Edge, Ridge, and Blob Detection with Symmetric Molecules
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Scale Invariant Interest Points with Shearlets
Scale Invariant Interest Points with Shearlets Miguel A. Duval-Poo1, Nicoletta Noceti1, Francesca Odone1, and Ernesto De Vito2 1Dipartimento di Informatica Bioingegneria Robotica e Ingegneria dei Sistemi (DIBRIS), Universit`adegli Studi di Genova, Italy 2Dipartimento di Matematica (DIMA), Universit`adegli Studi di Genova, Italy Abstract Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discon- tinuities such as edges and corners at multiple scales. In this work we address the problem of detecting and describing blob-like features in the shearlets framework. We derive a measure which is very effective for blob detection and closely related to the Laplacian of Gaussian. We demon- strate the measure satisfies the perfect scale invariance property in the continuous case. In the discrete setting, we derive algorithms for blob detection and keypoint description. Finally, we provide qualitative justifi- cations of our findings as well as a quantitative evaluation on benchmark data. We also report an experimental evidence that our method is very suitable to deal with compressed and noisy images, thanks to the sparsity property of shearlets. 1 Introduction Feature detection consists in the extraction of perceptually interesting low-level features over an image, in preparation of higher level processing tasks. In the last decade a considerable amount of work has been devoted to the design of effective and efficient local feature detectors able to associate with a given interesting point also scale and orientation information. Scale-space theory has been one of the main sources of inspiration for this line of research, providing an effective framework for detecting features at multiple scales and, to some extent, to devise scale invariant image descriptors. -
Hough Transform, Descriptors Tammy Riklin Raviv Electrical and Computer Engineering Ben-Gurion University of the Negev Hough Transform
DIGITAL IMAGE PROCESSING Lecture 7 Hough transform, descriptors Tammy Riklin Raviv Electrical and Computer Engineering Ben-Gurion University of the Negev Hough transform y m x b y m 3 5 3 3 2 2 3 7 11 10 4 3 2 3 1 4 5 2 2 1 0 1 3 3 x b Slide from S. Savarese Hough transform Issues: • Parameter space [m,b] is unbounded. • Vertical lines have infinite gradient. Use a polar representation for the parameter space Hough space r y r q x q x cosq + ysinq = r Slide from S. Savarese Hough Transform Each point votes for a complete family of potential lines: Each pencil of lines sweeps out a sinusoid in Their intersection provides the desired line equation. Hough transform - experiments r q Image features ρ,ϴ model parameter histogram Slide from S. Savarese Hough transform - experiments Noisy data Image features ρ,ϴ model parameter histogram Need to adjust grid size or smooth Slide from S. Savarese Hough transform - experiments Image features ρ,ϴ model parameter histogram Issue: spurious peaks due to uniform noise Slide from S. Savarese Hough Transform Algorithm 1. Image à Canny 2. Canny à Hough votes 3. Hough votes à Edges Find peaks and post-process Hough transform example http://ostatic.com/files/images/ss_hough.jpg Incorporating image gradients • Recall: when we detect an edge point, we also know its gradient direction • But this means that the line is uniquely determined! • Modified Hough transform: for each edge point (x,y) θ = gradient orientation at (x,y) ρ = x cos θ + y sin θ H(θ, ρ) = H(θ, ρ) + 1 end Finding lines using Hough transform -
Fast Image Registration Using Pyramid Edge Images
Fast Image Registration Using Pyramid Edge Images Kee-Baek Kim, Jong-Su Kim, Sangkeun Lee, and Jong-Soo Choi* The Graduate School of Advanced Imaging Science, Multimedia and Film, Chung-Ang University, Seoul, Korea(R.O.K) *Corresponding author’s E-mail address: [email protected] Abstract: Image registration has been widely used in many image processing-related works. However, the exiting researches have some problems: first, it is difficult to find the accurate information such as translation, rotation, and scaling factors between images; and it requires high computational cost. To resolve these problems, this work proposes a Fourier-based image registration using pyramid edge images and a simple line fitting. Main advantages of the proposed approach are that it can compute the accurate information at sub-pixel precision and can be carried out fast for image registration. Experimental results show that the proposed scheme is more efficient than other baseline algorithms particularly for the large images such as aerial images. Therefore, the proposed algorithm can be used as a useful tool for image registration that requires high efficiency in many fields including GIS, MRI, CT, image mosaicing, and weather forecasting. Keywords: Image registration; FFT; Pyramid image; Aerial image; Canny operation; Image mosaicing. registration information as image size increases [3]. 1. Introduction To solve these problems, this work employs a pyramid-based image decomposition scheme. Image registration is a basic task in image Specifically, first, we use the Gaussian filter to processing to combine two or more images that are remove the noise because it causes many undesired partially overlapped. -
Scale Invariant Feature Transform (SIFT) Why Do We Care About Matching Features?
Scale Invariant Feature Transform (SIFT) Why do we care about matching features? • Camera calibration • Stereo • Tracking/SFM • Image moiaicing • Object/activity Recognition • … Objection representation and recognition • Image content is transformed into local feature coordinates that are invariant to translation, rotation, scale, and other imaging parameters • Automatic Mosaicing • http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html We want invariance!!! • To illumination • To scale • To rotation • To affine • To perspective projection Types of invariance • Illumination Types of invariance • Illumination • Scale Types of invariance • Illumination • Scale • Rotation Types of invariance • Illumination • Scale • Rotation • Affine (view point change) Types of invariance • Illumination • Scale • Rotation • Affine • Full Perspective How to achieve illumination invariance • The easy way (normalized) • Difference based metrics (random tree, Haar, and sift, gradient) How to achieve scale invariance • Pyramids • Scale Space (DOG method) Pyramids – Divide width and height by 2 – Take average of 4 pixels for each pixel (or Gaussian blur with different ) – Repeat until image is tiny – Run filter over each size image and hope its robust How to achieve scale invariance • Scale Space: Difference of Gaussian (DOG) – Take DOG features from differences of these images‐producing the gradient image at different scales. – If the feature is repeatedly present in between Difference of Gaussians, it is Scale Invariant and should be kept. Differences Of Gaussians -
Exploiting Information Theory for Filtering the Kadir Scale-Saliency Detector
Introduction Method Experiments Conclusions Exploiting Information Theory for Filtering the Kadir Scale-Saliency Detector P. Suau and F. Escolano {pablo,sco}@dccia.ua.es Robot Vision Group University of Alicante, Spain June 7th, 2007 P. Suau and F. Escolano Bayesian filter for the Kadir scale-saliency detector 1 / 21 IBPRIA 2007 Introduction Method Experiments Conclusions Outline 1 Introduction 2 Method Entropy analysis through scale space Bayesian filtering Chernoff Information and threshold estimation Bayesian scale-saliency filtering algorithm Bayesian scale-saliency filtering algorithm 3 Experiments Visual Geometry Group database 4 Conclusions P. Suau and F. Escolano Bayesian filter for the Kadir scale-saliency detector 2 / 21 IBPRIA 2007 Introduction Method Experiments Conclusions Outline 1 Introduction 2 Method Entropy analysis through scale space Bayesian filtering Chernoff Information and threshold estimation Bayesian scale-saliency filtering algorithm Bayesian scale-saliency filtering algorithm 3 Experiments Visual Geometry Group database 4 Conclusions P. Suau and F. Escolano Bayesian filter for the Kadir scale-saliency detector 3 / 21 IBPRIA 2007 Introduction Method Experiments Conclusions Local feature detectors Feature extraction is a basic step in many computer vision tasks Kadir and Brady scale-saliency Salient features over a narrow range of scales Computational bottleneck (all pixels, all scales) Applied to robot global localization → we need real time feature extraction P. Suau and F. Escolano Bayesian filter for the Kadir scale-saliency detector 4 / 21 IBPRIA 2007 Introduction Method Experiments Conclusions Salient features X HD(s, x) = − Pd,s,x log2Pd,s,x d∈D Kadir and Brady algorithm (2001): most salient features between scales smin and smax P. -
Hough Transform 1 Hough Transform
Hough transform 1 Hough transform The Hough transform ( /ˈhʌf/) is a feature extraction technique used in image analysis, computer vision, and digital image processing.[1] The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a parameter space, from which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform. The classical Hough transform was concerned with the identification of lines in the image, but later the Hough transform has been extended to identifying positions of arbitrary shapes, most commonly circles or ellipses. The Hough transform as it is universally used today was invented by Richard Duda and Peter Hart in 1972, who called it a "generalized Hough transform"[2] after the related 1962 patent of Paul Hough.[3] The transform was popularized in the computer vision community by Dana H. Ballard through a 1981 journal article titled "Generalizing the Hough transform to detect arbitrary shapes". Theory In automated analysis of digital images, a subproblem often arises of detecting simple shapes, such as straight lines, circles or ellipses. In many cases an edge detector can be used as a pre-processing stage to obtain image points or image pixels that are on the desired curve in the image space. Due to imperfections in either the image data or the edge detector, however, there may be missing points or pixels on the desired curves as well as spatial deviations between the ideal line/circle/ellipse and the noisy edge points as they are obtained from the edge detector. -
Sobel Operator and Canny Edge Detector ECE 480 Fall 2013 Team 4 Daniel Kim
P a g e | 1 Sobel Operator and Canny Edge Detector ECE 480 Fall 2013 Team 4 Daniel Kim Executive Summary In digital image processing (DIP), edge detection is an important subject matter. There are numerous edge detection methods such as Prewitt, Kirsch, and Robert cross. Two different types of edge detectors are explored and analyzed in this paper: Sobel operator and Canny edge detector. The performance of two edge detection methods are then compared with several input images. Keywords : Digital Image Processing, Edge Detection, Sobel Operator, Canny Edge Detector, Computer Vision, OpenCV P a g e | 2 Table of Contents 1| Introduction……………………………………………………………………………. 3 2|Sobel Operator 2.1 Background……………………………………………………………………..3 2.2 Example………………………………………………………………………...4 3|Canny Edge Detector 3.1 Background…………………………………………………………………….5 3.2 Example………………………………………………………………………...5 4|Comparison of Sobel and Canny 4.1 Discussion………………………………………………………………………6 4.2 Example………………………………………………………………………...7 5|Conclusion………………………………………………………………………............7 6|Appendix 6.1 OpenCV Sobel tutorial code…............................................................................8 6.2 OpenCV Canny tutorial code…………..…………………………....................9 7|Reference………………………………………………………………………............10 P a g e | 3 1) Introduction Edge detection is a crucial step in object recognition. It is a process of finding sharp discontinuities in an image. The discontinuities are abrupt changes in pixel intensity which characterize boundaries of objects in a scene. In short, the goal of edge detection is to produce a line drawing of the input image. The extracted features are then used by computer vision algorithms, e.g. recognition and tracking. A classical method of edge detection involves the use of operators, a two dimensional filter. An edge in an image occurs when the gradient is greatest. -
Context-Aware Features and Robust Image Representations 5 6 ∗ 7 P
CAKE_article_final.tex Click here to view linked References 1 2 3 4 Context-Aware Features and Robust Image Representations 5 6 ∗ 7 P. Martinsa, , P. Carvalhoa,C.Gattab 8 aCenter for Informatics and Systems, University of Coimbra, Coimbra, Portugal 9 bComputer Vision Center, Autonomous University of Barcelona, Barcelona, Spain 10 11 12 13 14 Abstract 15 16 Local image features are often used to efficiently represent image content. The limited number of types of 17 18 features that a local feature extractor responds to might be insufficient to provide a robust image repre- 19 20 sentation. To overcome this limitation, we propose a context-aware feature extraction formulated under an 21 information theoretic framework. The algorithm does not respond to a specific type of features; the idea is 22 23 to retrieve complementary features which are relevant within the image context. We empirically validate the 24 method by investigating the repeatability, the completeness, and the complementarity of context-aware fea- 25 26 tures on standard benchmarks. In a comparison with strictly local features, we show that our context-aware 27 28 features produce more robust image representations. Furthermore, we study the complementarity between 29 strictly local features and context-aware ones to produce an even more robust representation. 30 31 Keywords: Local features, Keypoint extraction, Image content descriptors, Image representation, Visual 32 saliency, Information theory. 33 34 35 1. Introduction While it is widely accepted that a good local 36 37 feature extractor should retrieve distinctive, accu- 38 Local feature detection (or extraction, if we want 39 rate, and repeatable features against a wide vari- to use a more semantically correct term [1]) is a 40 ety of photometric and geometric transformations, 41 central and extremely active research topic in the 42 it is equally valid to claim that these requirements fields of computer vision and image analysis. -
View Matching with Blob Features
View Matching with Blob Features Per-Erik Forssen´ and Anders Moe Computer Vision Laboratory Department of Electrical Engineering Linkoping¨ University, Sweden Abstract mographic transformation that is not part of the affine trans- formation. This means that our results are relevant for both This paper introduces a new region based feature for ob- wide baseline matching and 3D object recognition. ject recognition and image matching. In contrast to many A somewhat related approach to region based matching other region based features, this one makes use of colour is presented in [1], where tangents to regions are used to de- in the feature extraction stage. We perform experiments on fine linear constraints on the homography transformation, the repeatability rate of the features across scale and incli- which can then be found through linear programming. The nation angle changes, and show that avoiding to merge re- connection is that a line conic describes the set of all tan- gions connected by only a few pixels improves the repeata- gents to a region. By matching conics, we thus implicitly bility. Finally we introduce two voting schemes that allow us match the tangents of the ellipse-approximated regions. to find correspondences automatically, and compare them with respect to the number of valid correspondences they 2. Blob features give, and their inlier ratios. We will make use of blob features extracted using a clus- tering pyramid built using robust estimation in local image regions [2]. Each extracted blob is represented by its aver- 1. Introduction age colour pk,areaak, centroid mk, and inertia matrix Ik. I.e. -
Edge Detection Low Level
Image Processing - Lesson 10 Image Processing - Computer Vision Edge Detection Low Level • Edge detection masks Image Processing representation, compression,transmission • Gradient Detectors • Compass Detectors image enhancement • Second Derivative - Laplace detectors • Edge Linking edge/feature finding • Hough Transform image "understanding" Computer Vision High Level UFO - Unidentified Flying Object Point Detection -1 -1 -1 Convolution with: -1 8 -1 -1 -1 -1 Large Positive values = light point on dark surround Large Negative values = dark point on light surround Example: 5 5 5 5 5 -1 -1 -1 5 5 5 100 5 * -1 8 -1 5 5 5 5 5 -1 -1 -1 0 0 -95 -95 -95 = 0 0 -95 760 -95 0 0 -95 -95 -95 Edge Definition Edge Detection Line Edge Line Edge Detectors -1 -1 -1 -1 -1 2 -1 2 -1 2 -1 -1 2 2 2 -1 2 -1 -1 2 -1 -1 2 -1 -1 -1 -1 2 -1 -1 -1 2 -1 -1 -1 2 gray value gray x edge edge Step Edge Step Edge Detectors -1 1 -1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 -1 1 1 1 1 1 1 gray value gray -1 -1 1 1 1 -1 1 1 x edge edge Example Edge Detection by Differentiation Step Edge detection by differentiation: 1D image f(x) gray value gray x 1st derivative f'(x) threshold |f'(x)| - threshold Pixels that passed the threshold are -1 -1 1 1 -1 -1 -1 -1 Edge Pixels -1 -1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 1 1 -1 1 1 Gradient Edge Detection Gradient Edge - Examples ∂f ∂x ∇ f((x,y) = Gradient ∂f ∂y ∂f ∇ f((x,y) = ∂x , 0 f 2 f 2 Gradient Magnitude ∂ + ∂ √( ∂ x ) ( ∂ y ) ∂f ∂f Gradient Direction tg-1 ( / ) ∂y ∂x ∂f ∇ f((x,y) = 0 , ∂y Differentiation in Digital Images Example Edge horizontal - differentiation approximation: ∂f(x,y) Original FA = ∂x = f(x,y) - f(x-1,y) convolution with [ 1 -1 ] Gradient-X Gradient-Y vertical - differentiation approximation: ∂f(x,y) FB = ∂y = f(x,y) - f(x,y-1) convolution with 1 -1 Gradient-Magnitude Gradient-Direction Gradient (FA , FB) 2 2 1/2 Magnitude ((FA ) + (FB) ) Approx. -
Histogram of Directions by the Structure Tensor
Histogram of Directions by the Structure Tensor Josef Bigun Stefan M. Karlsson Halmstad University Halmstad University IDE SE-30118 IDE SE-30118 Halmstad, Sweden Halmstad, Sweden [email protected] [email protected] ABSTRACT entity). Also, by using the approach of trying to reduce di- Many low-level features, as well as varying methods of ex- rectionality measures to the structure tensor, insights are to traction and interpretation rely on directionality analysis be gained. This is especially true for the study of the his- (for example the Hough transform, Gabor filters, SIFT de- togram of oriented gradient (HOGs) features (the descriptor scriptors and the structure tensor). The theory of the gra- of the SIFT algorithm[12]). We will present both how these dient based structure tensor (a.k.a. the second moment ma- are very similar to the structure tensor, but also detail how trix) is a very well suited theoretical platform in which to they differ, and in the process present a different algorithm analyze and explain the similarities and connections (indeed for computing them without binning. In this paper, we will often equivalence) of supposedly different methods and fea- limit ourselves to the study of 3 kinds of definitions of di- tures that deal with image directionality. Of special inter- rectionality, and their associated features: 1) the structure est to this study is the SIFT descriptors (histogram of ori- tensor, 2) HOGs , and 3) Gabor filters. The results of relat- ented gradients, HOGs). Our analysis of interrelationships ing the Gabor filters to the tensor have been studied earlier of prominent directionality analysis tools offers the possibil- [3], [9], and so for brevity, more attention will be given to ity of computation of HOGs without binning, in an algo- the HOGs. -
Pavement Crack Detection by Ridge Detection on Fractional Calculus and Dual-Thresholds
International Journal of Multimedia and Ubiquitous Engineering Vol.10, No.4 (2015), pp.19-30 http://dx.doi.org/10.14257/ijmue.2015.10.4.03 Pavement Crack Detection by Ridge Detection on Fractional Calculus and Dual-thresholds Song Hongxun, Wang Weixing, Wang Fengping, Wu Linchun and Wang Zhiwei Shaanxi Road Traffic Intelligent Detection and Equipment Engineering Technology Research Center, Chang’an University, Xi’an, China School of Information Engineering, Chang’an University, Xi’an, China songhongx @163.com Abstract In this paper, a new road surface crack detection algorithm is proposed; it is based on the ridge edge detection on fractional calculus and the dual-thresholds on a binary image. First, the multi-scale reduction of image data is used to shrink an original image to eliminate noise, which can not only smooth an image but also enhance cracks. Then, the main cracks are extracted by using the ridge edge detection on fractional calculus in a grey scale image. Subsequently, the resulted binary image is further processed by applying both short and long line thresholds to eliminate short curves and noise for getting rough crack segments. Finally the gaps in cracks are connected with a curve connection function which is an artificial intelligence routine. The experiments show that the algorithm for pavement crack images has the good performance of noise immunity, accurate positioning, and high accuracy. It can accurately locate and detect small and thin cracks that are difficult to identify by other traditional algorithms. Keywords: Crack; Multiscale; Image enhancement; Ridge edge; Threshold 1. Introduction In a time period, any road can be damaged gradually due to traffic loads and the other natural/artificial factors, and cracks are the most common road pavement surface defects that need to mend as early as possible.