I would have some questions about the Fourier descriptor and the physical interpretation of the individual coefficients. I'm rather new to this concept, so I would be looking for a simple answer.
To start with I have a curve in xy [mm] coordinates (188x2 points). To calculate the descriptor I use the function found in R.C. Gonzales 'Digital Image Processing using Matlab' (p. 629). From that I get a vector with the descriptors An (188x1). As far as I understand the concept of the descriptor I can 'filter' out the high frequencies by reconstructing the shape again with only a handful of descriptors.
Here are my questions now:
I read that, the DC component A0 is the position of my shape in the image and its the mean values of the x,y coordinates. I understand that, I could calculate the position directly form my x,y coordinates, but I was wondering where this DC component is in the descriptor vector, since its a even number of values. Is it the term with the highest value?
Which brings me to my second question. If I recalculate the shape with only 2 descriptors I obtain a circle around the mean position with a certain radius. Is the radius then the second highest value?
Last question. Im mainly interested in the ellipses that is created with recalculating the shape with 4 factors. But I would also like to understand the whole concept correctly. I read that the A-1 and A1 coefficients represent the major (d) and minor (e) axis of this ellipses. And that with d = 2(|A-1| + |A1|) and e = 2(|A-1| - |A1|) the axis can be calculated in a length unit. Do I have to scale these values somehow? Because if I pick the third and fourth highest values, the result is not what I expect.
I hope someone can help me better understand this. Thank you in advance.