Hough lines not reaching the edge of an image

I am tryiing to detect all the lines in the following image:

Using the following code I am able to detect almost all lines:

%Find the line detected

I = imread('img3.png');
J = histeq(I);
BW = edge(J,'canny');
[H,T,R] = hough(BW);
P = houghpeaks(H,30,'Threshold',0.7*max(H(:)),'nhoodsize',[5 5]);
lines = houghlines(BW,T,R,P );
figure, imshow(I, []), hold on, max_len = 0;
for k = 1:length(lines)
 xy = [lines(k).point1; lines(k).point2];
 plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green');
 plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow');
 plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red');
 len = norm(lines(k).point1 - lines(k).point2);
 if ( len > max_len)
 max_len = len;
 xy_long = xy;
 end
end

% highlight the longest line segment
plot(xy_long(:,1),xy_long(:,2),'LineWidth',2,'Color','red');

This gives the following image

However as you can see the lines do not go all the way to the edge of the image. I have tried shrinking the nhood size but this meant double detection of some lines and no extension of lines to the edge.

Also is it possible to detect the very top and bottom lines? I understand that these lines won't have as many votes due to them being shorter, I've modified the threshold but end up with spurious diagonal lines and still no detection of the top and bottom lines.

Thanks in advance

Answer 1

[VINAYAK LUHA]

Hi Joe,

I understand that you have applied hough lines detection on an image and were able to detect almost all lines. Further you want to know how to extend these lines and also to detect the remaning lines which were missed.

For the initial concern of extending lines, you can determine where each line intersects with the edges of the image. These intersection points can then be utilized to redraw the extended lines. Here's the MATLAB code that illustrates this process:

I = imread('image.png');
J = histeq(I);
BW = edge(J,'canny');
[H,T,R] = hough(BW);
P = houghpeaks(H,30,'Threshold',0.7*max(H(:)),'nhoodsize',[5 5]);
lines = houghlines(BW,T,R,P);
figure, imshow(I, []), hold on, max_len = 0;

image_height = size(I, 1);
image_width = size(I, 2);

for k = 1:length(lines)
    % Calculate the slope (m) and y-intercept (b) of the line
    x1 = lines(k).point1(1);
    y1 = lines(k).point1(2);
    x2 = lines(k).point2(1);
    y2 = lines(k).point2(2);
    m = (y2 - y1) / (x2 - x1);
    b = y1 - m * x1;
    
    % Find intersection with the left border (x=1)
    y_left = m * 1 + b;
    left_point = [1, y_left];
    
    % Find intersection with the right border (x=image_width)
    y_right = m * image_width + b;
    right_point = [image_width, y_right];
    
    % Find intersection with the top border (y=1)
    x_top = (1 - b) / m;
    top_point = [x_top, 1];
    
    % Find intersection with the bottom border (y=image_height)
    x_bottom = (image_height - b) / m;
    bottom_point = [x_bottom, image_height];
    
    % Check which points are actually within the borders
    points = [left_point; right_point; top_point; bottom_point];
    points = points(points(:,1) >= 1 & points(:,1) <= image_width & ...
                    points(:,2) >= 1 & points(:,2) <= image_height, :);
    
    % Sort points by x-coordinate (or y-coordinate if the line is closer to vertical)
    if abs(m) > 1
        points = sortrows(points, 2); % Sort by y if the line is steep
    else
        points = sortrows(points, 1); % Sort by x otherwise
    end
    
    % Take the two end points for the line segment
    point1 = points(1, :);
    point2 = points(end, :);
    
    % Plot the extended line
    plot([point1(1), point2(1)], [point1(2), point2(2)], 'LineWidth',2,'Color','green');
end

Result

Regarding the secondary part of the query, to detect the remaining lines or refine the detections, you can impose constraints on the angles of detection, filter out lines based on their orientation, and exclude similar lines by considering the proximity between them.

Hope this answers your query.

Regards,

Vinayak Luha