**Problem**

This post continues our series of posts on a programmatic investigation of the effects of the location and thickness of horizontal, vertical, and diagonal lines on the magnitude and phase components of 2D FFT. In this post, we will continue our investigation of horizontal lines by modifying their thickness. The previous post is here.

**Centrally Positioned Horizontal Line Thickened**

**Figure 1**shows a horizontal line centrally positioned in the image and thickened.

Figure 1. Centrally positioned horizontal line thickened (hor_line_01d.jpg) |

We add the path, read the image, and display it.

img_hor_line_01d = imread('hor_line_01d', 'jpg');

figure;

imshow(img_hor_line_01d);

title('HOR LINE 01d');

Here is how we compute the 2D FFT of the image. The image is converted into a 2D double matrix. The fftshift command positions the 0,0 origin to the center of the image. We compute the absolute magnitude of each value in the 2D matrix and take the log of each value. 1 is added to each value before taking the log, because log(0) is not defined.

%% ff2 magnitude

fftHorLine01d = fft2(double(img_hor_line_01d));

fftHorLine01d = fftshift(fftHorLine01d);

fftHorLine01d = abs(fftHorLine01d);

fftHorLine01d = log(fftHorLine01d+1);

fftHorLine01d = mat2gray(fftHorLine01d);

The magnitude image is shown in

**Figure 2**. As can be seen in

**Figure 2**, the FFT magnitude shows a line orthogonal to the line in

**Figure 1**.

figure;

imshow(fftHorLine01d), colormap(gray);

title('HOR LINE 01d FFT2 Magnitude');

Figure 2. 2D FFT magnitude of Figure 1 |

**Figure 3**.

%% fft2 phase

fftHorLine01d_PHASE = fft2(double(img_hor_line_01d));

fftHorLine01d_PHASE = fftshift(fftHorLine01d_PHASE);

fftHorLine01d_PHASE = angle(fftHorLine01d_PHASE);

figure;

imshow(fftHorLine01d_PHASE, [-pi, pi]), colormap(gray);

title('HOR LINE 01d FFT2 Phase');

Figure 3. 2D FFT phase of Figure 1 |