Abstract
Haralick texture features are common texture descriptors in image analysis. To compute the Haralick features, the image gray-levels are reduced, a process called quantization. The resulting features depend heavily on the quantization step, so Haralick features are not reproducible unless the same quantization is performed. The aim of this work was to develop Haralick features that are invariant to the number of quantization gray-levels. By redefining the gray-level co-occurrence matrix (GLCM) as a discretized probability density function, it becomes asymptotically invariant to the quantization. The invariant and original features were compared using logistic regression classification to separate two classes based on the texture features. Classifiers trained on the invariant features showed higher accuracies, and had similar performance when training and test images had very different quantizations. In conclusion, using the invariant Haralick features, an image pattern will give the same texture feature values independent of image quantization.
Highlights
The easiest and most intuitive image features for most applications in image analysis are first order statistics computed from histograms of the gray-level values in images, like their mean, variance, skewness and kurtosis
The aim of this work is to propose a modified set of Haralick texture features that are asymptotically invariant to the image quantization, while preserving most of the interpretations of the original features
Note that the original features are plotted on a logarithmic scale on the vertical axis, whereas the invariant features are plotted on a linear scale
Summary
The easiest and most intuitive image features for most applications in image analysis are first order statistics computed from histograms of the gray-level values in images, like their mean, variance, skewness and kurtosis. Such features involve the values of individual pixels, but ignore the spatial interaction between pixels. Most texture analysis methods use higher-order statistics, and consider the relation between two or more pixels at a time Methods such as local binary patterns [1], wavelets [2] and Gabor filters [3] can be used to assess texture in images.
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