Two Dimensional Shape and Texture Quantification

Isaac N. Bankman Thomas S. Spisz

Johns Hopkins University

Sotiris Pavlopoulos

National Technical

University of Athens

Shape Quantification 215

1.1 Compactness • 1.2 Spatial Moments • 1.3 Radial Distance Measures • 1.4 Chain Codes • 1.5 Fourier Descriptors • 1.6 Thinning

Texture Quantification 223

2.1 Statistical Moments • 2.2 Co-Occurrence Matrix Measures • 2.3 Spectral Measures • 2.4 Fractal Dimension • 2.5 Run-length Statistics

References 228

Two of the most informative visual cues in medical image interpretation, shape, and texture can be quantified with numerous automated techniques that address different aspects of the data. This chapter describes relatively established techniques for two-dimensional (2D) shape and texture quantification, which contribute to many clinical and research applications.

Section 1 presents shape quantification techniques, that operate on the segmented image in three different ways. Compactness and spatial moments provide quantitative shape measures by applying geometric and statistical computations to all pixels within a segmented region. Radial distance measures, chain codes, and Fourier descriptors operate only on boundary pixels by using geometric, statistical, and spectral computations to provide mechanisms for encoding and representing a closed contour. When structures of interest are elongated or branching, the essential shape information is contained in the medial lines that can be obtained by thinning algorithms. Quantitative shape measures such as length, angle, curvature, or orientation can be computed subsequently on the skeletonized representation.

Examination of medical images often requires interpretation of tissue appearance, which is generally described with terms such as smoothness, grain, regularity, or homogeneity. This attribute relates to the local intensity variations and can be quantified by using texture metrics discussed in Section 2. Statistical moments are derived directly from the intensity histogram of the image. Co-occurrence matrix measures are computed from a 2D histogram, which preserves spatial information. Spectral measures obtained from the Fourier transform of the image can quantify texture, particularly when repetitive patterns are present. The field of fractals provides the fractal dimension, which can be used as a texture metric based on analysis at multiple scales. The run-length statistics quantify texture by analyzing linear pixel strands that have the same value in the image.

Unlike shape, texture is a representation of a selected region. It can be assigned to a small local area as well as to a relatively large image section, within a segmented region, or inside a preset region of interest. A local texture measure can be associated with each pixel of the entire image and the resulting texture image may be used for segmentation when the distinct structures of interest have similar intensity levels but differ in smoothness.

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