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2017 | OriginalPaper | Buchkapitel

12. Classification and Clustering

verfasst von : Klaus D. Toennies

Erschienen in: Guide to Medical Image Analysis

Verlag: Springer London

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Abstract

Assigning semantics to segments is required if segmentation has not been combined with object detection. Classification is then based on evaluating segment attributes such as shape and appearance. The dimension of feature space is often high (>10) and the number of samples to train a classifier or to deduce a clustering is low. Methods are different compared to classification or clustering of pixels or voxels. For the most part, likelihood functions are not estimated and the classification criterion is directly based on the training data. Feature reduction techniques, classifiers, and clustering methods that focus on analysis in sparse feature spaces are the topic of this chapter. Among the different methods treated in this chapter, deep convolutional neural networks stand out, as their variable applicability has been found widespread use that encompasses applications on a pixel basis. The methods presented here complement the methodology presented in Chap. 7.

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Vorheriges Kapitel Shape, Appearance and Spatial Relationships

Nächstes Kapitel Validation

Consider, for instance, Haralick’s texture features from the co-occurrence matrix. Many of the features measure quantities which may behave similar for a class of segments. The same may be true for shape features. E.g., the size of a segment may be closely related to its elongatedness if segments are cells in a microscopic image of two types of which the small ones are mostly circular while the larger ones are not.

The central limit theorem states that the probability density function of a sum of independent random variables having the same but unknown distribution characteristics will approximately be a Gaussian function if the variance for each variable is finite.

It should be remembered that the PCA is based on an estimate of the covariance matrix. The reliability of this estimate depends on the dimensionality of feature space and the number of samples.

The proof of this is a bit lengthy and will not be shown here. For a detailed treatment of backpropagation networks see Bishop (1995). The reasons why backpropagation produces a gradient descent are, briefly, the following: At each node, the gathering function sums up weighted results from the previous node and the derivative of a sum of functions is the sum of its derivatives. Fortunately, for computing the derivative of some weights, all previous weights can be treated as constants in the derivation. Applying the activation function to the sum is the application of a function to another function so that the chain rule applies to its derivative.

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Titel: Classification and Clustering
verfasst von: Klaus D. Toennies
Verlag: Springer London
Buch: Guide to Medical Image Analysis
Print ISBN: 978-1-4471-7318-2

Electronic ISBN: 978-1-4471-7320-5

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-1-4471-7320-5_12

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