Color texture analysis based on fractal descriptors Andre ´ Ricardo Backes a,n , Dalcimar Casanova b,1 , Odemir Martinez Bruno b,1 a Faculdade de Computac - ~ ao, Universidade Federal de Uberlˆ andia, Av. Jo ~ ao Naves de A ´ vila, 2121, 38408-100, Uberlˆ andia, MG, Brazil b Instituto de Fı ´sica de S ~ ao Carlos (IFSC), Universidade de S ~ ao Paulo, Av. Trabalhador S ~ ao Carlense, 400 13560-970 S ~ ao Carlos, SP, Brazil article info Article history: Received 11 May 2011 Received in revised form 29 September 2011 Accepted 15 November 2011 Available online 25 November 2011 Keywords: Color texture analysis Fractal dimension Complexity Feature extraction Classification abstract Color texture classification is an important step in image segmentation and recognition. The color information is especially important in textures of natural scenes, such as leaves surfaces, terrains models, etc. In this paper, we propose a novel approach based on the fractal dimension for color texture analysis. The proposed approach investigates the complexity in R, G and B color channels to characterize a texture sample. We also propose to study all channels in combination, taking into consideration the correlations between them. Both these approaches use the volumetric version of the Bouligand–Minkowski Fractal Dimension method. The results show a advantage of the proposed method over other color texture analysis methods. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction The identification of visual patterns has long been an area of computer vision with active research. Texture analysis can be very useful for experiments of image classification and identifica- tion. While the ability of a human to distinguish different textures is apparent, the automated description and recognition of these same patterns have proven to be quite complex. Over the years, researchers have studied different texture analysis approaches. Many of these approaches represent the local behavior of the texture via statistical [1], structural [2] or spectral [3–5] properties of the image. Good surveys can be found in [5–11]. The conjecture presented in [12], where second-order probability distributions [6,13] are enough for human discrimina- tion of two texture patterns, has motivated the use of statistical approaches. This conjecture showed not to hold strictly particu- larities when textures present some structure [14]. Structural approaches, then, attempt to describe a texture by rules, which govern the position of primitive elements, which make up the texture [15]. In addition, signal processing methods, such as Gabor filters [4,16,17], Fourier analysis [18] and Wavelet packets [19], were motivated by psychophysical researches, which have given evidences that the human brain does a frequency analysis of the image [20,21]. These approaches represent the texture as an image in a space whose coordinate system has an interpretation that is closely related to the characteristics of a texture (such as frequency or size). However, these methods fail to distinguish many natural textures that show no periodic structure [22]. Natural textures may not present any detectable quasi-periodic structure. Instead, they exhibit random, but persistent, patterns that result in a cloud-like texture appearance. Examples of these cloudy textures are widely found on nature (pictures of clouds, smoke, leaves surfaces, terrain models, etc.). Fractals offer an interesting alternative to these approaches. Due to its irregularities, most of the natural surfaces have non- integer dimension. Therefore, it seems plausible that the fractal model might also be applied successfully to analyze images. This reduces the classification problem to estimating the fractal dimension of the texture. Since the fractal feature is an inherent property of the region/surface/object, it can be considered a more reliable measure [23]. In fact, according with [24], the fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. The fractal dimension (D) shows a strong correlation with human perception of surface roughness. Several methods have been devel- oped to estimate D for image analysis. In [25], the fractal dimension is estimated using the Fourier power spectrum of the image’s intensity surface modeled as fractal Brownian motion surface. In [26], Mandelbrot’s idea of the E-blanket method is adopted and extended for surface area calculation. The box-counting method, developed by [27], and its improved version, called differential box- counting (DBC) and developed by [28–30], have been used for several tasks of texture comparison and classification, and object characterization [31,32]. Subsequently, [33,34] have applied the Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/pr Pattern Recognition 0031-3203/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.patcog.2011.11.009 n Corresponding author. Tel.: þ55 34 32394499. E-mail addresses: arbackes@yahoo.com.br, backes@facom.ufu.br (A.R. Backes), dalcimar@gmail.com (D. Casanova), bruno@ifsc.usp.br (O.M. Bruno). 1 Tel.: þ55 16 3373 8728; fax: þ55 16 3373 9879. Pattern Recognition 45 (2012) 1984–1992