Introduction - Feature Extraction and Image Processing - page 16

perhaps the two most popular of the mathematical systems. We shall describe Matlab later,
as it is different from Mathcad, though the aim is the same. The website links for the main
mathematical packages are given in Table 1.3 .

Table 1.3 Mathematical package websites

General

Math-Net Links to the Math-Net

http://www.math-net.de/

Mathematical World (Germany)

Vendors

Mathcad MathSoft http://www.mathcad.com/

Mathematica Wolfram Research http://www.wri.com/

Matlab Mathworks

http://www.mathworks.com/

1.5.2 Hello Mathcad, Hello images!

The current state of evolution is Mathcad 2001; this adds much to version 6 which was
where the system became useful as it included a programming language for the first time.
Mathcad offers a compromise between many performance factors, and is available at low
cost. If you do not want to buy it, there was a free worksheet viewer called Mathcad
Explorer which operates in read-only mode. There is an image processing handbook available
with Mathcad, but it does not include many of the more sophisticated feature extraction
techniques.
Mathcad uses worksheets to implement mathematical analysis. The flow of calculation
is very similar to using a piece of paper: calculation starts at the top of a document, and
flows left-to-right and downward. Data is available to later calculation (and to calculation
to the right), but is not available to prior calculation, much as is the case when calculation
is written manually on paper. Mathcad uses the Maple mathematical library to extend its
functionality. To ensure that equations can migrate easily from a textbook to application,
Mathcad uses a WYSIWYG (What You See Is What You Get) notation (its equation editor
is actually not dissimilar to the Microsoft Equation (Word) editor).
Images are actually spatial data, data which is indexed by two spatial co-ordinates. The
camera senses the brightness at a point with co-ordinates x , y . Usually, x and y refer to the
horizontal and vertical axes, respectively. Throughout this text we shall work in orthographic
projection , ignoring perspective , where real world co-ordinates map directly to x and y co-
ordinates in an image. The homogeneous co-ordinate system is a popular and proven
method for handling three-dimensional co-ordinate systems ( x , y and z where z is depth).
Since it is not used directly in the text, it is included as Appendix 1 (Section 9.1). The
brightness sensed by the camera is transformed to a signal which is then fed to the A/D
converter and stored as a value within the computer, referenced to the co-ordinates x, y in
the image. Accordingly, a computer image is a matrix of points. For a greyscale image, the
value of each point is proportional to the brightness of the corresponding point in the scene
viewed, and imaged, by the camera. These points are the picture elements, or pixels .