Elliptical Fourier shape descriptors

Forward and reverse elliptical Fourier transforms of x,y data

Description

These two functions impliment the system of elliptical Fourier shape descriptors first described by Kuhl and Giardina in "Elliptic Fourier features of a closed contour" Computer Graphics and Image Processing 18:236-258 1982. fEfourier is the forward transform which creates a "shape spectrum" of a closed x,y outline, rEfourier takes a specified number of harmonics from the spectrum and reconstructs the x,y outline. The functions are not only useful for the creation of shape descriptors but also for smoothing outlines or reducing an arbitrary outline to a specified number of points.

• Acknowledgements: This submission has inspired the following:; Elliptical Fourier Shape Descriptors GUI, Elliptic fourier for shape analysis
• MATLAB release: MATLAB 7.2 (R2006a)

[praveen kumar]

 

[Vidyaangi Patil]

 

[Graeme Penney]

Overall excellent, though I suspect there may be a bug. I get much more sensible results if I omit the -1 from line 39 of fEfourier.m
iNoOfPoints = size(rDeltaT,1) - 1.

[Trevor Beugeling]

The algorithm works great. However, I am having some difficulties using the normalization options. If I enable either the size or orientation normalization (or both), the data returned after using the rEfourier function is not correct. Is there some extra processing that is required when converting normalized descriptors back into a closed contour?

[Sungeun Eom]

Thanks for your work, but I have found two bugs in calculating rTheta1 and rPsi1. You didn't check whether it is a semimajor or semiminor axis. This is one fix for the problem for your information:

1) rTheta1 (line 137-138)
rTheta1 = 0.5 * atan(2 * (rFSDsTemp(1,2) * rFSDsTemp(2,2) + rFSDsTemp(3,2) * rFSDsTemp(4,2)) / ...
        (rFSDsTemp(1,2)^2 + rFSDsTemp(3,2)^2 - rFSDsTemp(2,2)^2 - rFSDsTemp(4,2)^2));
    rTheta2 = 0.5 * (pi + atan(2 * (rFSDsTemp(1,2) * rFSDsTemp(2,2) + rFSDsTemp(3,2) * rFSDsTemp(4,2)) / ...
        (rFSDsTemp(1,2)^2 + rFSDsTemp(3,2)^2 - rFSDsTemp(2,2)^2 - rFSDsTemp(4,2)^2)) );
    x11 = rFSDsTemp(1,2)*cos(rTheta1) + rFSDsTemp(2,2)*sin(rTheta1);
    y11 = rFSDsTemp(3,2)*cos(rTheta1) + rFSDsTemp(4,2)*sin(rTheta1);
    axisDist1 = x11^2 + y11^2;
    x22 = rFSDsTemp(1,2)*cos(rTheta2) + rFSDsTemp(2,2)*sin(rTheta2);
    y22 = rFSDsTemp(3,2)*cos(rTheta2) + rFSDsTemp(4,2)*sin(rTheta2);
    axisDist2 = x22^2 + y22^2;
    if (axisDist2 > axisDist1)
        rTheta1 = rTheta2;
    end

2) rPsi1 (line 148)
if (rStarFSDs(3,2)~=0)
        if (rStarFSDs(1,2)>=0)
            rPsi1 = atan(rStarFSDs(3,2) / rStarFSDs(1,2));
        else
            rPsi1 = atan(rStarFSDs(3,2) / rStarFSDs(1,2)) + pi;
        end
    else
        if (rStarFSDs(1,2)>0)
            rPsi1 = atan(rStarFSDs(3,2) / rStarFSDs(1,2));
        else
            rPsi1 = atan(rStarFSDs(3,2) / rStarFSDs(1,2)) + pi;
        end
    end

[YOUSHIA youshbob]

YYOOUU SSSSSSSSTTTTTTTIINNNKKKKKKKKKKK!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[Xiaoming Liu]

Very good, easy to use. one question, if I need to use it as features, how to organize the 4 coefficients?

[Filippo Leite]

 

[Abdul Rana]

Is it posssible for you to upload a detailed help description along with this file?

[sanqin zhao]

Excellent codes. I have also found the same problem that You didn't check whether it is a semimajor or semiminor axis.Meanwhile, the code can use the vectorization to speed up.For example, 'rDeltaX = diff(b(:,1)); rDeltaY = diff(b(:,2));' can replace the for loop.

[michael scheinfeild]

can we have some example how to use this code ?