How to calculate curvature of isoline of image
Gradient magnitude and angle can be found using a Sobel operator. It's more sophisticated than the [1, 0, -1]. This is commonly used either directly for edge detection, or as part of a more complex algorithm.

Or, if I've misunderstood, and you want only the curvature of the 2D isoline, this answer on Math Overflow might be of use.