In this paper we propose an edge-direct visual odometry algorithm that efficiently utilizes edge pixels to find the relative pose that minimizes the photometric error between images. Prior work on exploiting edge pixels instead treats edges as features and employ various techniques to match edge lines or pixels, which adds unnecessary complexity. Direct methods typically operate on all pixel intensities, which proves to be highly redundant. In contrast our method builds on direct visual odometry methods naturally with minimal added computation. It is not only more efficient than direct dense methods since we iterate with a fraction of the pixels, but also more accurate. We achieve high accuracy and efficiency by extracting edges from only one image, and utilize robust Gauss-Newton to minimize the photometric error of these edge pixels. This simultaneously finds the edge pixels in the reference image, as well as the relative camera pose that minimizes the photometric error. We test various edge detectors, including learned edges, and determine that the optimal edge detector for this method is the Canny edge detection algorithm using automatic thresholding. We highlight key differences between our edge direct method and direct dense methods, in particular how higher levels of image pyramids can lead to significant aliasing effects and result in incorrect solution convergence. We show experimentally that reducing the photometric error of edge pixels also reduces the photometric error of all pixels, and we show through an ablation study the increase in accuracy obtained by optimizing edge pixels only. We evaluate our method on the RGB-D TUM benchmark on which we achieve state-of-the-art performance.
Any system that extracts edges must choose between several edge extraction algorithms. The most prominent are Canny edges @cite_6 , followed by edges extracted from Laplacian of Gaussian (LoG) filters which are efficiently implemented using Difference of Gaussians (DoG). Another type of edge that is not as popular but is very simple are Sobel edges. More recently, there has been research involving the learning of edge features. In @cite_20 the authors utilize structured forests, and in @cite_15 the authors utilize deep learning. Instead of selecting one, we test various edge extraction algorithms with our system select the optimal edge extraction algorithm. Note that @cite_15 requires the use of a GPU and is far from real-time, so we do not consider this method.
@cite_15 @cite_20 @cite_6
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The human vision is usually considered a multiscale, hierarchical knowledge extraction system. Inspired by this fact, multiscale techniques for computer vision perform a sequential analysis, driven by different interpretations of the concept of scale. In the case of edge detection, the scale usually relates to the size of the region where the intensity changes are measured or to the size of the regularization filter applied before edge extraction. Multiscale edge detection methods constitute an effort to combine the spatial accuracy of fine-scale methods with the ability to deal with spurious responses inherent to coarse-scale methods. In this work we introduce a multiscale method for edge detection based on increasing Gaussian smoothing, the Sobel operators and coarse-to-fine edge tracking. We include visual examples and quantitative evaluations illustrating the benefits of our proposal. We propose to employ bilateral filters to solve the problem of edge detection. The proposed methodology presents an efficient and noise robust method for detecting edges. Classical bilateral filters smooth images without distorting edges. In this paper, we modify the bilateral filter to perform edge detection, which is the opposite of bilateral smoothing. The Gaussian domain kernel of the bilateral filter is replaced with an edge detection mask, and Gaussian range kernel is replaced with an inverted Gaussian kernel. The modified range kernel serves to emphasize dissimilar regions. The resulting approach effectively adapts the detection mask according as the pixel intensity differences. The results of the proposed algorithm are compared with those of standard edge detection masks. Comparisons of the bilateral edge detector with Canny edge detection algorithm, both after non-maximal suppression, are also provided. The results of our technique are observed to be better and noise-robust than those offered by methods employing masks alone, and are also comparable to the results from Canny edge detector, outperforming it in certain cases. Deep learning is a promising approach for extracting accurate information from raw sensor data from IoT devices deployed in complex environments. Because of its multilayer structure, deep learning is also appropriate for the edge computing environment. Therefore, in this article, we first introduce deep learning for IoTs into the edge computing environment. Since existing edge nodes have limited processing capability, we also design a novel offloading strategy to optimize the performance of IoT deep learning applications with edge computing. In the performance evaluation, we test the performance of executing multiple deep learning tasks in an edge computing environment with our strategy. The evaluation results show that our method outperforms other optimization solutions on deep learning for IoT. Traditional differential-based edge detection suffers from abrupt degradation in performance when images are corrupted by impulse noises. The morphological operators such as the median filters and weighted median filters possess the intrinsic ability to counteract impulse noise. In this paper, by combining the biwindow configuration with weighted median filters, anisotropic morphological directional derivatives (AMDDs) robust to impulse noise are proposed to measure the local grayscale variation around a pixel. For ideal step edges, the AMDD spatial response and directional representation are derived. The characteristics and edge resolution of two kinds of typical biwindows are analyzed thoroughly. In terms of the AMDD spatial response and directional representation of ideal step edges, the spatial matched filter is used to extract the edge strength map (ESM) from the AMDDs of an image. The spatial and directional matched filters are used to extract the edge direction map (EDM). Embedding the extracted ESM and EDM into the standard route of the differential-based edge detection, an anti-impulse-noise AMDD-based edge detector is constructed. It is compared with the existing state-of-the-art detectors on a recognized image dataset for edge detection evaluation. The results show that it attains competitive performance in noise-free and Gaussian noise cases and the best performance in impulse noise cases. In this work we present a novel algorithm for realtime visual odometry for a monocular camera. The main idea is to develop an approach between classical feature-based visual odometry systems and modern direct dense semi-dense methods, trying to benefit from the best attributes of both. Similar to feature-based systems, we extract information from the images, instead of working with raw image intensities as direct methods. In particular, the information extracted are the edges present in the image, while the rest of the algorithm is designed to take advantage of the structural information provided when pixels are treated as edges. Edge extraction is an efficient and higly parallelizable operation. The edge depth information extracted is dense enough to allow acceptable surface fitting, similar to modern semi-dense methods. This is a valuable attribute that feature-based odometry lacks. Experimental results show that the proposed method has similar drift than state of the art feature-based and direct methods, and is a simple algorithm that runs at realtime and can be parallelized. Finally, we have also developed an inertial aided version that successfully stabilizes an unmanned air vehicle in complex indoor environments using only a frontal camera, while running the complete solution in the embedded hardware on board the vehicle. While many visual simultaneous localization and mapping (SLAM) systems use point features as landmarks, few take advantage of the edge information in images. Those SLAM systems that do observe edge features do not consider edges with all degrees of freedom. Edges are difficult to use in vision SLAM because of selection, observation, initialization and data association challenges. A map that includes edge features, however, contains higher-order geometric information useful both during and after SLAM. We define a well-localized edge landmark and present an efficient algorithm for selecting such landmarks. Further, we describe how to initialize new landmarks, observe mapped landmarks in subsequent images, and address the data association challenges of edges. Our methods, implemented in a particle-filter SLAM system, operate at frame rate on live video sequences. The main contribution of this paper is an extended Kalman filter (EKF)based algorithm for estimating the 6 DOF pose of a camera using monocular images of an indoor environment. In contrast to popular visual simultaneous localisation and mapping algorithms, the technique proposed relies on a pre-built map represented as an unsigned distance function of the ground plane edges. Images from the camera are processed using a Convolutional Neural Network (CNN)to extract a ground plane edge image. Pixels that belong to these edges are used in the observation equation of the EKF to estimate the camera location. Use of the CNN makes it possible to extract ground plane edges under significant changes to scene illumination. The EKF framework lends itself to use of a suitable motion model, fusing information from any other sensors such as wheel encoders or inertial measurement units, if available, and rejecting spurious observations. A series of experiments are presented to demonstrate the effectiveness of the proposed technique. Abstract This paper proposes an artificial neural network that extracts axes of symmetry from visual patterns. The input patterns can be plane figures, complicated line drawings or gray-scaled natural images taken by CCD cameras. The network has a hierarchical multi-layered architecture, which resembles that of the lower stages of the neocognitron. It consists of a contrast-extracting layer, edge-extracting layers (simple and complex types), and layers extracting symmetry axes. The network extracts oriented edges from the input image first, and then tries to extract axes of symmetry. Our network checks conditions of symmetry, not directly from the oriented edges, but from a blurred version of them. The use of blurred signals not only reduces the computational cost greatly, but also endows the network with a large tolerance to deformation of input patterns. It is important to get blurred signals, not directly from an input image, but from the oriented edges. Although information of edge locations becomes ambiguous after the blurring operation, most of important features of the original image can still remain stable. If the input image is directly blurred, however, most of the important features in the image will be lost. We present a new image editing method, particularly effective for sharpening major edges by increasing the steepness of transition while eliminating a manageable degree of low-amplitude structures. The seemingly contradictive effect is achieved in an optimization framework making use of L0 gradient minimization, which can globally control how many non-zero gradients are resulted in to approximate prominent structure in a sparsity-control manner. Unlike other edge-preserving smoothing approaches, our method does not depend on local features, but instead globally locates important edges. It, as a fundamental tool, finds many applications and is particularly beneficial to edge extraction, clip-art JPEG artifact removal, and non-photorealistic effect generation. Let G = (V, E) be a directed graph with positive edge weights, let s, t be two specified vertices in this graph, and let π(s, t) be the shortest path between them. In the replacement paths problem we want to compute, for every edge e on π(s, t), the shortest path from s to t that avoids e. The naive solution to this problem would be to remove each edge e, one at a time, and compute the shortest s - t path each time; this yields a running time of O(mn + n2 log n). Gotthilf and Lewenstein [8] recently improved this to O(mn+n2 log log n), but no o(mn) algorithms are known. We present the first approximation algorithm for replacement paths in directed graphs with positive edge weights. Given any e e [0, 1), our algorithm returns (1 + e)-approximate replacement paths in O(e-1 log2 n log(nC c)(m+n log n)) = O(m log(nC c) e) time, where C is the largest edge weight in the graph and c is the smallest weight. We also present an even faster (1 + e) approximate algorithm for the simpler problem of approximating the k shortest simple s - t paths in a directed graph with positive edge weights. That is, our algorithm outputs k different simple s - t paths, where the kth path we output is a (1 + e) approximation to the actual kth shortest simple s - t path. The running time of our algorithm is O(ke-1 log2 n(m + n log n)) = O(km e). The fastest exact algorithm for this problem has a running time of O(k(mn+n2 log log n)) = O(kmn) [8]. The previous best approximation algorithm was developed by Roditty [15]; it has a stretch of 3 2 and a running time of O(km√n) (it does not work for replacement paths). Note that all of our running times are nearly optimal except for the O (log(nC c)) factor in the replacements paths algorithm. Also, our algorithm can solve the variant of approximate replacement paths where we avoid vertices instead of edges. When computing descriptors of image data, the type of information that can be extracted may be strongly dependent on the scales at which the image operators are applied. This article presents a systematic methodology for addressing this problem. A mechanism is presented for automatic selection of scale levels when detecting one-dimensional image features, such as edges and ridges. A novel concept of a scale-space edge is introduced, defined as a connected set of points in scale-space at which: (i) the gradient magnitude assumes a local maximum in the gradient direction, and (ii) a normalized measure of the strength of the edge response is locally maximal over scales. An important consequence of this definition is that it allows the scale levels to vary along the edge. Two specific measures of edge strength are analyzed in detail, the gradient magnitude and a differential expression derived from the third-order derivative in the gradient direction. For a certain way of normalizing these differential descriptors, by expressing them in terms of so-called γ-normalized derivatives, an immediate consequence of this definition is that the edge detector will adapt its scale levels to the local image structure. Specifically, sharp edges will be detected at fine scales so as to reduce the shape distortions due to scale-space smoothing, whereas sufficiently coarse scales will be selected at diffuse edges, such that an edge model is a valid abstraction of the intensity profile across the edge. Since the scale-space edge is defined from the intersection of two zero-crossing surfaces in scale-space, the edges will by definition form closed curves. This simplifies selection of salient edges, and a novel significance measure is proposed, by integrating the edge strength along the edge. Moreover, the scale information associated with each edge provides useful clues to the physical nature of the edge. With just slight modifications, similar ideas can be used for formulating ridge detectors with automatic selection, having the characteristic property that the selected scales on a scale-space ridge instead reflect the width of the ridge. It is shown how the methodology can be implemented in terms of straightforward visual front-end operations, and the validity of the approach is supported by theoretical analysis as well as experiments on real-world and synthetic data. Text detection in videos is challenging due to low resolution and complex background of videos. Besides, an arbitrary orientation of scene text lines in video makes the problem more complex and challenging. This paper presents a new method that extracts text lines of any orientations based on gradient vector flow (GVF) and neighbor component grouping. The GVF of edge pixels in the Sobel edge map of the input frame is explored to identify the dominant edge pixels which represent text components. The method extracts edge components corresponding to dominant pixels in the Sobel edge map, which we call text candidates (TC) of the text lines. We propose two grouping schemes. The first finds nearest neighbors based on geometrical properties of TC to group broken segments and neighboring characters which results in word patches. The end and junction points of skeleton of the word patches are considered to eliminate false positives, which output the candidate text components (CTC). The second is based on the direction and the size of the CTC to extract neighboring CTC and to restore missing CTC, which enables arbitrarily oriented text line detection in video frame. Experimental results on different datasets, including arbitrarily oriented text data, nonhorizontal and horizontal text data, Hua's data and ICDAR-03 data (camera images), show that the proposed method outperforms existing methods in terms of recall, precision and f-measure. In computer vision, the one-parameter family of images obtained from the Laplacian-of-a-Gaussian-filtered version of the image, parameterized by the width of the Gaussian, has proved to be a useful data structure for the extraction of feature data. In particular, the zero crossings of this so-called scale-space data are associated with edges and have been proposed by D. Marr (1982) and others as the basis of a representation of the image data. The question arises as to whether the representation is complete and stable. The authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations. They formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error, and they present results showing that the reconstruction is possible but can be unstable. They further show that the method applies when gradient data along the zero crossings are included in the representation, and they demonstrate empirically that the reconstruction is then stable. > A fundamental question for edge detection is how faint an edge can be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce a hierarchical edge detection algorithm designed to detect faint curved edges in noisy images. In our formalism we view edge detection as a search in a space of feasible curves, and derive expressions to characterize the behavior of the optimal detection threshold as a function of curve length and the combinatorics of the search space. We then present an algorithm that efficiently searches for edges through a very large set of curves by hierarchically constructing difference filters that match the curves traced by the sought edges. We demonstrate the utility of our algorithm in simulations and in applications to challenging real images. This paper shows that the introduction of non-uniform blur is very useful for comparing images, and proposes a neural network model that extracts axes of symmetry from visual patterns. The blurring operation greatly increases robustness against deformations and various kinds of noise, and largely reduces computational cost. Asymmetry between two groups of signals can be detected in a single action by the use of non-uniform blur having a cone-shaped distribution.The proposed model is a hierarchical multi-layered network, which consists of a contrast-extracting layer, edge-extracting layers (simple and complex types), and layers extracting symmetry axes. The model extracts oriented edges from an input image first, and then tries to extract axes of symmetry. The model checks conditions of symmetry, not directly from the oriented edges, but from a blurred version of the response of edge-extracting layer. The input patterns can be complicated line drawings, plane figures or gray-scaled natural images taken by CCD cameras. Recent years have witnessed the emergence of new image smoothing techniques which have provided new insights and raised new questions about the nature of this well-studied problem. Specifically, these models separate a given image into its structure and texture layers by utilizing non-gradient based definitions for edges or special measures that distinguish edges from oscillations. In this study, we propose an alternative yet simple image smoothing approach which depends on covariance matrices of simple image features, aka the region covariances. The use of second order statistics as a patch descriptor allows us to implicitly capture local structure and texture information and makes our approach particularly effective for structure extraction from texture. Our experimental results have shown that the proposed approach leads to better image decompositions as compared to the state-of-the-art methods and preserves prominent edges and shading well. Moreover, we also demonstrate the applicability of our approach on some image editing and manipulation tasks such as image abstraction, texture and detail enhancement, image composition, inverse halftoning and seam carving. Abstract We present a system at the junction between Computer Vision and Computer Graphics, to produce a three-dimensional (3D) model of an object as observed in a single image, with a minimum of high-level interaction from a user. The input to our system is a single image. First, the user points, coarsely, at image features (edges) that are subsequently automatically and reproducibly extracted in real-time. The user then performs a high level labeling of the curves (e.g. limb edge, cross-section) and specifies relations between edges (e.g. symmetry, surface or part). NURBS are used as working representation of image edges. The objects described by the user specified, qualitative relationships are then reconstructed either as a set of connected parts modeled as Generalized Cylinders, or as a set of 3D surfaces for 3D bilateral symmetric objects. In both cases, the texture is also extracted from the image. Our system runs in real-time on a PC. Edge server placement problem is a hot topic in mobile edge computing. In this paper, we study the problem of energy-aware edge server placement and try to find a more effective placement scheme with low energy consumption. Then, we formulate the problem as a multi-objective optimization problem and devise a particle swarm optimization based energy-aware edge server placement algorithm to find the optimal solution. We evaluate the algorithm based on the real dataset from Shanghai Telecom and the results show our algorithm can reduce more than 10 energy consumption with over 15 improvement in computing resource utilization, compared to other algorithms. The purpose of object matching is to decide the similarity between two objects. This paper introduces 24 possible distance measures based on the Hausdorff distance between two point sets. These measures can be used to match two sets of edge points extracted from any two objects. Based on experiments on synthetic images containing various levels of noise, the authors determined that one of these distance measures, called the modified Hausdorff distance (MHD) has the best performance for object matching. The advantages of MHD ever other distances are also demonstrated on several edge snaps of objects extracted from real images. The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m n and d log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.