you can check the following paper:

https://pdfs.semanticscholar.org/a284/851170635a6f9ad07a31001e6a5ab4724480.pdf

https://www.ripublication.com/irph/ijict_spl/ijictv4n10spl_04.pdf

hope you can benefit from them

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Conference Paper A Fast FPGA Based Architecture for Sobel Edge Detection

As far as I know : Sobel , direct convolution operators are first oder and hence low complexity while LoG ,Canny are second order hence greater is the complexity

There will not be just an answer to this general question.

Let me suggest a method:

You want to identify the edge of an object in a scene. For instance a square painted in blue.

1) start from inside the square M(0)

2) blow a balloon (a circle) of center M(0) until it hits the border of the square (pixels not homogeneously blue as on square)

3)deflate a balloon enclosing the square until it hits the square.

You now have a circle outside and another inside.

It's been quick and low complexity

Now you just focus your attention to edge detection between the circles, a much reduced area.

You could do this with basic shapes different from a circle, whatever is closest to the object of interest...

Video is basically sequence of images. So, any edge detection method for image can also be used for video.

A classic paper about edge detection review is "Edge Detection Techniques - An Overview"

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.1821

There are many standard edge detection algorithms such as Sobel', 'Prewitt', 'Roberts', 'Canny'. Canny's method is considered very robust. Sobel edge detection works quite fast, it returns a binary image (Black and White) containing 1s where the it finds edges in the input image and 0s elsewhere.

If you are using MATLAB software (suggested), then please have a look at

https://www.mathworks.com/help/images/ref/edge.html

Thanks.

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