Local Frequency Descriptor (Magnitude)

Considers a neighboring function defined on a circle of radius R at each pixel:

We define local frequency components as the magnitude of the coefficients of the 1D Fourier transform of the neighboring function. By applying different bandpass filters on the 2D Fourier transform of the local frequency components, we define our Local Frequency Descriptors (LFD).

$f_n=\sum_{k=0}^{N-1}t_{k}e^{-2\pi ink/N},$

Five texture samples and their first two frequency channels are shown below.

LFD features are constructed by taking a 2D Fourier transform on these channels and applying circular and directional band-pass filters.

The LFD features are added dynamically from low frequencies to high. The features defined in this paper are invariant to rotation. As well, they are robust to noise. The experimental results on the Outex, CUReT, and KTH-TIPS datasets show that the proposed method outperforms state-of-the-art texture analysis methods. The results also show that the proposed method is very robust to noise.

Download the paper from here .

Download the Matlab code implementation from here: [code]. Please cite the following reference if you use this code:

R. Maani, S. Kalra, and Y.H. Yang, "Noise robust rotation invariant features for texture classification", Pattern Recognition 46(8), pp. 2103–2116, 2013.