Wouldn't this pseudocode give some image values greater than 255?
I'm implementing the sobel filter according to the following pseudocode taken from Wikipedia:
function sobel(A : as two dimensional image array)
Gx=[-1 0 1; -2 0 2; -1 0 1]
Gy=[-1 -2 -1; 0 0 0; 1 2 1]
rows = size(A,1)
columns = size(A,2)
mag=zeros(A)
for i=1:rows-2
for j=1:columns-2
S1=sum(sum(Gx.*A(i:i+2,j:j+2)))
S2=sum(sum(Gy.*A(i:i+2,j:j+2)))
mag(i+1,j+1)=sqrt(S1.^2+S2.^2)
end for
end for
threshold = 70 %varies for application [0 255]
output_image = max(mag,threshold)
output_image(output_image==round(threshold))=0;
return output_image
end function
However, upon applying this algorithm, I'm getting many output_image values above 255, and that makes sense considering how Gx and Gy are defined. How can I modify this algorithm such that the values don't go above 255 and finally that the results look more like this?:
--- Edit ---
There was some error in my filter implementation and I think that's why the values were above 255. After fixing the error, the values range between 0 - 16. Since now all values are below 70, applying a threshold of 70 sends everything to 0. So I set a lower threshold, 5, and multiplied the rest of the values by 10 (to enhance the edges since they are in the 5-16 range) and got the following result:
I also tried the normalization method mentioned in the comments but got a similar noisy image.
--- Edit 2 ---
Since the actual code was requested, I'm posting the code, which is written in Halide.
int main(int argc, char **argv) {
Var x, y, k, c;
Buffer<uint8_t> left_buffer = load_image("images/stereo/bike.jpg");
Expr clamped_x = clamp(x, 0, left_buffer.width() - 1);
Expr clamped_y = clamp(y, 0, left_buffer.height() - 1);
Func left_original("left_original");
left_original(x, y) = left_buffer(clamped_x, clamped_y);
left_original.compute_root();
// 3x3 sobel filter
Buffer<uint8_t> sobel_1(3);
sobel_1(0) = -1;
sobel_1(1) = 0;
sobel_1(2) = 1;
Buffer<uint8_t> sobel_2(3);
sobel_2(0) = 1;
sobel_2(1) = 2;
sobel_2(2) = 1;
RDom conv_x(-1, 2);
RDom conv_y(-1, 2);
Func output_x_inter("output_x_inter");
output_x_inter(x, y) = sum(left_original(x - conv_x, y) * sobel_1(conv_x + 1));
output_x_inter.compute_root();
Func output_x("output_x");
output_x(x, y) = sum(output_x_inter(x, y - conv_y) * sobel_2(conv_y + 1));
output_x.compute_root();
Func output_y("output_y");
output_y(x, y) = sum(conv_y, sum(conv_x, left_original(x - conv_x, y - conv_y) * sobel_2(conv_x + 1)) * sobel_1(conv_y + 1));
output_y.compute_root();
Func output("output");
output(x, y) = sqrt(output_x(x, y) * output_x(x, y) + output_y(x, y) * output_y(x, y));
output.compute_root();
output.trace_stores();
RDom img(0, left_buffer.width(), 0, left_buffer.height());
Func max("max");
max(k) = f32(0);
max(0) = maximum(output(img.x, img.y));
max.compute_root();
Func min("min");
min(k) = f32(0);
min(0) = minimum(output(img.x, img.y));
min.compute_root();
Func output_u8("output_u8");
// The following line sends all the values of output <= 5 to zero, and multiplies the resulting values by 10 to enhance the intensity of the edges.
output_u8(x, y) = u8(select(output(x, y) <= 5, 0, output(x, y))*10);
output_u8.compute_root();
output_u8.trace_stores();
Buffer<uint8_t> output_buff = output_u8.realize(left_buffer.width(), left_buffer.height());
save_image(output_buff, "images/stereo/sobel/out.png");
}
--- Edit 3 ---
As one answer suggested, I changed all types to float except the last one, which must be unsigned 8-bit type. Here's the code, and the result that I'm getting.
int main(int argc, char **argv) {
Var x, y, k, c;
Buffer<uint8_t> left_buffer = load_image("images/stereo/bike.jpg");
Expr clamped_x = clamp(x, 0, left_buffer.width() - 1);
Expr clamped_y = clamp(y, 0, left_buffer.height() - 1);
Func left_original("left_original");
left_original(x, y) = left_buffer(clamped_x, clamped_y);
left_original.compute_root();
// 3x3 sobel filter
Buffer<float_t> sobel_1(3);
sobel_1(0) = -1;
sobel_1(1) = 0;
sobel_1(2) = 1;
Buffer<float_t> sobel_2(3);
sobel_2(0) = 1;
sobel_2(1) = 2;
sobel_2(2) = 1;
RDom conv_x(-1, 2);
RDom conv_y(-1, 2);
Func output_x_inter("output_x_inter");
output_x_inter(x, y) = f32(sum(left_original(x - conv_x, y) * sobel_1(conv_x + 1)));
output_x_inter.compute_root();
Func output_x("output_x");
output_x(x, y) = f32(sum(output_x_inter(x, y - conv_y) * sobel_2(conv_y + 1)));
output_x.compute_root();
RDom img(0, left_buffer.width(), 0, left_buffer.height());
Func output_y("output_y");
output_y(x, y) = f32(sum(conv_y, sum(conv_x, left_original(x - conv_x, y - conv_y) * sobel_2(conv_x + 1)) * sobel_1(conv_y + 1)));
output_y.compute_root();
Func output("output");
output(x, y) = sqrt(output_x(x, y) * output_x(x, y) + output_y(x, y) * output_y(x, y));
output.compute_root();
Func max("max");
max(k) = f32(0);
max(0) = maximum(output(img.x, img.y));
max.compute_root();
Func min("min");
min(k) = f32(0);
min(0) = minimum(output(img.x, img.y));
min.compute_root();
// output_inter for scaling
Func output_inter("output_inter");
output_inter(x, y) = f32((output(x, y) - min(0)) * 255 / (max(0) - min(0)));
output_inter.compute_root();
Func output_u8("output_u8");
output_u8(x, y) = u8(select(output_inter(x, y) <= 70, 0, output_inter(x, y)));
output_u8.compute_root();
output_u8.trace_stores();
Buffer<uint8_t> output_buff = output_u8.realize(left_buffer.width(), left_buffer.height());
save_image(output_buff, "images/stereo/sobel/out.png");
}
--- Edit 4 ---
As @CrisLuengo suggested, I simplified my code and outputted the result of the following:
output(x, y) = u8(min(sqrt(output_x(x, y) * output_x(x, y) + output_y(x, y) * output_y(x, y)), 255));
Since many values are way above 255, these many values are clamped to 255 and thus we get a "washed out" image:
I figured it out finally, but I'm not sure why Halide is behaving this way. When I do this:
RDom conv_x(-1, 2);
RDom conv_y(-1, 2);
Func output_x_inter("output_x_inter");
output_x_inter(x, y) = f32(sum(left_original(x - conv_x, y) * sobel_1(conv_x + 1)));
Func output_x("output_x");
output_x(x, y) = f32(sum(output_x_inter(x, y - conv_y) * sobel_2(conv_y + 1)));
Things don't work. But when I "unroll" the sum function things work:
Func output_x_inter("output_x_inter");
output_x_inter(x, y) = f32(left_original(x + 1, y) * sobel_1(0) + left_original(x, y) * sobel_1(1) + left_original(x - 1, y) * sobel_1(2));
Func output_x("output_x");
output_x(x, y) = f32(output_x_inter(x, y + 1) * sobel_2(0) + output_x_inter(x, y) * sobel_2(1) + output_x_inter(x, y - 1) * sobel_2(2));