Industrial Applications of Colour Texture Classification Based on Anisotropic Diffusion

Abstract

A novel method of colour texture classification based on anisotropic diffusion is proposed and is investigated with different colour spaces. The objective is to explore the colour spaces for their suitability in automatic classification of certain textures in industrial applications, namely, granite tiles and wood textures, using computer vision. The directional subbands of digital image of material samples are obtained using wavelet transform. The anisotropic diffusion is employed to obtain the texture components of directional subbands. Further, statistical features are extracted from the texture components. The linear discriminant analysis (LDA) is employed on feature space to achieve class separability. The proposed method has been experimented on RGB, HSV, YCbCr and Lab colour spaces. The k-NN classifier is used for texture classification. For experimentation, image samples from MondialMarmi database of granite tiles and Parquet database of hard wood are considered. The experimental results are encouraging due to reduced time complexity, reduced feature set size and improved classification accuracy as compared to the state-of-the-art-methods.

Appendices

Appendix

A Wavelet transform

Wavelet analysis is a particular time-scale representation of signals. It has wide range of applications in physics, signal processing and applied mathematics. The theoretical aspect and implementation of wavelet transform are available in [18]. The wavelet transform uses the Haar function in edge extraction, image coding and binary logic design, The one level of Haar wavelet decomposition decomposes the input image into four subbands, namely, A, H, V and D respectively. The Fig. 2 shows test input image and its one level wavelet decomposition. The subband A (Approximation) contains the global properties of the input image. The H (horizontal) subband contains the horizontal details of input image. The V (vertical) subband includes information of vertical details whereas D (diagonal) subband embraces the diagonal details of image. Due to the low computing requirements, the Haar transform has been used for image processing and pattern recognition.

Fig. 2.

Wavelet transform: (a) Test image, (b) One-level decomposition, (c) One level decomposition of image in (a).

B Anisotropic diffusion

Perona and Malik [8] proposed anisotropic diffusion process, where diffusion takes place to smooth image while preserving edge sharpness. It was demonstrated [8] that this process clearly outperforms the canny edge detector, making image boundaries sharp. The nonlinear PDE for smoothing image on a continuous domain as suggested in [8] is shown in the Eq. (1):

$$\begin{aligned} \left\{ \begin{array}{l}\frac{\partial {I}}{\partial {t}}=div\left[ c\left( \left| \nabla {}I\right| \right) \nabla {I}\right] \\ I_{\left( t=0\right) }=I_{0}\end{array}\right. \end{aligned}$$

(1)

where $\nabla$ denotes the gradient operator, div is divergence operator, c(x) represents diffusion coefficient, $\left| \right|$ is the magnitude and $I_{0}$ denotes initial image. The two diffusion coefficients are given by the Eqs. (2) and (3):

$$\begin{aligned} c(x)=\frac{1}{1+(\frac{x}{k})^{2}} \end{aligned}$$

(2)

and

$$\begin{aligned} c(x)=exp\left\lfloor {-(x/k)^{2}}\right\rfloor \end{aligned}$$

(3)

where k is an edge magnitude parameter. In the anisotropic diffusion method, the gradient magnitude is used to detect an image edge or boundary as a step discontinuity in intensity. If $\left| \nabla {I}\right|>>{k}$ then $c\left( \nabla {I}\right) \rightarrow {0}$, and we have an all-pass filter. If $\left| \nabla {I}\right|<<{k}$ then $c\left( \nabla {I}\right) \rightarrow {1}$ and we achieve isotropic diffusion (Gaussian filtering). A discrete form of the Eq. (1) is given by the Eq. (4):

$$\begin{aligned} I_{s}^{t+\varDelta {t}}=I_{s}^{t}+\frac{\lambda }{\left| \overline{\eta _{s}}\right| }\sum _{p\in \overline{\eta _{s}}}{c(\nabla {I_{s,p}^{t}})\nabla {I_{s,p}^{t}}} \end{aligned}$$

(4)

where $I_{s}^{t}$ is the discretely sampled image, s denotes the pixel position in a discrete two-dimensional (2-D) grid, and $0\le \lambda \le {1/4}$ is a scalar that controls the numerical stability, ${\overline{\eta _{s}}}$ is the number of pixels in the window (usually four, except at the image boundaries), and $\nabla {I}_{s,p}^{t}={I}_{p}^{t}-{I}_{s}^{t}, \forall {p}\in {\overline{\eta _{s}}}$.