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- Introduction to Statistical Pattern Recognition - Keinosuke Fukunaga - Google книги

Then, new values indicating the smoothness of the local areas are obtained, and a weight is assigned to each pixel, prioritizing textured areas to smooth areas. The parameters: c i is the centroid of cluster C i , x n and v n are the color vector and the perceptual weight for pixel n. D i is the total distortion for C i. With the centroid value, as denoted by Equation 2 - after the vector quantization and merged clusters, pixels with the same color have two or more clusters, affected by GLA global distortion.

For merging close clusters with minimum distance between preset thresholds for two centroids, an agglomerative clustering algorithm is performed on c i Duda and Hart, , as the quantization parameter needed for spatial distribution. After clustering merging for color quantization, a label is assigned for each quantized color, representing a color class for image pixels quantized to the same color. The image pixel colors are replaced by their corresponding color class labels, creating a class-map. C is the number of classes obtained in the quantization.

The parameter S T represents the sum of quantized image points within the average in all Z elements. Thereby, the relation between S B and S W , denotes the measures of distances of this class relation, for arbitrary nonlinear class distributions. J for higher values indicates an increasing distance between the classes and points for each other, considering images with homogeneous color regions. The distance and consequently, the J value, decrease for images with uniformly color classes. J K represents J calculated over region k , M k is the number of points in region k , N is the total number of points in the class-map, with all regions in class-map summation.

Therefore, the idea of J-image is the generation of a gray-scale image whose pixel values are the J values calculated over local windows centered on these pixels. With a higher value for J-image, the pixel should be near region boundaries. Expected local windows dimensions determines the size of image regions, for intensity and color edges in smaller sizes, and the opposite occurs detecting texture boundaries.

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Using a region-growing method to segment the image, this one is considered initially as one single region. The algorithm for spatial segmentation starts segment all the regions in the image at an initial large scale until the minimum specified scale is reached. This final scale is settled manually for the appropriate image size. The initial scale 1 corresponds to 64x64 image size, scale 2 to x image size, scale 3 to x image size, with due proportion for increasing scales and the double image size. The sequential images evince not only the color quantization spatial distributions forming a map of classes , but also the space segmentation J-image representing edges and regions of textured side.

Each window size is associated with a scale image analysis.

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The concept of J-image, together with different scales, allows the segmentation of regions by referring to texture parameters. Regions with the lowest values of J-image are called valleys. The lowest values are applied with a heuristic algorithm. Thus, it is possible to determine the starting point of efficient growth, which depends on the addition of similar valleys.

The algorithm ends when there are spare pixels to be added to those regions. It was observed that the oranges represent the largest number of image pixels, given its characteristics of high contrast with other objects on the scene. The first identifies the largest part of the tree.

The second scene denotes the regions' set details in orchards, excluding darker regions. Not only irregularities of each leaf are segmented, as well as abnormalities of color tones in fruit itself, allowing later analysis of disease characteristics. The third category identifies most of the trees, but with higher incidence of top and bottom regions. It is fundamental that an ANN-based classification method associated with a statistical pattern recognition be used.

Also, the network with less MSE in the neurons to color space proportion is used to classify the entities. Derived from back-propagation, the iRPROP algorithm improved resilient back-propagation Lulio, is both fast and accurate, with easy parameter adjustment.

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It features an Octave Eaton, module which was adopted for the purposes of this work and it is classified with HSV H — hue, S — saturation, V — value color space channels histograms of categories 32, 64, and neurons in a hidden layer training for each color space channel: H, HS, and HSV. The output layer has three neurons, each of them having a predetermined class. The charts below Figures 5 , 6 , 7 , 8 denote the ratio of mean square error MSE and amount of times to obtain the best performance index during the validation data towards the training and test sets.

All ANN-based topologies are trained with a threshold lower than 0. The most appropriate segment and topology classifications are those using vectors extracted from HSV color space. Also, a network with less MSE in the H was used so as to classify the planting area; for class navigable area soil , HSV was chosen; as for the class sky, the HS The response times are given for combinations of training, testing, validation and all data sets. Statistical methods are employed as a combination of results with ANN, showing how accuracy in non-linear features vectors can be best applied in a MLP algorithm with a statistical improvement, which processing speed is essentially important, for pattern classification.

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Bayes Theorem and Naive Bayes Comaniciu and Meer, both use a technique for iterations inspection, namely MCA Main Component Analysis , which uses a linear transformation that minimizes co-variance while it maximizes variance. Features found through this transformation are totally uncorrelated, so the redundancy between them is avoided. Thus, the components features represent the key information contained in data, reducing the number of dimensions. With a smaller dimension of iterations, HSV is chosen as the default space color in most applications Grasso and Recce, Bayes Theorem introduces a modified mathematical equation for the Probability Density Function PDF , which estimates the training set in a conditional statistics.

Equation 8 denotes the solution for p C i y relating the PDF to conditional class i classes in natural scene , and y is a n -dimensional feature vector. Naive Bayes implies independence for vector features, what means that each class assumes the conditional parameter for the PDF, following Equation 9 Morimoto et al, In Fig.

This amount, for HSV case, is reduced for the fruit class, as the dispersion of pixels is greater in this color space. In this color space, the estimation in the recognition of objects related to the fruits is given by the PDF of each dimension, correcting the current values by the hope of each area not matched to the respective class. Also in Fig. This allows the correction of the next results by priori estimation approximating, in the PDF of each dimension. It can be seen that, the ratio of the estimation must be lesser for the increasing of the dimensions number and its subsequent classification, in all cases.

In-class quiz "re-do" of Feb 7 quiz. Generative models part 2 and the exponential family.

Programming project 2 data out. The exponential family is covered in Section 2.

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## "Introduction to Statistical Pattern Recognition" by K. Fukunaga OldKiwi - Rhea

Written assignment 2 due. In-class quiz. Bayesian logistic regression. Written assignment 3 out. Support vector machines part 1. Programming project 3 data out. Markov random fields. Basic inference. Written assignment 4 out. Basic sampling. Markov chain Monte Carlo. Read Chapter 11 up through Topic proposal due.

Read the original paper up to Section 5.

## Introduction to Statistical Pattern Recognition - Keinosuke Fukunaga - Google книги

The Bayesian approach is applied via variational inference which we cover later. Gaussian mixture models.

Expectation maximization for GMMs.