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### Highlights from Elliptic fourier for shape analysis

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# Elliptic fourier for shape analysis

### Auralius Manurung (view profile)

06 Sep 2011 (Updated )

Implementation of elliptic fourier for shape analysis.

File Information
Description

1) plot_chain_code(ai, color, line_width)
This function will plot the given chain code. The chain code (ai) should be in
column vector.
Example:
>> ai = [5 4 1 2 3 4 3 0 0 1 0 1 0 0 0 7 7 1 1 0 7 5 4 5 4 5 0 6 5 4 1 3 4 4 4 4 6];
>> plot_chain_code(ai)

2) plot_fourier_approx(ai, n, m, normalized, color, line_width)

This function will plot the Fourier approximation, given a chain code (ai),
number of harmonic elements (n), and number of points for reconstruction (m).
Normalization can be applied by setting "normalized = 1".

3) output = calc_traversal_dist(ai, n, m, normalized)

This function will generate position coordinates of chain code (ai). Number of
harmonic elements (n), and number of points for reconstruction (m) must be
specified.
The output is a matrix of [x1, y1; x2, y2; ...; xm, ym].

3) output = fourier_approx(ai, n, m, normalized)

This function will generate position coordinates of Fourier approximation of
chain code (ai). Number of harmonic elements (n), and number of points for
reconstruction (m) must be specified.
The output is a matrix of [x1, y1; x2, y2; ...; xm, ym].

4) output = calc_harmonic_coefficients(ai, n)

This function will calculate the n-th set of four harmonic coefficients.
The output is [an bn cn dn]

5) [A0, C0] = calc_dc_components(ai)

This function will calculate the bias coefficients A0 and C0.

6) output = calc_traversal_dist(ai)

Traversal distance is defined as accumulated distance travelled by every
component of the chain code assuming [0 0] is the starting position.
Example:
>> x = calc_traversal_dist([1 2 3])
x =
1 1
1 2
0 3

7) output = calc_traversal_time(ai)

Traversal time is defined as accumulated time consumed by every
component of the chain code.
Example:
>> x = calc_traversal_time([1 2 3])
x =

1.4142
2.4142
3.8284

Acknowledgements

Elliptical Fourier Shape Descriptors inspired this file.

MATLAB release MATLAB 7.8 (R2009a)
MATLAB Search Path
```/
/eliptic_fourier```
19 May 2016 Auralius Manurung

### Auralius Manurung (view profile)

Hi Chrstopher Cramer,

Yes! You are absolutely right!

Comment only
29 Jan 2016 Chrstopher Cramer

### Chrstopher Cramer (view profile)

Hi Auralius, nice work. I think I've found a couple of additional errors. In both calc_harmonic_coefficients.m and calc_dc_components.m, you have a conditional:

if (p > 2)

in all of these cases, this should either be:

if (p > 1)

or maybe

if (p >= 2)

19 Nov 2012 Auralius Manurung

### Auralius Manurung (view profile)

Hi João Neves,

Sorry for the late reply and thank you for your valuable inputs.

You are definitely right. I will fix this in the next update.

Cheers,
Auralius

Comment only
13 Nov 2012 João Neves

### João Neves (view profile)

Fantastic work, however I would like to know if there is an error in the calc_dc_components function.
Is this line correct?

sum_c0 = sum_c0 + delta_x / (2 * delta_t) * (t(p))^2 + delta * t(p);

or it should be

sum_c0 = sum_c0 + delta_y / (2 * delta_t) * (t(p))^2 + delta * t(p);

Thanks again for this great work

08 Sep 2011 1.1

Added function descriptions for better understanding

27 Nov 2012 1.3

Corrected mistake on the equation based on João Neves' suggestion.

19 May 2016 1.3

Updated as per feedback from Chrstopher Cramer.