The OpenCV Laplacian function (first used in vision by Marr [Marr82]) implements a discrete approximation to the Laplacian operator: [66]
Because the Laplacian operator can be defined in terms of second derivatives, you might well suppose that the discrete implementation works something like the second-order Sobel derivative. Indeed it does, and in fact the OpenCV implementation of the Laplacian operator uses the Sobel operators directly in its computation.
void cvLaplace( const CvArr*src, CvArr*dst, intapertureSize = 3);
The cvLaplace() function takes the usual source and
destination images as arguments as well as an aperture size. The source can be either an
8-bit (unsigned) image or a 32-bit (floating-point) image. The destination must be a 16-bit
(signed) image or a 32-bit (floating-point) image. This aperture is precisely the same as
the aperture appearing in the Sobel derivatives and, in effect, gives the size of the region over which the
pixels are sampled in the computation of the second derivatives.
The Laplace operator can be used in a variety of contexts. A common application is to detect "blobs." Recall that the form of the Laplacian operator is a sum of second derivatives along the x-axis and y-axis. This means that a single point or any small blob (smaller than the aperture) that is surrounded by higher values will tend to maximize this function. Conversely, a point or small blob that is surrounded by lower values will tend to maximize the negative of this function.
With this in mind, the Laplace operator can also be used as a kind of edge detector. To see how this is done, consider the first derivative of a function, which will (of course) be large wherever the function is changing rapidly. Equally important, it will grow rapidly as we approach an edge-like discontinuity and shrink rapidly as we move past the discontinuity. Hence the derivative will be at a local maximum somewhere within this range. Therefore we can look to the 0s of the second derivative for locations of such local maxima. Got that? Edges in the original image will be 0s of the Laplacian. Unfortunately, both substantial and less meaningful edges will be 0s of the Laplacian, but this is not a problem because we can simply filter out those pixels that also have larger values of the first (Sobel) derivative. Figure 6-6 shows an example of using a Laplacian on an image together with details of the first and second derivatives and their zero crossings.