Understanding Fourier Series in MATLAB for Image Shape Classification"

[Zozobra]

Hi all,

I'm struggling to get my head around a problem with Fourier series in MATLAB and so far my attempts have been in vein.

The problem: I'm looking at an image shape classification technique which first finds the center of an image and then maps the radius from the center to image edge over 64 evenly spaced angles (range 0-2pi radians), so that we're looking at the image in polar coordinated relative to the center of the particle.

Using Fourier analysis the radius as a function of angle (a) can then be represented as:

R(a) = A0/2 + sum(Ak*sin*k*a + Bk*cos*k*a) for the sum k=1:32

My question is how to go about calculating the Fourier components A0, Ak and Bk given that my f(x) is not a function but data?

Apologies for the lack of elegance in writing out the formula, I need to learn how to use the formula function here :)

Thanks!

 

[Adrmay]

</code>The Fourier coefficients can be calculated using the Discrete Fourier Transform (DFT). The DFT is a mathematical technique which takes a sequence of values, such as your R(a) data, and returns the corresponding Fourier coefficients.In MATLAB, you can calculate the DFT of your data using the fft() function. This will return a vector containing the complex-valued Fourier coefficients for your data. You can then extract the real-valued coefficients A0, Ak and Bk from the vector using the real() and imag() functions.For example, assuming your R(a) data is stored in a vector called r:<code>coeffs = fft(r);A0 = real(coeffs(1));Ak = real(coeffs(2:end));Bk = imag(coeffs(2:end));</code>

 

[oswaler]

Hi there,

Understanding Fourier series in MATLAB for image shape classification can be a complex task, but with some practice and guidance, it is definitely achievable. Firstly, it is important to understand that Fourier series is a mathematical tool used to represent a periodic function as a sum of sine and cosine functions. In your case, the radius as a function of angle (R(a)) can be represented as a Fourier series.

To calculate the Fourier components A0, Ak, and Bk, you will need to use the Fast Fourier Transform (FFT) algorithm in MATLAB. This algorithm allows you to convert a signal from the time domain to the frequency domain, where you can then extract the Fourier coefficients.

To begin, you will need to convert your data into a vector, where each element represents the radius at a specific angle. Then, you can use the FFT function in MATLAB to calculate the Fourier coefficients. The output of the FFT function will be a complex vector, where the first element represents A0, and the remaining elements represent Ak and Bk. You can use the abs() function to get the magnitude of the complex numbers, which will give you the values for A0, Ak, and Bk.

Once you have calculated the Fourier coefficients, you can then use the formula you provided to represent R(a) as a Fourier series. This will allow you to analyze the image shape and classify it based on the coefficients obtained.

I hope this helps in your understanding of Fourier series in MATLAB for image shape classification. With some practice and experimentation, you will be able to successfully utilize this technique in your research. Best of luck!