Local jet pattern: a robust descriptor for texture classification


Methods based on locally encoded image features have recently become popular for texture classification tasks, particularly in the existence of large intra-class variation due to changes in illumination, scale, and viewpoint. Inspired by the theories of image structure analysis, this work proposes an efficient, simple, yet robust descriptor namely local jet pattern (Ljp) for texture classification. In this approach, a jet space representation of a texture image is computed from a set of derivatives of Gaussian (DtGs) filter responses up to second order, so-called local jet vectors (Ljv), which also satisfy the Scale Space properties. The Ljp is obtained by using the relation of center pixel with its’ local neighborhoods in jet space. Finally, the feature vector of a texture image is formed by concatenating the histogram of Ljp for all elements of Ljv. All DtGs responses up to second order together preserves the intrinsic local image structure, and achieves invariance to scale, rotation, and reflection. This allows us to design a discriminative and robust framework for texture classification. Extensive experiments on five standard texture image databases, employing nearest subspace classifier (Nsc), the proposed descriptor achieves 100%, 99.92%, 99.75%, 99.16%, and 99.65% accuracy for Outex_TC10, Outex_TC12, KTH-TIPS, Brodatz, CUReT, respectively, which are better compared to state-of-the-art methods.

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Appendix: Effects of similarity transforms

Appendix: Effects of similarity transforms

In computer vision problems, a group of transforms are typically chosen to analyse the effect of geometrical structure those are invariant with respect to scaling, translation, rotation and reflection of an image, a constant intensity addition, and multiplication of image intensity by a positive factor and their combinations. In order to cope with the translation effect, we choose the analyzing point as the origin of the co-ordinate system.

In the jet space, Gaussian derivatives are represented by Hermite polynomials multiplied with Gaussian window (in (1)). The details within the window is expanded over the basis of Hermite polynomials, therefore even if the scale (σ) is fixed, it provides a multi-scale hierarchical image structure for \(\mathscr{L}\)-jet [29]

Rotation of a surface is a more difficult problem in image analysis. Consider the rotation effect on jet about the origin with an angle \(\theta \). Here the zero order derivative term of the jet (J(0,0)) remains unaffected. The first order derivative terms are transformed as follows,

$$\left( \begin{array}{cc} J_{(1,0)}\\J_{(0,1)} \end{array}\right) \to \left( \begin{array}{cc} \cos\theta & \sin\theta\\ -\sin\theta & \cos\theta \end{array}\right) \left( \begin{array}{cc} J_{(0,1)}\\J_{(1,0)} \end{array}\right) $$

and the second order terms are transformed according to

$$\left( \begin{array}{ccc} J_{(2,0)}\\J_{(1,1)}\\J_{(0,2)} \end{array}\right) \to \frac{1}{2} \left( \begin{array}{ccc} 1 + b & 2c & 1 - b\\ -c & 2b & c\\1 - b & -2c & 1 + b \end{array}\right) \left( \begin{array}{ccc} J_{(0,2)}\\J_{(1,1)}\\J_{(2,0)} \end{array}\right) $$

where \(b = \cos 2\theta \) and \(c = \sin 2\theta \). So, to return the starting values, the first order derivative structure requires a full \(2\pi \) rotation, while the second order derivative structure returns after a rotation by \(\pi \).

In case of reflection (i.e. the effect of jet about the line \(y = x\)), the zero order term of the jet is not affected. However, the first order derivative term is transformed according to, \( J_{(1,0)} \longleftrightarrow J_{(0,1)}\) and the second order derivative term, according to \( J_{(2,0)} \longleftrightarrow J_{(0,2)}\). Considering all the DtGs responses together, the \(\mathscr{L}\)-jet (\(\mathscr{L}\) = 6) achieves invariance to scale, rotation, or reflection.

Image structure analysis may be appropriate if it considers that intensities are non-negative unconstrained real numbers, and also do not exceed a maximum value. Therefore, the image structure should not be affected by adding a constant \((\alpha )\) to all intensities as in case of uniform illumination change. When such changes arise, only the zero order derivative term is affected and it simply transforms according to, \(J_{(0,0)} \to J_{(0,0)} + \alpha \).

It is also required that the image local structure should be invariant to the multiplication by a non-zero positive factor (𝜖 > 0) with all image intensities. In this case, the factor is simply multiplied with all terms of jet vector i.e, \(\mathbf {J} \to \epsilon \mathbf {J}\). Note that, it does not require multiplication of intensities by a negative factor to make it invariant to physical constrains.

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Roy, S.K., Chanda, B., Chaudhuri, B.B. et al. Local jet pattern: a robust descriptor for texture classification. Multimed Tools Appl 79, 4783–4809 (2020). https://doi.org/10.1007/s11042-018-6559-3

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  • Derivative-of-Gaussian (DtGs)
  • Jet space
  • Local jet vector (Ljv)
  • Local jet pattern (Ljp)
  • Texture classification