F1 perimeter of object f2 area of object f3 total hole

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Unformatted text preview: independent. f1 = Perimeter of object f2 = Area of object f3 = Total hole area f4 = Minimum radius f5 = Maximum radius f6 = Average radius f7 = Compactness ( f1/f2 ) 6 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department The set of features, f1-7 may be measured rapidly and simply from the binary image data and need to be used to classify the observed image within a given object class, however there will be variation in values due to the effects of camera translation and rotation, camera noise, quantization noise etc. The method of classification should deal with these variations. Two approaches available are statistical classifiers and decision trees. Statistical Classifiers Statistical classification considers the features observed as a vector of values to be compared with stored information for each object class . The ``best'' match is defined by Bayes theorem to be the one that maximizes: In general, this will depend on the covariance matrix showing how features depend on each other, but if the features can be considered as identically distributed, normal and independent then this justifies the use of the Euclidean distance to the mean of each feature vector. In most cases it is reasonable to assume that the measured distribution of a particular feature variable will be normal about the mean value. Thus the classification is performed by finding the class that minimizes: This method can be refined to use a weighted sum, or correlation applied to give a similarity weighting between classes. Figure 5 shows an example of a 2 class, 2 feature problem; the elliptical lines represent equal probability contours in the two dimensional feature space. If the distributions are normal, then the projections of the two dimensional functions onto the x and y axes will look like simple one-dimensional normal curves. In principle, it may be difficult to separate the two classes in either one dimensional feature space, but they may be sufficiently distinct in the two-dimensional feature space. This forms the basis of the statistical classification technique which is not considered fully here. Decision Trees The second approach is to construct a binary decision tree to successively eliminate objects by single decision thresholds. As an example of the latter approach, Figure 5 illustrates the distribution of feature measurements for a 5 class problem where the mean value of each distribution is given by and the variance is assumed constant for all distributions. To distinguish between the feature classes, (1,2,3) and (4,5), the threshold value should be set midway between class 3 and class 4; the larger the gap, the more reliable is the classification of the object into one of the two possible sets. The probability of misclassification of object 3 as object 4 ( or vice versa ) is given by Further decisions are required to separate objects 1 from 2 and so on. A binary decision tree is constructed in which those features which have the largest gaps are used initially and the 7 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department problem is treated recursively for each of the two sub-trees. The general principle is illustrated in Figure 6 Figure 5 below: Single feature measurement for a five class problem Figure 6 below: A decision tree for a five class problem 8 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department Tree Search Methods Basic approach: Nodes of the tree represent a scene to model primitive (e.g. edge, surface) match. Let Tree have m branches at each node that correspond to model primitives. Let level of tree represent a model primitive. The level and node position specify a match pair. Use a depth first tree search to find a match. One traversal through tree gives a match list -- a possible match of scene to model features. Representation called a search or interpretation tree. 9 Faculty of Engineering Robotics Technology MECH 4041 B. Eng (Hons.) Mechatronics S. Venkannah Mechanical and Production Engineering Department How do we perform matching? At each level of the tree, one of the edges from the scene is matched with each of the m possible edges in the model. Each node has m children representing taking the match proposed so far together with all possible matches for the current scene edge. A transformation representing the match so far can be maintained. Search tree in depth first manner and pruned by rejecting interpretations that fail to satisfy current match. The search space is large - - possible combinations for n scene primitives. A lot of computations? We can reduce the computational overheads by employing some local geometric constraints to prune the tree further. These are: Cheap to compute and employ. applied before the transformation test. For Edges we...
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