Phase & Magnitude analysis in Fourier Transform

Phase & Magnitude analysis in Fourier Transform

  The purpose of this post is to observe differences between textures which are quite similar but have slight differences. Here shows the texture samples. 

 Five samples are used for the experiment. The first sample is a grass texture, and we call it as an original sample. Rest four samples are variation of the original one. Long black rectangular is used for making variations. If it lies on top of the original sample, we call it as a 'Top'. In the same manner, 'Cen', 'Bot', and 'Right' are generated. 

 Now let's convert spatial data into frequency data using Fourier Transform. (For the convenience, we only examine R channel of samples - presented textures have three channels, RGB.) In the frequency domain, we can observe texture characteristics from two major components: magnitude and phase. Therefore, plotting those components is helpful to investigate differences  between those samples. Let's plot original one first. 

  then, let's plot rest four samples. 

  

 In terms of magnitude spectrum, we can find obvious differences. 'Top', 'Cen', 'Bot', and 'Right' samples have long huge white line at the center. 'Top', 'Cen', and 'Bot' have long vertical white line and 'right' sample has long white horizontal line. It represents the long black rectangle in the spatial domain. We can also observe that the white line lies on the same position in 'Top', 'Cen,' and 'Bot'. Since the frequency domain represents the data into signals, it is natural. 

 On the other hand, we cannot observe any significant differences from phase spectrum. They still seem mere random. MAYBE, since the phase have no locality (the data have similar phase distribution in all coordinates), we cannot find the obvious changes in the phase spectrum. Following graph shows the phase data is spread widely. 

(For the visualization purpose, we used log function to plot magnitude spectrum. Mat2gray normalization was also used for both magnitude and phase spectrum. Magnitude spectrum is the result of abs() function and phase spectrum is the result of angle() function of MATLAB)