I have this image:
What methods should I use to extract the veins from this image. Thank you.
I would like to direct you to 3 references:
C. Steger: “Extracting Curvilinear Structures: A Differential Geometric Approach”. In B. Buxton, R. Cipolla, eds., “Fourth European Conference on Computer Vision”, Lecture Notes in Computer Science, Volume 1064, Springer Verlag, pp. 630-641, 1996.
C. Steger: “Extraction of Curved Lines from Images”. In “13th International Conference on Pattern Recognition”, Volume II, pp. 251-255, 1996.
C. Steger: “An Unbiased Detector of Curvilinear Structures”. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 2, pp. 113-125, 1998.
In these works, Steger develops a subpixel curvilinear structure extraction algorithm, which is found to work very well for such images. I have also run the algorithm on your images and here you go:
Lines visualized on original image

I set the line thickness to 2 for better visualization, normal contours are at sub-pixel level.
For dealing with images like this in the past, I have always had good luck using the "Vesselness" filter designed by Frangi et al. It utilizes the eigenvectors of the Hessian to determine the probability of a given pixel belonging to a vessel. The code is available on the MATLAB File Exchange and using the default parameters I was able to get the following result.
img = imread('image.jpg');
img = 1 - (img(:,:,1) ./ max(max(img(:,:,1))));
f = FrangiFilter2D(img);