Estimate Image line gradient ( not pixel gradient) - image

Question

I have a problem whereby I want to estimate the gradient of the line on the contour. Please note that I dont need the pixel gradient but the rate of change of line.
If you see the attached image, you will see a binary image with green contour. I want to label each pixel based on the gradient of the pixel on the contour.
Why I need the gradient is because I want to compute the points where the gradient orientation changes from + to - or from - to +.
I cannot think of a good method, to estimate this point on the image. Could someone help me with suggestion on how I can estimate this points.

Answer 1

Here is a small program that computes the tangent at each contour pixel location in a very simple way (there exist other and probably better ways! the easy ones are: http://en.wikipedia.org/wiki/Finite_difference#Forward.2C_backward.2C_and_central_differences):
for a contour pixel c_{i} get the neighbors c_{i-1} and c_{i+1}
tangent direction at c_i is (c_{i-1} - c_{i+1}
So this is all on CONTOUR PIXELS but maybe you could so something similar if you compute the orthogonal to the full image pixel gradient... not sure about that ;)
here's the code:
int main()
{
cv::Mat input = cv::imread("../inputData/ContourTangentBin.png");
cv::Mat gray;
cv::cvtColor(input,gray,CV_BGR2GRAY);
// binarize
cv::Mat binary = gray > 100;
// find contours
std::vector<std::vector<cv::Point> > contours;
std::vector<cv::Vec4i> hierarchy;
findContours( binary.clone(), contours, hierarchy, CV_RETR_TREE, CV_CHAIN_APPROX_NONE ); // CV_CHAIN_APPROX_NONE to get each single pixel of the contour!!
for( int i = 0; i< contours.size(); i++ )
{
std::vector<cv::Point> & cCont = contours[i];
std::vector<cv::Point2f> tangents;
if(cCont.size() < 3) continue;
// 1. compute tangent for first point
cv::Point2f cPoint = cCont.front();
cv::Point2f tangent = cCont.back() - cCont.at(1); // central tangent => you could use another method if you like to
tangents.push_back(tangent);
// display first tangent
cv::Mat tmpOut = input.clone();
cv::line(tmpOut, cPoint + 10*tangent, cPoint-10*tangent, cv::Scalar(0,0,255),1);
cv::imshow("tangent",tmpOut);
cv::waitKey(0);
for(unsigned int j=1; j<cCont.size(); ++j)
{
cPoint = cCont[j];
tangent = cCont[j-1] - cCont[(j+1)%cCont.size()]; // central tangent => you could use another method if you like to
tangents.push_back(tangent);
//display current tangent:
tmpOut = input.clone();
cv::line(tmpOut, cPoint + 10*tangent, cPoint-10*tangent, cv::Scalar(0,0,255),1);
cv::imshow("tangent",tmpOut);
cv::waitKey(0);
//if(cv::waitKey(0) == 's') cv::imwrite("../outputData/ContourTangentTangent.png", tmpOut);
}
// now there are all the tangent directions in "tangents", do whatever you like with them
}
for( int i = 0; i< contours.size(); i++ )
{
drawContours( input, contours, i, cv::Scalar(0,255,0), 1, 8, hierarchy, 0 );
}
cv::imshow("input", input);
cv::imshow("binary", binary);
cv::waitKey(0);
return 0;
}
I used this image:
and got outputs like:
in the result you get a vector with a 2D tangent information (line direction) for each pixel of that contour.