The number of classes is usually known beforehand and

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Unformatted text preview: ics S. Venkannah Mechanical and Production Engineering Department Statistical pattern recognition • Object recognition is based on assigning classes to objects, and the device that does these assignments is called the classifier. The number of classes is usually known beforehand, and typically can be derived from the problem specification. • The classifier does not decide about the class from the object itself- rather, sensed object properties called patterns are used. • For statistical pattern recognition, quantitative description of objects is characteristic, elementary numerical descriptions- features- are used. The set of all possible patterns forms the pattern space or feature space. The classes form clusters in the feature space, which can be separated by discrimination hyper-surfaces. • A statistical classifier is a device with n inputs and 1 output. Each input is used to enter the information about one of n features measured from an object to be classified. An R class classifier generates one of R symbols ωr, the class identifiers. • Classification parameters are determined from a training set of examples during classifier learning. Two common learning strategies are probability density estimation and direct loss minimization. • Some classification methods do not need training sets for learning. Cluster analysis methods divide the set of processed patterns into subsets (clusters) based on the mutual similarity of subset elements. Neural nets • Most neural approaches are based on combinations of elementary processors (neurons), each of which takes a number of inputs and generates a single output. Associated with each input is a weight, and the output is a function of the weighted sum of inputs. Pattern recognition is one of many application areas of neural networks. • Feed forward networks are common in pattern recognition problems. Their training uses a training set of examples and is often based on the back propagation algorithm. • Self organizing networks do not require a training set to cluster the processed patterns. • Hopfield neural networks do not have designated inputs and outputs, but rather the current configuration represents the state. The Hopfield net acts as an associative memory where the exemplars are stored. Syntactic pattern recognition • For syntactic pattern recognition, qualitative description of objects is characteristic. The elementary properties of the syntactically described objects are called primitives. Relational structures are used to describe relations between the object primitives. • The set of all primitives is called the alphabet. The set of all words in t eh alphabet that can describe objects from one class is named the description language. A grammar represents a set of rules that must be followed when words of the specific language are constructed from the alphabet. • Grammar construction usually requires significant human interaction. In simple cases, an automated process of grammar construction from examples called grammar inference can be applied. 27 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah • Mechanical and Production Engineering Department The recognition decision of whether or not the word can be generated by a particular grammar is made during syntactic analysis. Recognition as graph matching • Matching of a model and an object graph description can be used fro recognition. An exact match of graphs is called graph isomorphism. Determination of graph isomorphism is computationally expensive. • In the real world, the object graph usually does not match the model graph exactly. Graph isomorphism cannot assess the level of mismatch. To identify objects represented by similar graphs, graph similarity can be determined. Optimization techniques in recognition • Optimization problems seek minimization or maximization of an objective function. Design of the objective function is a key factor in the performance of optimization algorithms. • Most conventional approaches to optimization use calculus based hill climbing methods. For these, the search can easily end in a local maximum, and the global maximum can be missed. • Genetic algorithms use natural evolution mechanisms of the survival of t he fittest to search for the maximum of an objective function. Potential solutions are represented as strings. Genetic algorithms search from a population of potential solutions, not a single solution. The sequence of reproduction, crossover, and mutation generates a new population of strings from the previous population. The fittest string represents the final solution. • Simulated annealing combine two basic optimization principles, divide and conquer and iterative improvement (hill climbing). This combination avoids getting stuck in local optima. Fuzzy systems. • Fuzzy systems are capable of representing diverse, non exact, uncertain, and inaccurate knowledge or information. They use qualifiers that are very close to the human way of expressing knowledge. • Fuzzy reasoning is performed in the context of a fuzzy system model that consists of control, solution, and working data variables; fuzzy sets; hedges; fuzzy rules; and a control mechanism. • Fuzzy sets represent properties of fuzzy spaces. Membership functions represent the fuzziness of the description and assess the degree of certainty about the membership of an element in the particular fuzzy set. Shape of fuzzy membership functions can be modified using fuzzy set hedges. A hedge and its fuzzy set constitute a single semantic entity called a linguistic variable. • Fuzzy if-then rule represent fuzzy associative memory in which knowledge is stored. • In fuzzy reasoning, information carried in individual fuzzy sets is combined to make a decision. The functional relationship determining the degree of membership in related fuzzy regions is called the method of composition and results in definition of a fuzzy solution space. To arrive at the decision, de-fuzzification is performed. 28 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department Processes of composition and de-fuzzification form the basis of fuzzy reasoning. Problem 1 (Class) Area Height Width No. of No. of (cx, cy) Character Holes Strokes center ‘A’ Med Hi ¾ 1 3 ½, 2/3 ‘B’ Med Hi ¾ 2 1 1/3, ½ ‘8’ Med Hi 2/3 2 0 ½, ½ ‘0’ Med Hi 2/3 1 0 ½, ½ ‘1’ Lo Hi ¼ 0 1 ½, ½ ‘W’ Hi Hi 1 0 4 ½, 2/3 ‘X’ Hi Hi ¾ 0 2 ½, ½ ‘*’ Med Lo ½ 0 0 ½, ½ ‘-‘ Lo Lo 2/3 0 1 ½, ½ ‘/’ Lo Hi 2/3 0 1 ½, ½ Note: Med- Medium, Lo- Low, Hi- High, Lar- Large Best axis 90 90 90 90 90 90 ? ? 0 60 Least inertia Med Lar Med Lar Lo Lar Lar Lar Lo Lo Draw a decision tree that implements the above classification procedure. Reference : 1. 2. 3. 4. 5. 6. Image Processing, Analysis, and Machine Vision by Milan Sonka et al Robotics: Control, Sensing, Vision, and Intelligence by K. S. Fu et al Computer Vision by Shapiro and Stockman Digital Image Processing by R. C. Gonzalez & R. E. Woods 29 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics...
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