What does it mean "derivative of an image"? I am reading a book about OpenCV, it speaks about some derivative of images like sobel. I am confused about image derivative! What is derived from? How can we derived from an image? I know we consider an image(1-channel) as a n*m matrix with 0 to 255 intensity numbers. How can we derive from this matrix?
EDIT: a piece of text of the book:

Derivatives   and Gradients
One   of  the most    basic   and important   convolutions    is  computing   derivatives
(or   approximations  to  them).  There   are many    ways    to  do  this,   but only    a   few
are   well    suited  to  a   given   situation.
In    general,    the most    common  operator    used    to  represent   differentiation is  the
Sobel derivative  operator.   Sobel
operators exist   for any order   of  derivative  as  well    as  for mixed   partial
derivatives   (e.g.,  ∂ 2 /∂x∂y).
The term Derivative of an Image in the context you mention has two meanings.


A matrix, image, or floating point number that is derived from an image via convolution, passing the image through a two dimensional NN, the application of an FFT analysis, or some other process.  In this context, the word Derivative implies the direction of calculation: Image B is derived from image A.
A matrix or cube that represents the rate of change at in the image being processed.  The change being measured between only two adjacent pixels in a single dimension and only one direction at a time, but the applications of this technique is very limited, and such a sequence is of differences, not at all reasonable approximations of the derivative of light.  What is more useful in real recognition systems are two dimensional or hexagonal windowing (Gausian, Hamming, Hanning, trapazoidal, cosine, ...) across space and, for video, through time.  The calculus term derivative should always reference the theoretical surface being approximated using these techniques, not the discrete matrix or cube that approximates the surface.


Such multidimensional convolution and neural network based approaches are less sensitive to capture noise and orientation nuances.  Two dimensional whole image or windowed FFT techniques have met with much success because filtering the expected frequency range of features to be detected is merely an attenuation process.  Two and three dimensional splines can also be tuned to be useful in the detection of features in an orientation independent way.

In addition to gray scale analysis, color and transparency channels can be selected for independent or parallel analysis or added to the dimension of the fitting model from which the derivative is taken.

Advances in deep networks have blossomed into a new area of image processing and recognition research, bringing new hope to robotics, automated transportation, and cybernetics in general.