Wouldn't this pseudocode give some image values greater than 255? - image-processing

Question

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:

Answer 1

I don't know the Halide syntax, I've just learned it exists. But I can point out one clear problem:
Buffer<uint8_t> sobel_1(3);
sobel_1(0) = -1;
You are assigning -1 to a uint8 type. That doesn't work as intended. Make the kernel a float, and do all computations as floats, then scale the result and store it in your uint8 output image.
When computing using small integer types, one has to be very careful with overflow and underflow. The Sobel computations could likely be done in the (signed) int16 type, but in my experience there is no advantage in that over using the float type, then scaling (or clamping) and casting the result to the output image's type.

Answer 2

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));