DOCSLIB.ORG

Mean Shift Theory and Applications

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mean Shift Theory and Applications Appearance-Based Tracking current frame + previous location likelihood over object location current location Mean-shift Tracking appearance model R.Collins, CSE, PSU (e.g. image template, or Mode-Seeking (e.g. mean-shift; Lucas-Kanade; CSE598G Spring 2006 particle filtering) color; intensity; edge histograms) Mean-Shift Motivation • Motivation – to track non-rigid objects, (like The mean-shift algorithm is an efficient a walking person), it is hard to specify approach to tracking objects whose an explicit 2D parametric motion model. appearance is defined by histograms. • Appearances of non-rigid objects can (not limited to only color) sometimes be modeled with color distributions Credits: Many Slides Borrowed from www.wisdom.weizmann.ac.il/~deniss/vision_spring04/files/mean_shift/mean_shift.ppt Mean Shift Theory and Applications Yaron Ukrainitz & Bernard Sarel Mean Shift Theory weizmann institute Advanced topics in computer vision even the slides on my own work! --Bob 1 Intuitive Description Intuitive Description Region of Region of interest interest Center of Center of mass mass Mean Shift Mean Shift vector vector Objective : Find the densest region Objective : Find the densest region Distribution of identical billiard balls Distribution of identical billiard balls Intuitive Description Intuitive Description Region of Region of interest interest Center of Center of mass mass Mean Shift Mean Shift vector vector Objective : Find the densest region Objective : Find the densest region Distribution of identical billiard balls Distribution of identical billiard balls Intuitive Description Intuitive Description Region of Region of interest interest Center of Center of mass mass Mean Shift Mean Shift vector vector Objective : Find the densest region Objective : Find the densest region Distribution of identical billiard balls Distribution of identical billiard balls 2 Intuitive Description What is Mean Shift ? Region of interest A tool for: Center of Finding modes in a set of data samples, manifesting an mass underlying probability density function (PDF) in RN PDF in feature space • Color space Non-parametric • Scale spaceDensity Estimation • Actually any feature space you can conceive • … Discrete PDF Representation Data Non-parametric Density GRADIENT Estimation (Mean Shift) Objective : Find the densest region Distribution of identical billiard balls PDF Analysis Non-Parametric Density Estimation Non-Parametric Density Estimation Assumption : The data points are sampled from an underlying PDF Data point density implies PDF value ! Assumed Underlying PDF Real Data Samples Assumed Underlying PDF Real Data Samples Non-Parametric Density Estimation Appearance via Color Histograms R’ B’ G’ Color distribution (1D histogram discretize normalized to have unit weight) R’ = R << (8 - nbits) Total histogram size is (2^(8-nbits))^3 G’ = G << (8 - nbits) B’ = B << (8-nbits) example, 4-bit encoding of R,G and B channels yields a histogram of size 16*16*16 = 4096. Assumed Underlying PDF Real Data Samples 3 Smaller Color Histograms Color Histogram Example Histogram information can be much much smaller if we are willing to accept a loss in color resolvability. red green blue Marginal R distribution R’ G’ Marginal G distribution B’ discretize Marginal B distribution R’ = R << (8 - nbits) Total histogram size is 3*(2^(8-nbits)) G’ = G << (8 - nbits) B’ = B << (8-nbits) example, 4-bit encoding of R,G and B channels yields a histogram of size 3*16 = 48. Normalized Color Intro to Parzen Estimation (Aka Kernel Density Estimation) (r,g,b) (r’,g’,b’) = (r,g,b) / (r+g+b) Mathematical model of how histograms are formed Assume continuous data points Normalized color divides out pixel luminance (brightness), leaving behind only chromaticity (color) information. The result is less sensitive to variations due to illumination/shading. Parzen Estimation Example Histograms (Aka Kernel Density Estimation) Box filter Mathematical model of how histograms are formed [1 1 1] Assume continuous data points [ 1 1 1 1 1 1 1] Convolve with box filter of width w (e.g. [1 1 1]) Take samples of result, with spacing w [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] Resulting value at point u represents count of data points falling in range u-w/2 to u+w/2 Increased smoothing 4 Why Formulate it This Way? Kernel Density Estimation • Generalize from box filter to other filters • Parzen windows: Approximate probability density by estimating local density of points (same idea as a (for example Gaussian) histogram) • Gaussian acts as a smoothing filter. – Convolve points with window/kernel function (e.g., Gaussian) using scale parameter (e.g., sigma) from Hastie et al. Density Estimation at Different Scales Smoothing Scale Selection • Example: Density estimates for 5 data points with • Unresolved issue: how to pick the scale differently-scaled kernels (sigma value) of the smoothing filter • Scale influences accuracy vs. generality (overfitting) • Answer for now: a user-settable parameter from Duda et al. from Duda et al. Kernel Density Estimation Kernel Density Estimation Parzen Windows - General Framework Parzen Windows - Function Forms 1 n 1 n P()x K(x - xi ) A function of some finite number of data points P()x K(x - xi ) A function of some finite number of data points n i1 n i1 x1…xn x1…xn Kernel Properties: Data Data • Normalized K()xd x 1 In practice one uses the forms: Rd • Symmetric xK()xd x 0 d d or R K()x ck() xi K()x ck x i1 d • Exponential weight lim x K()x 0 decay x • ??? xxT K()xd x cI Same function on each dimension Function of vector length only Rd 5 Kernel Density Estimation Various Kernels Key Idea: n 1 n 1 P()x K(x - x ) A function of some finite number of data points P()x K(x - x ) i i n i1 x1…xn n i1 Superposition of kernels, centered at each data point is equivalent Examples: Data to convolving the data points with the kernel. 2 c 1 x x 1 • Epanechnikov Kernel K E ()x 0 otherwise convolution c x 1 • Uniform Kernel KU ()x 0 otherwise * Kernel Data 1 2 • Normal Kernel K N ()x c exp x 2 Kernel Density Estimation Key Idea: Gradient n 1 n 1 P(x ) K(x - x ) Give up estimating the PDF ! i P(x ) K(x-xi) n i1 Estimate ONLY the gradient ni1 2 Gradient of superposition of kernels, centered at each data point Using the x - x K(x - x ) ck i is equivalent to convolving the data points with gradient of the kernel. Kernel form: i h We get : Size of window convolution n x g c n c n i i P ()x k g i 1 x * n i n i n i1 i 1 g i gradient of Kernel Data i 1 g(x ) k()x ComputingKernel Density The EstimationMean Shift Computing The Mean Shift Gradient n x g c n c n i i P ()x k g i 1 x n i n i n i1 i 1 g i i 1 Yet another Kernel density estimation ! Simple Mean Shift procedure: • Compute mean shift vector n 2 x g n x - x n n i i x g i c c i 1 i P ()x k g x i1 h i i n m() x x 2 n i1 n i 1 n g x - x i g i i 1 h i 1 g(x ) k()x •Translate the Kernel window by m(x) g(x ) k()x 6 Mean Shift Mode Detection Mean Shift Properties What happens if we reach a saddle point ? • Automatic convergence speed – the mean shift Adaptive vector size depends on the gradient itself. Gradient Ascent Perturb the mode position • Near maxima, the steps are small and refined and check if we return back • Convergence is guaranteed for infinitesimal steps only infinitely convergent, (therefore set a lower bound) • For Uniform Kernel ( ), convergence is achieved in a finite number of steps Updated Mean Shift Procedure: • Find all modes using the Simple Mean Shift Procedure • Normal Kernel ( ) exhibits a smooth trajectory, but • Prune modes by perturbing them (find saddle points and plateaus) is slower than Uniform Kernel ( ). • Prune nearby – take highest mode in the window Real Modality Analysis Real Modality Analysis Tessellate the space Run the procedure in parallel The blue data points were traversed by the windows towards the mode with windows Real Modality Analysis Adaptive Mean Shift An example Window tracks signify the steepest ascent directions 7 Mean Shift Strengths & Weaknesses Strengths : Weaknesses : • Application independent tool • The window size (bandwidth selection) is not trivial • Suitable for real data analysis Mean Shift Applications • Inappropriate window size can • Does not assume any prior shape cause modes to be merged, (e.g. elliptical) on data clusters or generate additional “shallow” modes Use adaptive window • Can handle arbitrary feature size spaces • Only ONE parameter to choose • h (window size) has a physical meaning, unlike K-Means Clustering Clustering Synthetic Examples Cluster : All data points in the attraction basin of a mode Attraction basin : the region for which all trajectories lead to the same mode Simple Modal Structures Complex Modal Structures Mean Shift : A robust Approach Toward Feature Space Analysis, by Comaniciu, Meer Clustering Clustering Real Example Real Example Feature space: Initial window L*u*v representation centers L*u*v space representation Modes found Modes after Final clusters pruning 8 Clustering Real Example Non-Rigid Object Tracking 2D (L*u) Final clusters space representation … … Not all trajectories in the attraction basin reach the same mode Kernel Based Object Tracking, by Comaniciu, Ramesh, Meer (CRM) Non-Rigid Object Tracking Mean-Shift Object Tracking General Framework: Target Representation Real-Time Choose a Represent the Object-Based reference Choose a model in the Surveillance Driver Assistance Video Compression model in the feature space chosen feature current frame space … Current … frame Mean-Shift Object Tracking Using Mean-Shift for General Framework: Target Localization Tracking in Color Images Start from the Search in the Find best position of the model’s candidate by Two approaches: model in the neighborhood maximizing a current frame in next frame similarity func.
Load more

Recommended publications
  • Mean Shift Paper by Comaniciu and Meer Presentation by Carlo Lopez-Tello What Is the Mean Shift Algorithm?
    Mean Shift Paper by Comaniciu and Meer Presentation by Carlo Lopez-Tello What is the Mean Shift Algorithm? ● A method of finding peaks (modes) in a probability distribution ● Works without assuming any underlying structure in the distribution ● Works on multimodal distributions ● Works without assuming the number of modes Why do we care about modes? ● Given a data set we can assume that it was sampled from some pdf ● Samples are most likely to be drawn from a region near a mode ● We can use the modes to cluster the data ● Clustering has many applications: filtering, segmentation, tracking, classification, and compression. Why do we care about modes? Why use mean shift for clustering? ● K-means needs to know how many clusters to use. Clusters data into voronoi cells. ● Histograms require bin size and number of bins ● Mixture models require information about pdf structure Intuition ● We have a set of data that represents discrete samples of a distribution ● Locally we can estimate the density of the distribution with a function ● Compute the gradient of this estimation function ● Use gradient ascent to find the peak of the distribution How does it work? ● We estimate the density using: ● Where h (bandwidth) is the region around x where we are trying to estimate the density and k is some kernel function ● Instead of using the gradient of f, we use the mean shift vector: How to find a mode? 1. Start at any point 2. Compute mean shift 3. if mean shift is zero: possible mode found 4. else move to where mean shift is pointing go to 2 ● To find multiple modes we need to try all points that are more than h distance apart ● Prune modes by perturbing them and checking for convergence ● Combine modes that are close together.
    [Show full text]
  • Identification Using Telematics
    risks Article Identification Using Telematics: An Algorithm to Identify Dwell Locations Christopher Grumiau 1, Mina Mostoufi 1,* , Solon Pavlioglou 1,* and Tim Verdonck 2,3 1 Allianz Benelux, 1000 Brussels, Belgium; [email protected] 2 Department of Mathematics (Faculty of Science), University of Antwerp, 2000 Antwerpen, Belgium; [email protected] 3 Department of Mathematics (Faculty of Science), Katholieke Universiteit Leuven, 3000 Leuven, Belgium * Correspondence: mina.mostoufi@allianz.be (M.M.); [email protected] (S.P.) Received: 16 June 2020; Accepted: 21 August 2020; Published: 1 September 2020 Abstract: In this work, a method is proposed for exploiting the predictive power of a geo-tagged dataset as a means of identification of user-relevant points of interest (POI). The proposed methodology is subsequently applied in an insurance context for the automatic identification of a driver’s residence address, solely based on his pattern of movements on the map. The analysis is performed on a real-life telematics dataset. We have anonymized the considered dataset for the purpose of this study to respect privacy regulations. The model performance is evaluated based on an independent batch of the dataset for which the address is known to be correct. The model is capable of predicting the residence postal code of the user with a high level of accuracy, with an f1 score of 0.83. A reliable result of the proposed method could generate benefits beyond the area of fraud, such as general data quality inspections, one-click quotations, and better-targeted marketing. Keywords: telematics; address identification; POI; machine learning; mean shift clustering; DBSCAN clustering; fraud detection 1.
    [Show full text]
  • DBSCAN++: Towards Fast and Scalable Density Clustering
    DBSCAN++: Towards fast and scalable density clustering Jennifer Jang 1 Heinrich Jiang 2 Abstract 2, it quickly starts to exhibit quadratic behavior in high di- mensions and/or when n becomes large. In fact, we show in DBSCAN is a classical density-based clustering Figure1 that even with a simple mixture of 3-dimensional procedure with tremendous practical relevance. Gaussians, DBSCAN already starts to show quadratic be- However, DBSCAN implicitly needs to compute havior. the empirical density for each sample point, lead- ing to a quadratic worst-case time complexity, The quadratic runtime for these density-based procedures which is too slow on large datasets. We propose can be seen from the fact that they implicitly must compute DBSCAN++, a simple modification of DBSCAN density estimates for each data point, which is linear time which only requires computing the densities for a in the worst case for each query. In the case of DBSCAN, chosen subset of points. We show empirically that, such queries are proximity-based. There has been much compared to traditional DBSCAN, DBSCAN++ work done in using space-partitioning data structures such can provide not only competitive performance but as KD-Trees (Bentley, 1975) and Cover Trees (Beygelzimer also added robustness in the bandwidth hyperpa- et al., 2006) to improve query times, but these structures are rameter while taking a fraction of the runtime. all still linear in the worst-case. Another line of work that We also present statistical consistency guarantees has had practical success is in approximate nearest neigh- showing the trade-off between computational cost bor methods (e.g.
    [Show full text]
  • Deep Mean-Shift Priors for Image Restoration
    Deep Mean-Shift Priors for Image Restoration Siavash A. Bigdeli Meiguang Jin Paolo Favaro University of Bern University of Bern University of Bern [email protected] [email protected] [email protected] Matthias Zwicker University of Bern, and University of Maryland, College Park [email protected] Abstract In this paper we introduce a natural image prior that directly represents a Gaussian- smoothed version of the natural image distribution. We include our prior in a formulation of image restoration as a Bayes estimator that also allows us to solve noise-blind image restoration problems. We show that the gradient of our prior corresponds to the mean-shift vector on the natural image distribution. In addition, we learn the mean-shift vector field using denoising autoencoders, and use it in a gradient descent approach to perform Bayes risk minimization. We demonstrate competitive results for noise-blind deblurring, super-resolution, and demosaicing. 1 Introduction Image restoration tasks, such as deblurring and denoising, are ill-posed problems, whose solution requires effective image priors. In the last decades, several natural image priors have been proposed, including total variation [29], gradient sparsity priors [12], models based on image patches [5], and Gaussian mixtures of local filters [25], just to name a few of the most successful ideas. See Figure 1 for a visual comparison of some popular priors. More recently, deep learning techniques have been used to construct generic image priors. Here, we propose an image prior that is directly based on an estimate of the natural image probability distribution. Although this seems like the most intuitive and straightforward idea to formulate a prior, only few previous techniques have taken this route [20].
    [Show full text]
  • Comparative Analysis of Clustering Techniques for Movie Recommendation
    MATEC Web of Conferences 225, 02004 (2018) https://doi.org/10.1051/matecconf/201822502004 UTP-UMP-VIT SES 2018 Comparative Analysis of Clustering Techniques for Movie Recommendation Aditya TS1, Karthik Rajaraman2, and M. Monica Subashini3,* 1School of Electronics Engineering, VIT University, Vellore, India. 2School of Computer Science Engineering, VIT University, Vellore, India 3School of Electrical Engineering, VIT University, Vellore, India Abstract. Movie recommendation is a subject with immense ambiguity. A person might like a movie but not a very similar movie. The present recommending systems focus more on just few parameters such as Director, cast and genre. A lot of Power intensive methods such as Deep Convolutional Neural Network (CNN) has been used which demands the use of Graphics processors that require more energy. We try to accomplish the same task using lesser Energy consuming algorithms such as clustering techniques. In this paper, we try to create a more generalized list of similar movies in order to provide the user with more variety of movies which he/she might like, using clustering algorithms. We will compare how choosing different parameters and number of features affect the cluster's content. Also, compare how different algorithms such as K-mean, Hierarchical, Birch and mean shift clustering algorithms give a varied result and conclude which method will suit for which scenarios of movie recommendations. We also conclude on which algorithm clusters stray data points more efficiently and how different algorithms provide different advantages and disadvantages. 1 Introduction A movie recommendation system using four different clustering algorithms is built on the same cleaned dataset with identical features.
    [Show full text]
  • The Variable Bandwidth Mean Shift and Data-Driven Scale Selection
    The Variable Bandwidth Mean Shift and Data-Driven Scale Selection Dorin Comaniciu Visvanathan Ramesh Peter Meer Imaging & Visualization Department Electrical & Computer Engineering Department Siemens Corp orate Research Rutgers University 755 College Road East, Princeton, NJ 08540 94 Brett Road, Piscataway, NJ 08855 Abstract where the d-dimensional vectors fx g representa i i=1:::n random sample from some unknown density f and the Wepresenttwo solutions for the scale selection prob- kernel, K , is taken to be a radially symmetric, non- lem in computer vision. The rst one is completely non- negative function centered at zero and integrating to parametric and is based on the the adaptive estimation one. The terminology xedbandwidth is due to the fact of the normalized density gradient. Employing the sam- d that h is held constant across x 2 R . As a result, the ple p oint estimator, we de ne the Variable Bandwidth xed bandwidth pro cedure (1) estimates the densityat Mean Shift, prove its convergence, and show its sup eri- eachpoint x by taking the average of identically scaled orityover the xed bandwidth pro cedure. The second kernels centered at each of the data p oints. technique has a semiparametric nature and imp oses a For p ointwise estimation, the classical measure of the lo cal structure on the data to extract reliable scale in- ^ closeness of the estimator f to its target value f is the formation. The lo cal scale of the underlying densityis mean squared error (MSE), equal to the sum of the taken as the bandwidth which maximizes the magni- variance and squared bias tude of the normalized mean shift vector.
    [Show full text]
  • A Comparison of Clustering Algorithms for Face Clustering
    University of Groningen Research internship A comparison of clustering algorithms for face clustering Supervisors: Author: A.Sobiecki A.F. Bijl (2581582) Dr M.H.F.Wilkinson Groningen, the Netherlands, July 24, 2018 1 Abstract Video surveillance methods become increasingly widespread and popular in many organizations, including law enforcement, traffic con- trol and residential applications. In particular, the police performs inves- tigations based on searching specific people in videos and in pictures. Because the number of such videos is increasing, manual examination of all frames becomes impossible. Some degree of automation is strongly needed. Face clustering is a method to group faces of people into clusters contain- ing images of one single person. In the current study several clustering algorithms are described and applied on different datasets. The five clustering algorithms are: k-means, threshold clustering, mean shift, DBSCAN and Approximate Rank-Order. In the first experiments these clustering techniques are applied on subsets and the whole Labeled Faces in the Wild (LFW) dataset. Also a dataset containing faces of people appearing in videos of ISIS is tested to evaluate the performance of these clustering algorithms. The main finding is that threshold clustering shows the best performance in terms of the f-measure and amount of false positives. Also DBSCAN has shown good performance during our experiments and is considered as a good algorithm for face clustering. In addition it is discouraged to use k-means and for large datsets
    [Show full text]
  • Generalized Mean Shift with Triangular Kernel Profile Arxiv:2001.02165V1 [Cs.LG] 7 Jan 2020
    Generalized mean shift with triangular kernel profile S. Razakarivony, A. Barrau .∗ January 8, 2020 Abstract The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements and generalizations, as well as deep theoretical analysis mainly focused on its convergence properties. In spite of encouraging results, this question has not received a clear general answer yet. In this paper we focus on a specific class of kernels, adapted in particular to the distributions clustering applications which motivated this work. We show that a novel Mean Shift variant adapted to them can be derived, and proved to converge after a finite number of iterations. In order to situate this new class of methods in the general picture of the Mean Shift theory, we alo give a synthetic exposure of existing results of this field. 1 Introduction The mean shift algorithm is a simple iterative algorithm introduced in [8], which became over years a cornerstone of data clustering. Technically, its purpose is to find local maxima of a function having the following shape: 2 ! 1 X jjx − xijj arXiv:2001.02165v1 [cs.LG] 7 Jan 2020 f(x) = k ; (1) Nhq h i q where (xi)1≤i≤N is a set of data points belonging to a vector space R , h is a scale factor, k(:) is a q convex and decreasing function from R≥0 to R≥0 and ||·|| denotes the Euclidean norm in R . This optimization is done by means of a sequence n ! x^n, which we will explicite in Sect.
    [Show full text]
  • Application of Deep Learning on Millimeter-Wave Radar Signals: a Review
    sensors Review Application of Deep Learning on Millimeter-Wave Radar Signals: A Review Fahad Jibrin Abdu , Yixiong Zhang * , Maozhong Fu, Yuhan Li and Zhenmiao Deng Department of Information and Communication Engineering, School of Informatics, Xiamen University, Xiamen 361005, China; [email protected] (F.J.A.); [email protected] (M.F.); [email protected] (Y.L.); [email protected] (Z.D.) * Correspondence: [email protected] Abstract: The progress brought by the deep learning technology over the last decade has inspired many research domains, such as radar signal processing, speech and audio recognition, etc., to apply it to their respective problems. Most of the prominent deep learning models exploit data representations acquired with either Lidar or camera sensors, leaving automotive radars rarely used. This is despite the vital potential of radars in adverse weather conditions, as well as their ability to simultaneously measure an object’s range and radial velocity seamlessly. As radar signals have not been exploited very much so far, there is a lack of available benchmark data. However, recently, there has been a lot of interest in applying radar data as input to various deep learning algorithms, as more datasets are being provided. To this end, this paper presents a survey of various deep learning approaches processing radar signals to accomplish some significant tasks in an autonomous driving application, such as detection and classification. We have itemized the review based on different radar signal representations, as it is one of the critical aspects while using radar data with deep learning models. Furthermore, we give an extensive review of the recent deep learning-based multi-sensor fusion models exploiting radar signals and camera images for object detection tasks.
    [Show full text]
  • Machine Learning – En Introduktion Josefin Rosén, Senior Analytical Expert, SAS Institute
    Machine learning – en introduktion Josefin Rosén, Senior Analytical Expert, SAS Institute [email protected] Twitter: @rosenjosefin #SASFORUMSE Copyright © 2015, SAS Institute Inc. All rights reserved. Machine learning – en introduktion Agenda Vad är machine learning? När, var och hur används machine learning? Exempel – deep learning Machine learning i SAS Copyright © 2015, SAS Institute Inc. All rights reserved. Machine learning – vad är det? Wikipedia: Machine learning, a branch of artificial intelligence, concerns the construction and study of systems that can learn from data. SAS: Machine learning is a branch of artificial intelligence that automates the building of systems that learn from data, identify patterns, and make decisions – with minimal human intervention. Copyright © 2015, SAS Institute Inc. All rights reserved. Vad är vad egentligen? Statistics Pattern Computational Neuroscience Recognition Data Science Data Mining Machine AI Learning Databases Information Retrieval Copyright © 2015, SAS Institute Inc. All rights reserved. Machine learning – vad är det? ”Komplicerade metoder, men användbara resultat” Copyright © 2015, SAS Institute Inc. All rights reserved. När används machine learning? När modellens prediktionsnoggrannhet är viktigare än tolkningen av modellen När traditionella tillvägagångssätt inte passar, t ex när man har: fler variabler än observationer många korrelerade variabler ostrukturerad data fundamentalt ickelinjära eller ovanliga fenomen Copyright © 2015, SAS Institute Inc. All rights reserved. Beslutsträd Träningsdata Regression Neuralt nätverk Copyright © 2015, SAS Institute Inc. All rights reserved. Var används machine learning? Några exempel: Rekommendationsapplikationer Fraud detection Prediktivt underhåll Textanalys Mönster och bildigenkänning Den självkörande Google-bilen Copyright © 2015, SAS Institute Inc. All rights reserved. Statistics Pattern Computational Neuroscience Recognition Data Science Data Mining Machine AI Learning Databases Information Retrieval Copyright © 2015, SAS Institute Inc.
    [Show full text]
  • Arxiv:1703.09964V1 [Cs.CV] 29 Mar 2017 Denoising, Or Each Magnification Factor in Super-Resolution
    Image Restoration using Autoencoding Priors Siavash Arjomand Bigdeli1 Matthias Zwicker1;2 1University of Bern 2University of Maryland, College Park [email protected] [email protected] Abstract Blurry Iterations 10, 30, 100 and 250 23:12dB 24:17dB 26:43dB 29:1dB 29:9dB We propose to leverage denoising autoencoder networks as priors to address image restoration problems. We build on the key observation that the output of an optimal denois- ing autoencoder is a local mean of the true data density, and the autoencoder error (the difference between the out- put and input of the trained autoencoder) is a mean shift vector. We use the magnitude of this mean shift vector, that is, the distance to the local mean, as the negative log like- lihood of our natural image prior. For image restoration, Figure 1. We propose a natural image prior based on a denoising we maximize the likelihood using gradient descent by back- autoencoder, and apply it to image restoration problems like non- propagating the autoencoder error. A key advantage of our blind deblurring. The output of an optimal denoising autoencoder approach is that we do not need to train separate networks is a local mean of the true natural image density, and the autoen- coder error is a mean shift vector. We use the magnitude of the for different image restoration tasks, such as non-blind de- mean shift vector as the negative log likelihood of our prior. To re- convolution with different kernels, or super-resolution at store an image from a known degradation, we use gradient descent different magnification factors.
    [Show full text]
  • Outline of Machine Learning
    Outline of machine learning The following outline is provided as an overview of and topical guide to machine learning: Machine learning – subfield of computer science[1] (more particularly soft computing) that evolved from the study of pattern recognition and computational learning theory in artificial intelligence.[1] In 1959, Arthur Samuel defined machine learning as a "Field of study that gives computers the ability to learn without being explicitly programmed".[2] Machine learning explores the study and construction of algorithms that can learn from and make predictions on data.[3] Such algorithms operate by building a model from an example training set of input observations in order to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions. Contents What type of thing is machine learning? Branches of machine learning Subfields of machine learning Cross-disciplinary fields involving machine learning Applications of machine learning Machine learning hardware Machine learning tools Machine learning frameworks Machine learning libraries Machine learning algorithms Machine learning methods Dimensionality reduction Ensemble learning Meta learning Reinforcement learning Supervised learning Unsupervised learning Semi-supervised learning Deep learning Other machine learning methods and problems Machine learning research History of machine learning Machine learning projects Machine learning organizations Machine learning conferences and workshops Machine learning publications
    [Show full text]