This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Computation error

### From Mathematics Is A Science

Pixcavator computes numerous characteristics of objects, see Measuring objects. In terms of errors of computation they fall into four categories.

# 1 Integers

For most of the measurements Pixcavator uses only integer arithmetic, so there is no error. These are Area, Saliency, Contrast, Intensity (gray level). (Of course the resolution affects how well the digital image represents the reality and, therefore, the accuracy. See Continuous vs discrete.)

# 2 Rational numbers

Some measurements aren't integers but come as ratios, in fact pairs, of integers. This is almost as good because the number is turned decimal only when it is displayed. So the error can be easily managed. The location of the Centroid (or the Center of mass) is a ratio of Moments. The Average contrast is saliency divided by the Area. Average intensity also falls into this category.

# 3 Approximations

Lengths of curves cannot be computed exactly in the digital environment. With Pixcavator, the worst-case-scenario, theoretical error is 8% (more testing is needed). Therefore other characteristics also have this error: Perimeter, Roundness, Thickness and length.

# 4 Floating point

Pixcavator does no employ floating point arithmetic. For what can happen when you round up floating point numbers, see this article The Patriot Missile Failure.

See also Robustness of geometry and Robustness of topology.