Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild

Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first deep-learning neural network for reflection and rotation symmetry detection (Sym-NET), trained on photos from MS-COCO (Microsoft-Common Object in COntext) dataset with nearly 11K consistent symmetry-labels from more than 400 human observers. We employ novel methods to convert discrete human labels into symmetry heatmaps, capture symmetry densely in an image and quantitatively evaluate Sym-NET against multiple existing computer vision algorithms. On CVPR 2013 symmetry competition testsets and unseen MS-COCO photos, Sym-NET significantly outperforms all other competitors. Beyond mathematically well-defined symmetries on a plane, Sym-NET demonstrates abilities to identify viewpoint-varied 3D symmetries, partially occluded symmetrical objects, and symmetries at a semantic level.Comment: To appear in the International Conference on Computer Vision (ICCV) 201

A robust particle detection algorithm based on symmetry

Particle tracking is common in many biophysical, ecological, and micro-fluidic applications. Reliable tracking information is heavily dependent on of the system under study and algorithms that correctly determines particle position between images. However, in a real environmental context with the presence of noise including particular or dissolved matter in water, and low and fluctuating light conditions, many algorithms fail to obtain reliable information. We propose a new algorithm, the Circular Symmetry algorithm (C-Sym), for detecting the position of a circular particle with high accuracy and precision in noisy conditions. The algorithm takes advantage of the spatial symmetry of the particle allowing for subpixel accuracy. We compare the proposed algorithm with four different methods using both synthetic and experimental datasets. The results show that C-Sym is the most accurate and precise algorithm when tracking micro-particles in all tested conditions and it has the potential for use in applications including tracking biota in their environment.Comment: Manuscript including supplementary material

MirrorFlow: Exploiting Symmetries in Joint Optical Flow and Occlusion Estimation

Optical flow estimation is one of the most studied problems in computer vision, yet recent benchmark datasets continue to reveal problem areas of today's approaches. Occlusions have remained one of the key challenges. In this paper, we propose a symmetric optical flow method to address the well-known chicken-and-egg relation between optical flow and occlusions. In contrast to many state-of-the-art methods that consider occlusions as outliers, possibly filtered out during post-processing, we highlight the importance of joint occlusion reasoning in the optimization and show how to utilize occlusion as an important cue for estimating optical flow. The key feature of our model is to fully exploit the symmetry properties that characterize optical flow and occlusions in the two consecutive images. Specifically through utilizing forward-backward consistency and occlusion-disocclusion symmetry in the energy, our model jointly estimates optical flow in both forward and backward direction, as well as consistent occlusion maps in both views. We demonstrate significant performance benefits on standard benchmarks, especially from the occlusion-disocclusion symmetry. On the challenging KITTI dataset we report the most accurate two-frame results to date.Comment: 14 pages, To appear in ICCV 201

Markov Chains on Orbits of Permutation Groups

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytical and empirical results demonstrate the effectiveness and efficiency of the approach.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

VV-Net: Voxel VAE Net with Group Convolutions for Point Cloud Segmentation

We present a novel algorithm for point cloud segmentation. Our approach transforms unstructured point clouds into regular voxel grids, and further uses a kernel-based interpolated variational autoencoder (VAE) architecture to encode the local geometry within each voxel. Traditionally, the voxel representation only comprises Boolean occupancy information which fails to capture the sparsely distributed points within voxels in a compact manner. In order to handle sparse distributions of points, we further employ radial basis functions (RBF) to compute a local, continuous representation within each voxel. Our approach results in a good volumetric representation that effectively tackles noisy point cloud datasets and is more robust for learning. Moreover, we further introduce group equivariant CNN to 3D, by defining the convolution operator on a symmetry group acting on $\mathbb{Z}^3$ and its isomorphic sets. This improves the expressive capacity without increasing parameters, leading to more robust segmentation results. We highlight the performance on standard benchmarks and show that our approach outperforms state-of-the-art segmentation algorithms on the ShapeNet and S3DIS datasets.Comment: Accepted by International Conference on Computer Vision (ICCV) 201

Rotational Rectification Network: Enabling Pedestrian Detection for Mobile Vision

Across a majority of pedestrian detection datasets, it is typically assumed that pedestrians will be standing upright with respect to the image coordinate system. This assumption, however, is not always valid for many vision-equipped mobile platforms such as mobile phones, UAVs or construction vehicles on rugged terrain. In these situations, the motion of the camera can cause images of pedestrians to be captured at extreme angles. This can lead to very poor pedestrian detection performance when using standard pedestrian detectors. To address this issue, we propose a Rotational Rectification Network (R2N) that can be inserted into any CNN-based pedestrian (or object) detector to adapt it to significant changes in camera rotation. The rotational rectification network uses a 2D rotation estimation module that passes rotational information to a spatial transformer network to undistort image features. To enable robust rotation estimation, we propose a Global Polar Pooling (GP-Pooling) operator to capture rotational shifts in convolutional features. Through our experiments, we show how our rotational rectification network can be used to improve the performance of the state-of-the-art pedestrian detector under heavy image rotation by up to 45

Active Community Detection with Maximal Expected Model Change

We present a novel active learning algorithm for community detection on networks. Our proposed algorithm uses a Maximal Expected Model Change (MEMC) criterion for querying network nodes label assignments. MEMC detects nodes that maximally change the community assignment likelihood model following a query. Our method is inspired by detection in the benchmark Stochastic Block Model (SBM), where we provide sample complexity analysis and empirical study with SBM and real network data for binary as well as for the multi-class settings. The analysis also covers the most challenging case of sparse degree and below-detection-threshold SBMs, where we observe a super-linear error reduction. MEMC is shown to be superior to the random selection baseline and other state-of-the-art active learners

Probably Approximately Symmetric: Fast rigid Symmetry Detection with Global Guarantees

We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a sub-linear algorithm. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithm's complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data-set. This is the first large-scale evaluation of any symmetry detection technique that we are aware of

AMAT: Medial Axis Transform for Natural Images

We introduce Appearance-MAT (AMAT), a generalization of the medial axis transform for natural images, that is framed as a weighted geometric set cover problem. We make the following contributions: i) we extend previous medial point detection methods for color images, by associating each medial point with a local scale; ii) inspired by the invertibility property of the binary MAT, we also associate each medial point with a local encoding that allows us to invert the AMAT, reconstructing the input image; iii) we describe a clustering scheme that takes advantage of the additional scale and appearance information to group individual points into medial branches, providing a shape decomposition of the underlying image regions. In our experiments, we show state-of-the-art performance in medial point detection on Berkeley Medial AXes (BMAX500), a new dataset of medial axes based on the BSDS500 database, and good generalization on the SK506 and WH-SYMMAX datasets. We also measure the quality of reconstructed images from BMAX500, obtained by inverting their computed AMAT. Our approach delivers significantly better reconstruction quality with respect to three baselines, using just 10% of the image pixels. Our code and annotations are available at https://github.com/tsogkas/amat .Comment: 10 pages (including references), 5 figures, accepted at ICCV 201

Adversarial Occlusion-aware Face Detection

Occluded face detection is a challenging detection task due to the large appearance variations incurred by various real-world occlusions. This paper introduces an Adversarial Occlusion-aware Face Detector (AOFD) by simultaneously detecting occluded faces and segmenting occluded areas. Specifically, we employ an adversarial training strategy to generate occlusion-like face features that are difficult for a face detector to recognize. Occlusion mask is predicted simultaneously while detecting occluded faces and the occluded area is utilized as an auxiliary instead of being regarded as a hindrance. Moreover, the supervisory signals from the segmentation branch will reversely affect the features, aiding in detecting heavily-occluded faces accordingly. Consequently, AOFD is able to find the faces with few exposed facial landmarks with very high confidences and keeps high detection accuracy even for masked faces. Extensive experiments demonstrate that AOFD not only significantly outperforms state-of-the-art methods on the MAFA occluded face detection dataset, but also achieves competitive detection accuracy on benchmark dataset for general face detection such as FDDB.Comment: Accepted by ACPR201