What's the state-of-the-art algorithms in image edge detection?
Despite its age, Canny Edge Detection is still a state of the art filter. The results produced by this algorithm make for it always being included in image editing software. Solid and descriptive edges that are often overly represented by other filters. It lacks the simplicity of, say, the Boolean Edge Detection, included in the paper, "Edge Detection Techniques: Evaluations and Comparisons" by Ehsan Nadernejad, Sara Sharifzadeh, Hamid Hassanpour.

The quality of Edge Detection and Segmentation filters are difficult to appraise, and algorithm speed is usually the most important consideration when implementing them.

For code and discussion, you should take your research to codeproject.com, and lookup Image Edge Detection.