An efficient parallel algorithm for geometrically characterising drawings of a class of 3-D objects

Labelling the lines of a planar line drawing of a 3-D object in a way that reflects the geometric properties of the object is a much studied problem in computer vision, considered to be an important step towards understanding the object from its 2-D drawing. Combinatorially, the labellability problem is a Constraint Satisfaction Problem and has been shown to be NP-complete even for images of polyhedral scenes. In this paper, we examine scenes that consist of a set of objects each obtained by rotating a polygon around an arbitrary axis. The objects are allowed to arbitrarily intersect or overlay. We show that for these scenes, there is a sequential lineartime labelling algorithm. Moreover, we show that the algorithm has a fast parallel version that executes inO(log3 n) time on an Exclusive-Read-Exclusive-Write Parallel Random Access Machine withO(n 3/log3 n) processors. The algorithm not only answers the decision problem of labellability, but also produces a legal labelling, if there is one. This parallel algorithm should be contrasted with the techniques of dealing with special cases of the constraint satisfaction problem. These techniques employ an effective, but inherently sequential, relaxation procedure in order to restrict the domains of the variables.

The process of merging two arbitrary partitions of a given finite set 𝒰 of n elements is known as coarsest refinement. In the COARSEST REFINEMENT PROBLEM we are given two arbitrary partitions 𝒳, 𝒴 of the set 𝒰 such that 𝒳 = {𝒳1, 𝒳2, ..., 𝒳 x} and 𝒴 = {𝒴1, 𝒴2, ..., 𝒴 y}, and determine a new partition 𝒵 = {𝒵1, 𝒵2, ..., 𝒵 z} such that each is a common non-empty subset of some 𝒳 a ∈ 𝒳 and some 𝒴 b ∈ 𝒴 and |𝒵| is as small as possible. This article describes a resource-efficient parallel algorithm to solve this problem. More specifically, we show that a coarsest refinement can be computed in O( t( n) + log n) parallel time using max{nlogn,p(n)} processors, where t( n) denotes the running time of a parallel stable sorting algorithm that uses p( n) processors on an EREW PRAM. This result depends on t( n) and p( n). We give a table that shows the best known time and processor complexities for a parallel stable sorting algorithm. If the parallel stable sorting algorithms by Ajtai et al., Cole, and Leighton are used, the coarsest refinement can be computed in O(log n) parallel time using n processors on an EREW PRAM. On the other hand, if the parallel stable sorting algorithm by Bahig et al. is used, the coarsest refinement can be computed in O(lognlog(nlogn)) parallel time using nlogn processors on an EREW PRAM. In addition, we show that on, a RAM machine, our parallel algorithm runs as asymptotically efficient as the fastest known sequential algorithm.

Novel view synthesis is a classic problem in computer vision. It refers to the generation of previously unseen views of a scene from a set of sparse input images taken from different viewpoints. One example of novel view synthesis is the interpolation of views in between the two images of a stereo camera. Another classic problem in computer vision is video frame interpolation, which is important for video processing. It refers to the generation of video frames in between existing ones and is commonly used to increase the frame rate of a video or to match the frame rate to the refresh rate of the monitor that the video is being displayed on. Interestingly, off-the-shelf video frame interpolation can directly be employed to successfully perform view interpolation to address the aforementioned stereo view interpolation problem. Video frame interpolation can be seen as temporal novel view synthesis. However, this perspective is usually not considered and novel view synthesis generally concerns generating unseen views in space rather than time. For this reason, the set of sparse input images that is used for spatial novel view synthesis is commonly either captured at the same time, or it is assumed that the scene is static. This paradigm limits the applicability of novel view synthesis in real-world scenarios though. This thesis addresses three applications of novel view synthesis and provides practical solutions that do not require difficult-to-acquire multi-view imagery: video frame interpolation which performs temporal video-to-video synthesis, synthesizing the 3D Ken Burns effect from a single image which performs spatial image-to-video synthesis, synthesizing video action shots which performs spatiotemporal video-to-video and video-to-image synthesis. These applications not only explore different dimensions of time and space, they also perform novel view synthesis on everyday image and video footage. This is in stark contrast to the large body of existing work which focuses on spatial novel view synthesis while requiring multiple input views that were either captured at the same time or under the assumption of a static scene.

Template matching is a fundamental problem in computer vision, with many applications. Existing methods use sliding window computation for choosing an image-window that best matches the template. For classic algorithms based on SSD, SAD and normalized cross-correlation, efficient algorithms have been developed allowing them to run in real-time. Current state of the art algorithms are based on nearest neighbor (NN) matching of small patches within the template to patches in the image. These algorithms yield state-of-the-art results since they can deal better with changes in appearance, viewpoint, illumination, non-rigid transformations, and occlusion. However, NN-based algorithms are relatively slow not only due to NN computation for each image patch, but also since their sliding window computation is inefficient. We therefore propose in this paper an efficient NN-based algorithm. Its accuracy is similar (in some cases slightly better) than the existing algorithms and its running time is 43–200 times faster depending on the sizes of the images and templates used. The main contribution of our method is an algorithm for incrementally computing the score of each image window based on the score computed for the previous window. This is in contrast to computing the score for each image window independently, as in previous NN-based methods. The complexity of our method is therefore O(|I|) instead of O(|I||T|), where I and T are the image and the template respectively.

Graph and hypergraph matching are fundamental problems in computer vision, which have been receiving a steadily growing attention in the last two decades due to the recent modern algorithms and models that are both fast and accurate. Graph and hypergraph matching are successful in tackling many real-world tasks that require 2D and 3D feature matching and alignment. Matching is a general problem in vision and graphs have always been quintessential for modeling information that has both local and longer range connections. Therefore, graph matching will continue to influence computer vision and robotics research, crossing over many different mathematical and computational models, including Bayesian networks, conditional and Markov random fields, spectral graph models, and, more recently, deep neural networks. While graph matching is limited to using pairwise relationships, hypergraph matching permits the use of relationships between sets of features of any order. Consequently, it carries the promise to make matching more robust to changes in scale, deformations, and outliers. In this chapter, we present several key ideas, computational models, and optimization methods that introduced in the literature the possibility to learn graph and hypergraph matching in a semi-supervised or even completely unsupervised fashion. We start by describing two methods for solving graph and hypergraph matching based on spectral matching and integer projected fixed point methods, introduced in Chap. 1. Then, based on the same intuition (also discussed in Chap. 1) that correct assignments form a strong cluster of agreements, we follow up by introducing the main approach to learning as it applies to graph and hypergraph matching, as well as the more general Maximum A Posteriori (MAP) inference problem in probabilistic graphical models (MRFs and CRFs). In the last part of the chapter, we demonstrate experimentally the effectiveness of the algorithms presented and, whenever possible, provide extensive comparisons to other top published methods. Moreover, we show that our learning approach is general and can significantly boost the performance of different state-of-the-art matching algorithms in the literature.

We consider parallel algorithms working in sequential global time, for example, circuits or parallel random access machines (PRAMs). Parallel abstract state machines (parallel ASMs) are such parallel algorithms, and the parallel ASM thesis asserts that every parallel algorithm is behaviorally equivalent to a parallel ASM. In an earlier article, we axiomatized parallel algorithms, proved the ASM thesis, and proved that every parallel ASM satisfies the axioms. It turned out that we were too timid in formulating the axioms; they did not allow a parallel algorithm to create components on the fly. This restriction did not hinder us from proving that the usual parallel models, like circuits or PRAMs or even alternating Turing machines, satisfy the postulates. But it resulted in an error in our attempt to prove that parallel ASMs always satisfy the postulates. To correct the error, we liberalize our axioms and allow on-the-fly creation of new parallel components. We believe that the improved axioms accurately express what parallel algorithms ought to be. We prove the parallel thesis for the new, corrected notion of parallel algorithms, and we check that parallel ASMs satisfy the new axioms.

Toward designing intelligent PDEs for computer vision: An optimal control approach

In the areas of computer vision and computer graphics, analyzing information about three-dimensional objects from two-dimensional images is essential. Shape from shading is a very fundamental problem in computer vision, which uses features and patterns in images to infer the shape of the object in our viewing direction. The influence of solving this problem is significant. For example, a typical application of shape from shading is in astronomy, in which we can obtain landscape features of a planet by analyzing the information from the image we get.

The simultaneous recovery of three-dimensional (3D) structure from motion (SfM) for the sequences of images, is one of the more difficult problems in computer vision. Classical approaches to the problem rely on using algebraic techniques to solve for these unknowns given two or more image. Motion analysis and 3D shape estimation based on the estimated motion is an important problem in computer vision. The correspondence problem is an important tool in SfM where in this paper a general 3D motion based on a simple rotation, tilt, roll and translation is proposed, and then is used for 3D shape estimation. The current work expands the 2D motion estimation (shift, rotation) to accommodate general 3D motion (shift, rotation, tilt and roll). The proposed work in this paper of motion estimation of moving object is based on Fourier Descriptor Transformation (FDT) analysis before and after motion. The FDT is also used to resolve the correspondence problem in a sequence of images. We test our method on several large-scale photo collections, show the efficacy of the introduced approach to improve reconstruction accuracy.

Which parts of an image evoke emotions in an observer? To answer this question, we introduce a novel problem in computer vision — predicting an Emotion Stimuli Map (ESM), which describes pixel-wise contribution to evoked emotions. Building a new image database, EmotionROI, as a benchmark for predicting the ESM, we find that the regions selected by saliency and objectness detection do not correctly predict the image regions which evoke emotion. Although objects represent important regions for evoking emotion, parts of the background are also important. Based on this fact, we propose using fully convolutional networks for predicting the ESM. Both qualitative and quantitative experimental results confirm that our method can predict the regions which evoke emotion better than both saliency and objectness detection.

Text recognition in natural scene images is a challenging problem in computer vision. Different than the optical character recognition (OCR), text recognition in natural scene images is more complex due to variations in text size, colors, fonts, orientations, complex backgrounds, occlusion, illuminations and uneven lighting conditions. In this paper, we propose a segmentation-free method based on a deep convolutional recurrent neural network to solve the problem of cursive text recognition, particularly focusing on Urdu text in natural scenes. Compared to the non-cursive scripts, Urdu text recognition is more complex due to variations in the writing styles, several shapes of the same character, connected text, ligature overlapping, stretched, diagonal and condensed text. The proposed model gets a whole word image as an input without pre-segmenting into individual characters, and then transforms into the sequence of the relevant features. Our model is based on three components: a deep convolutional neural network (CNN) with shortcut connections to extract and encode the features, a recurrent neural network (RNN) to decode the convolutional features, and a connectionist temporal classification (CTC) to map the predicted sequences into the target labels. To increase the text recognition accuracy further, we explore deeper CNN architectures like VGG-16, VGG-19, ResNet-18 and ResNet-34 to extract more appropriate Urdu text features, and compare the recognition results. To conduct the experiments, a new large-scale benchmark dataset of cropped Urdu word images in natural scenes is developed. The experimental results show that the proposed deep CRNN network with shortcut connections outperform than other network architectures. The dataset is publicly available and can be downloaded from <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://data.mendeley.com/datasets/k5fz57zd9z/1</uri> .

One of the fundamental problems of computer vision is to extract 3D shape and motion from images. This can be achieved when a scene or object is observed from different viewpoints or over a period of time. There is a wide range of applications, ranging from digitizing cultural heritage to vision-based autonomous robot navigation. This talk will present several approaches to solve this problem. First, we’ll discuss techniques for 3D shape recovery for static objects and scenes. One particular case is the 3D mapping and localization in large environments from images, e.g. urban 3D reconstruction from vehicleborne cameras or localization from cell-phone images. Next, we’ll shift our focus to modeling dynamic scenes, e.g. people who are moving around. In addition to explicitly 3D modeling an event, we'll consider the possibility to perform video-based rendering from casually captured videos. Speaker Bio-Sketch: Marc Pollefeys is a full professor in the Dept. of Computer Science of ETH Zurich since 2007 where he is the head of the Institute for Visual Computing and leads the Computer Vision and Geometry lab. He currently also remains associated with the Dept. of Computer Science of the University of North Carolina at Chapel Hill where he started as an assistant professor in 2002 and became an associate professor in 2005. Before this he was a postdoctoral researcher at the Katholieke Universiteit Leuven in Belgium, where he also received his M.S. and Ph.D. degrees in 1994 and 1999, respectively. His main area of research is computer vision. One of his main research goals is to develop flexible approaches to capture visual representations of real world objects, scenes and events. Dr. Pollefeys has received several prizes for his research, including a Marr prize, an NSF CAREER award, a Packard Fellowship and a European Research Council Starting Grant. He is the author or co-author of more than 130 peer-reviewed publications. He is the General Chair for the European Conference on Computer Vision 2014 (ECCV), was a Program Co-Chair for the IEEE Conference on Computer Vision and Pattern Recognition 2009 (CVPR), was general/program co-chair of the Third Symposium on 3D Data Processing, Visualization and Transmission and has organized workshops and courses at major vision and graphics conferences and has served on the program committees of many conferences. Prof. Pollefeys is/was on the Editorial Board of the IEEE Transactions on Pattern Analysis and Machine Intelligence and the International Journal of Computer Vision as well as several other journals in computer vision, graphics and robotics.

The authors provide optimal parallel solutions to several fundamental link distance problems set in trapezoided rectilinear polygons. All parallel algorithms are deterministic, run in logarithmic time, have an optimal time-processor product and are designed to run on EREW PRAM. The authors develop techniques (e.g. rectilinear window partition) for solving link distance problems in parallel which are expected to find applications in the design of other parallel computational geometry algorithms. They employ these parallel techniques for example to compute the link diameter, link center, and central diagonal of a rectilinear polygon. Their results also imply an optimal linear-time sequential algorithm for constructing a data structure to support rectilinear link distance queries between points.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graphs. However, graph matching that incorporates pairwise constraints can be formulated as a quadratic assignment problem (QAP), which is NP-complete and results in intrinsic computational difficulties. This paper presents a functional representation for graph matching (FRGM) that aims to provide more geometric insights on the problem and reduce the space and time complexities. To achieve these goals, we represent each graph by a linear function space equipped with a functional such as inner product or metric, that has an explicit geometric meaning. Consequently, the correspondence matrix between graphs can be represented as a linear representation map. Furthermore, this map can be reformulated as a new parameterization for matching graphs in Euclidean space such that it is consistent with graphs under rigid or nonrigid deformations. This allows us to estimate the correspondence matrix and geometric deformations simultaneously. We use the representation of edge-attributes rather than the affinity matrix to reduce the space complexity and propose an efficient optimization strategy to reduce the time complexity. The experimental results on both synthetic and real-world datasets show that the FRGM can achieve state-of-the-art performance.

Finite state automata are of fundamental importance in theory as well as applications in computer science. This dissertation presents several parallel algorithms for processing of them, including minimizing the number of states for a given finite state automaton, finding homing sequences for a given finite state automaton, converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. Implementation of some algorithms, as well as their experimental results, are also given. For minimization of deterministic finite automata, we present a parallel algorithm and discuss its implementation on a practical parallel machine using data parallel and message passing paradigms. Its time complexity on a p processor EREW PRAM $(p\\le n)$ for inputs of size n is $O({n\\log\\sp2n\\over p}+\\log n\\ \\log p)$ uniformly on almost all instances. The work done by our algorithm is thus within a factor of $O(\\log n)$ of the best known sequential algorithm. The space used by our algorithm is linear in the input size. The actual resource requirements of our implementations are consistent with these estimates. For finding homing sequences of deterministic finite automata, we present both deterministic and randomized algorithms. Two randomized algorithms of time complexity $O(log\\sp2n)$ are given. One of the randomized algorithms produces a homing sequence of length $O(n\\ log\\sp2n)$ for almost all DFA's with n states. The deterministic algorithm is based on a well known sequential algorithm. The implementation of the deterministic parallel algorithm shows that it can handle randomly generated instances with millions of states, and all DFA's with thousands of states using currently available parallel machines. Finally, we present an efficient parallel algorithm for converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. The resulting automaton is natural representation of a regular expression and has some important and practical uses in the document processing area. The time complexity of the algorithm is $O(\\log n)$ and the number of processors used is $O(n\\sp2).$