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Automatic methods for image recognition and classification are increasingly being used in the field of biomedical image processing (Maree, 2005; Esgiar & Chakravorty, 2007). Robust classification algorithms are particularly useful in applications involving large-scale image databases with associated operations such as content based retrieval and analysis. In recent years, there has been a rapid growth in the availability and use of new techniques and systems for cell and tissue imaging. Tissue diagnostics play a key role in the screening, treatment and monitoring of diseases. Large tissue image databases containing hundreds of specimens and histological types are commonly used in diagnostic services and research in the areas of tissue engineering and telemedicine (Filippas et al., 2003). Further, online databases containing tissue microarray images are now publicly available for research groups. Therefore, there is a renewed interest in methods for tissue image classification, indexing and mining (Gholap et al., 2005). In this paper we present a framework based on multi-fractal formalism for the construction of efficient feature descriptors for tissue image classification and retrieval. The primary motivation for our work is the need for robust algorithms for classifying tissue images based on spatial relationships between various structures present in each tissue class. Such algorithms could be further extended to complement histological techniques for identifying/indexing regions of pathological interest.
Tissue and cell images can be categorized into a broad class of irregularly shaped statistically self-similar objects, suggesting the application fractal based methods for their classification. Shapes with statistical self-similarity are characterized by the property that they have certain statistical properties or measures that are preserved across various scales. Several examples can be found in nature, such as trees, mountainous terrains, clouds and blood vessels (Mandelbrot, 1982). Fractal structures can be classified using a numerical measure called the fractal dimension. Such a classification of tissue images into normal and cancerous, purely on the basis of fractal dimension computed from the image, can be found in (Esgiar & Chakravorty, 2007). It has been shown that tissue images contain a collection of several fractal structures with varying dimension at varying strengths (Reljin, Reljin, & Pavlovic, 2000; Reljin & Reljin, 2002). The composition of several fractal dimensions is called multi-fractality (Falconer, 2003; Arbeiter & Patzschke, 1996). The multi-fractal theory and the associated multi-fractal spectrum are useful for describing the irregularities of biomedical images (Uma, Ramakrishnan, & Anathakrishna, 1996; Qi & Yu, 2008). Methods based on multi-fractal spectra have been recently developed for the analysis of retinal images (Stosic & Stosic, 2006), digital mammograms (Stojic, Reljin, & Reljin, 2006), brain MRI images (Ruan & Bloyet, 2000) and DNA sequences (Kinsner & Zhang, 2009). Multi-fractal geometry has also been used for the analysis of various other phenomena such as sleep EEGs (Song et al., 2007), human gait (Munoz-Diasdado, 2005), and facial expressions (Yap et al., 2009).