Image Sharing with Steganography and Authentication - Visual Cryptography and Secret Image Sharing - page 432

signal D 0 must be created from the former signal D. Interpolation is a classical
solution for calculating the new samples from another digital signal. Take
bilinear interpolation for example. A new sample in signal D 0 is expected to
be an average value of the two neighboring original samples in D. Assuming
that (x, f(x)) and (y, f(y)) are two neighboring samples in D, we can calculate
a new sample (z, f (z)) in D' according to Equation 16.10.

f(z) = yz

yx f(x) + zx yx f(y):

(16.10)

16.3.3 Canny Edge Detector
Edge detection is a kind of commonly used technique in image processing.
The areas in an image with strong intensity contrasting from one pixel to the
next are called edges. The purpose of edge detection is filtering out useless
information in an image and significantly reducing the amount of data, while
preserving the important structural properties.
Since the pioneering work by Roberts in 1965 [19], a mass of schemes have
been developed for detecting edges. The Canny edge detection algorithm is
known to many as the optimal edge detector proposed by J. Canny in 1986
[12], which finds edges by looking for local maxima of the gradient of the input
image. The gradient is calculated using the derivative of a Gaussian filter. The
Canny edge detector contains several adjustable parameters, listed as follows,
which can affect the computation time and effectiveness of the algorithm itself.
The first parameter is the size of the Gaussian filter, the smoothing filter used
in the first stage, which directly affects the results of the Canny detection
algorithm. Generally, smaller filters cause less blurring, and allow detection of
small, sharp lines. On the contrary, larger filters cause more blurring, smearing
out the value of a given pixel over a larger area of the image. Two thresholds
are the other parameters. Actually, a too high threshold may make missing
important information. On the other hand, a threshold set too low will falsely
identify irrelevant information as important. Therewith, the detection would
be more likely to be fooled by noise. The Canny edge detection method uses
two thresholds, to detect strong and weak edges, and includes the weak edges
in the output only if they are connected to strong edges.
The Canny edge detector works in a multistage process. First of all, the
image is smoothed by Gaussian convolution. Afterwards, to highlight regions
of the image with high first spatial derivatives, a simple 2-D first derivative
operator is applied to the smoothed image and edges give rise to ridges in the
gradient magnitude image. Then, the algorithm tracks along the top of these
ridges and sets to zero all pixels that are not actually on the ridge top so as
to give a thin line in the output, a process known as nonmaximal suppression.
The tracking process exhibits hysteresis controlled by two thresholds, denoted
by T 1 and T 2 , where T 1 > T 2 . Tracking can only begin at a point on a ridge
higher than T 1 and then continues in both directions out from that point until