiv2018

Bounding and Counting Linear Regions of Deep Neural Networks

We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions on rectifier networks, which are exact for inputs of dimension one; (ii) a first upper bound for multi-layer maxout networks; and (iii) a first method to perform exact enumeration or counting of the number of regions by modeling the DNN with a mixed-integer linear formulation. These bounds come from leveraging the dimension of the space defining each linear region. The results also indicate that a deep rectifier network can only have more linear regions than every shallow counterpart with same number of neurons if that number exceeds the dimension of the input.

cs.LG↗

arXiv2018

A Minimal Closed-Form Solution for Multi-Perspective Pose Estimation using Points and Lines

We propose a minimal solution for pose estimation using both points and lines for a multi-perspective camera. In this paper, we treat the multi-perspective camera as a collection of rigidly attached perspective cameras. These type of imaging devices are useful for several computer vision applications that require a large coverage such as surveillance, self-driving cars, and motion-capture studios. While prior methods have considered the cases using solely points or lines, the hybrid case involving both points and lines has not been solved for multi-perspective cameras. We present the solutions for two cases. In the first case, we are given 2D to 3D correspondences for two points and one line. In the later case, we are given 2D to 3D correspondences for one point and two lines. We show that the solution for the case of two points and one line can be formulated as a fourth degree equation. This is interesting because we can get a closed-form solution and thereby achieve high computational efficiency. The later case involving two lines and one point can be mapped to an eighth degree equation. We show simulations and real experiments to demonstrate the advantages and benefits over existing methods.

cs.CV↗

arXiv2018

VLASE: Vehicle Localization by Aggregating Semantic Edges

In this paper, we propose VLASE, a framework to use semantic edge features from images to achieve on-road localization. Semantic edge features denote edge contours that separate pairs of distinct objects such as building-sky, road- sidewalk, and building-ground. While prior work has shown promising results by utilizing the boundary between prominent classes such as sky and building using skylines, we generalize this approach to consider semantic edge features that arise from 19 different classes. Our localization algorithm is simple, yet very powerful. We extract semantic edge features using a recently introduced CASENet architecture and utilize VLAD framework to perform image retrieval. Our experiments show that we achieve improvement over some of the state-of-the-art localization algorithms such as SIFT-VLAD and its deep variant NetVLAD. We use ablation study to study the importance of different semantic classes and show that our unified approach achieves better performance compared to individual prominent features such as skylines.

cs.CV↗

arXiv2018

How Could Polyhedral Theory Harness Deep Learning?

The holy grail of deep learning is to come up with an automatic method to design optimal architectures for different applications. In other words, how can we effectively dimension and organize neurons along the network layers based on the computational resources, input size, and amount of training data? We outline promising research directions based on polyhedral theory and mixed-integer representability that may offer an analytical approach to this question, in contrast to the empirical techniques often employed.

math.OC↗

arXiv2018

Building Anatomically Realistic Jaw Kinematics Model from Data

This paper considers a different aspect of anatomical face modeling: kinematic modeling of the jaw, i.e., the Temporo-Mandibular Joint (TMJ). Previous work often relies on simple models of jaw kinematics, even though the actual physiological behavior of the TMJ is quite complex, allowing not only for mouth opening, but also for some amount of sideways (lateral) and front-to-back (protrusion) motions. Fortuitously, the TMJ is the only joint whose kinematics can be accurately measured with optical methods, because the bones of the lower and upper jaw are rigidly connected to the lower and upper teeth. We construct a person-specific jaw kinematic model by asking an actor to exercise the entire range of motion of the jaw while keeping the lips open so that the teeth are at least partially visible. This performance is recorded with three calibrated cameras. We obtain highly accurate 3D models of the teeth with a standard dental scanner and use these models to reconstruct the rigid body trajectories of the teeth from the videos (markerless tracking). The relative rigid transformations samples between the lower and upper teeth are mapped to the Lie algebra of rigid body motions in order to linearize the rotational motion. Our main contribution is to fit these samples with a three-dimensional nonlinear model parameterizing the entire range of motion of the TMJ. We show that standard Principal Component Analysis (PCA) fails to capture the nonlinear trajectories of the moving mandible. However, we found these nonlinearities can be captured with a special modification of autoencoder neural networks known as Nonlinear PCA. By mapping back to the Lie group of rigid transformations, we obtain parameterization of the jaw kinematics which provides an intuitive interface allowing the animators to explore realistic jaw motions in a user-friendly way.

cs.GR↗

arXiv2018

Analytical Modeling of Vanishing Points and Curves in Catadioptric Cameras

Vanishing points and vanishing lines are classical geometrical concepts in perspective cameras that have a lineage dating back to 3 centuries. A vanishing point is a point on the image plane where parallel lines in 3D space appear to converge, whereas a vanishing line passes through 2 or more vanishing points. While such concepts are simple and intuitive in perspective cameras, their counterparts in catadioptric cameras (obtained using mirrors and lenses) are more involved. For example, lines in the 3D space map to higher degree curves in catadioptric cameras. The projection of a set of 3D parallel lines converges on a single point in perspective images, whereas they converge to more than one point in catadioptric cameras. To the best of our knowledge, we are not aware of any systematic development of analytical models for vanishing points and vanishing curves in different types of catadioptric cameras. In this paper, we derive parametric equations for vanishing points and vanishing curves using the calibration parameters, mirror shape coefficients, and direction vectors of parallel lines in 3D space. We show compelling experimental results on vanishing point estimation and absolute pose estimation for a wide range of catadioptric cameras in both simulations and real experiments.

cs.CV↗

arXiv2018

Class Subset Selection for Transfer Learning using Submodularity

In recent years, it is common practice to extract fully-connected layer (fc) features that were learned while performing image classification on a source dataset, such as ImageNet, and apply them generally to a wide range of other tasks. The general usefulness of some large training datasets for transfer learning is not yet well understood, and raises a number of questions. For example, in the context of transfer learning, what is the role of a specific class in the source dataset, and how is the transferability of fc features affected when they are trained using various subsets of the set of all classes in the source dataset? In this paper, we address the question of how to select an optimal subset of the set of classes, subject to a budget constraint, that will more likely generate good features for other tasks. To accomplish this, we use a submodular set function to model the accuracy achievable on a new task when the features have been learned on a given subset of classes of the source dataset. An optimal subset is identified as the set that maximizes this submodular function. The maximization can be accomplished using an efficient greedy algorithm that comes with guarantees on the optimality of the solution. We empirically validate our submodular model by successfully identifying subsets of classes that produce good features for new tasks.

cs.CV↗

arXiv2017

Submodular Function Maximization for Group Elevator Scheduling

We propose a novel approach for group elevator scheduling by formulating it as the maximization of submodular function under a matroid constraint. In particular, we propose to model the total waiting time of passengers using a quadratic Boolean function. The unary and pairwise terms in the function denote the waiting time for single and pairwise allocation of passengers to elevators, respectively. We show that this objective function is submodular. The matroid constraints ensure that every passenger is allocated to exactly one elevator. We use a greedy algorithm to maximize the submodular objective function, and derive provable guarantees on the optimality of the solution. We tested our algorithm using Elevate 8, a commercial-grade elevator simulator that allows simulation with a wide range of elevator settings. We achieve significant improvement over the existing algorithms.

cs.AI↗