Unsupervised Tracking, Roughness and Quantitative Indices
TL;DR: Three quantitative indices based on rough sets, feature similarity and Bhattacharya distance are proposed to evaluate the performance of tracking and detect the mis-tracked frames in the process of tracking to make those corrected.
Abstract: This paper presents a novel methodology for tracking a single moving object in a video sequence applying the concept of rough set theory. The novelty of this technique is that it does not consider any prior information about the video sequence unlike many existing techniques. The first target model is constructed using the median filtering based foreground detection technique and after that the target is reconstructed in every frame according to the rough set based feature reduction concept incorporating a measure of indiscernibility instead of indiscernibility matrix. The area of interest is initially defined roughly in every frame based on the object shift in the previous frames, and after reduction of redundant features the object is tracked. The measure of indiscernibility of a feature is defined based on its degree of belonging DoB to the target. Three quantitative indices based on rough sets, feature similarity and Bhattacharya distance are proposed to evaluate the performance of tracking and detect the mis-tracked frames in the process of tracking to make those corrected. Unlike many existing measures, the proposed ones do not require to know the ground truth or trajectory of the video sequence. Extensive experimental results are given to demonstrate the effectiveness of the method. Comparative performance is demonstrated both visually and quantitatively.
Citations
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TL;DR: A new concept of neighborhood granule formation over images is introduced here which proves to be effective in reducing the indiscernibility of the rule-base and provides more accurate results in the task of tracking.
Abstract: This paper deals with several new methodologies and concepts in the area of rough set theoretic granular computing which are then applied in video tracking. A new concept of neighborhood granule formation over images is introduced here. These granules are of arbitrary shapes and sizes unlike other existing granulation techniques and hence more natural. The concept of rough-rule base is used for video tracking to deal with the uncertainties and incompleteness as well as to gain in computation time. A new neighborhood granular rough rule base is formulated which proves to be effective in reducing the indiscernibility of the rule-base. This new rule-base provides more accurate results in the task of tracking. Two indices to evaluate the performance of tracking are defined. These indices do not need ground truth information or any estimation technique like the other existing ones. All these features are demonstrated with suitable experimental results.
7 citations
References
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TL;DR: It is proved the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density.
Abstract: A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.
11,727 citations
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Abstract: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U={u} which is characterized by its membership function μF, then a proposition of the form “X is F,” where X is a variable taking values in U, induces a possibility distribution ∏X which equates the possibility of X taking the value u to μF(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution ∏x in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle. A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form “X is F is α-possible,” where α is a number in the interval [0, 1], is formulated and illustrated by examples.
8,918 citations
"Unsupervised Tracking, Roughness an..." refers methods in this paper
...In case of our experiment, we have used Zadeh’s S-function [30] as the distance function....
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Book•
31 Oct 1991
TL;DR: Theoretical Foundations.
Abstract: I. Theoretical Foundations.- 1. Knowledge.- 1.1. Introduction.- 1.2. Knowledge and Classification.- 1.3. Knowledge Base.- 1.4. Equivalence, Generalization and Specialization of Knowledge.- Summary.- Exercises.- References.- 2. Imprecise Categories, Approximations and Rough Sets.- 2.1. Introduction.- 2.2. Rough Sets.- 2.3. Approximations of Set.- 2.4. Properties of Approximations.- 2.5. Approximations and Membership Relation.- 2.6. Numerical Characterization of Imprecision.- 2.7. Topological Characterization of Imprecision.- 2.8. Approximation of Classifications.- 2.9. Rough Equality of Sets.- 2.10. Rough Inclusion of Sets.- Summary.- Exercises.- References.- 3. Reduction of Knowledge.- 3.1. Introduction.- 3.2. Reduct and Core of Knowledge.- 3.3. Relative Reduct and Relative Core of Knowledge.- 3.4. Reduction of Categories.- 3.5. Relative Reduct and Core of Categories.- Summary.- Exercises.- References.- 4. Dependencies in Knowledge Base.- 4.1. Introduction.- 4.2. Dependency of Knowledge.- 4.3. Partial Dependency of Knowledge.- Summary.- Exercises.- References.- 5. Knowledge Representation.- 5.1. Introduction.- 5.2. Examples.- 5.3. Formal Definition.- 5.4. Significance of Attributes.- 5.5. Discernibility Matrix.- Summary.- Exercises.- References.- 6. Decision Tables.- 6.1. Introduction.- 6.2. Formal Definition and Some Properties.- 6.3. Simplification of Decision Tables.- Summary.- Exercises.- References.- 7. Reasoning about Knowledge.- 7.1. Introduction.- 7.2. Language of Decision Logic.- 7.3. Semantics of Decision Logic Language.- 7.4. Deduction in Decision Logic.- 7.5. Normal Forms.- 7.6. Decision Rules and Decision Algorithms.- 7.7. Truth and Indiscernibility.- 7.8. Dependency of Attributes.- 7.9. Reduction of Consistent Algorithms.- 7.10. Reduction of Inconsistent Algorithms.- 7.11. Reduction of Decision Rules.- 7.12. Minimization of Decision Algorithms.- Summary.- Exercises.- References.- II. Applications.- 8. Decision Making.- 8.1. Introduction.- 8.2. Optician's Decisions Table.- 8.3. Simplification of Decision Table.- 8.4. Decision Algorithm.- 8.5. The Case of Incomplete Information.- Summary.- Exercises.- References.- 9. Data Analysis.- 9.1. Introduction.- 9.2. Decision Table as Protocol of Observations.- 9.3. Derivation of Control Algorithms from Observation.- 9.4. Another Approach.- 9.5. The Case of Inconsistent Data.- Summary.- Exercises.- References.- 10. Dissimilarity Analysis.- 10.1. Introduction.- 10.2. The Middle East Situation.- 10.3. Beauty Contest.- 10.4. Pattern Recognition.- 10.5. Buying a Car.- Summary.- Exercises.- References.- 11. Switching Circuits.- 11.1. Introduction.- 11.2. Minimization of Partially Defined Switching Functions.- 11.3. Multiple-Output Switching Functions.- Summary.- Exercises.- References.- 12. Machine Learning.- 12.1. Introduction.- 12.2. Learning From Examples.- 12.3. The Case of an Imperfect Teacher.- 12.4. Inductive Learning.- Summary.- Exercises.- References.
7,826 citations
23 Jun 1999
TL;DR: This paper discusses modeling each pixel as a mixture of Gaussians and using an on-line approximation to update the model, resulting in a stable, real-time outdoor tracker which reliably deals with lighting changes, repetitive motions from clutter, and long-term scene changes.
Abstract: A common method for real-time segmentation of moving regions in image sequences involves "background subtraction", or thresholding the error between an estimate of the image without moving objects and the current image. The numerous approaches to this problem differ in the type of background model used and the procedure used to update the model. This paper discusses modeling each pixel as a mixture of Gaussians and using an on-line approximation to update the model. The Gaussian, distributions of the adaptive mixture model are then evaluated to determine which are most likely to result from a background process. Each pixel is classified based on whether the Gaussian distribution which represents it most effectively is considered part of the background model. This results in a stable, real-time outdoor tracker which reliably deals with lighting changes, repetitive motions from clutter, and long-term scene changes. This system has been run almost continuously for 16 months, 24 hours a day, through rain and snow.
7,660 citations
TL;DR: The goal of this article is to review the state-of-the-art tracking methods, classify them into different categories, and identify new trends to discuss the important issues related to tracking including the use of appropriate image features, selection of motion models, and detection of objects.
Abstract: The goal of this article is to review the state-of-the-art tracking methods, classify them into different categories, and identify new trends. Object tracking, in general, is a challenging problem. Difficulties in tracking objects can arise due to abrupt object motion, changing appearance patterns of both the object and the scene, nonrigid object structures, object-to-object and object-to-scene occlusions, and camera motion. Tracking is usually performed in the context of higher-level applications that require the location and/or shape of the object in every frame. Typically, assumptions are made to constrain the tracking problem in the context of a particular application. In this survey, we categorize the tracking methods on the basis of the object and motion representations used, provide detailed descriptions of representative methods in each category, and examine their pros and cons. Moreover, we discuss the important issues related to tracking including the use of appropriate image features, selection of motion models, and detection of objects.
5,318 citations