Prior knowledge for pattern recognition: Difference between revisions

Revision as of 04:58, 29 September 2011

Revision as of 23:38, 1 December 2011

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A very common type of prior knowledge in pattern recognition is the invariance of the class (or the output of the classifier) to a [[Transformation (geometry)|transformation]] of the input pattern. This type of knowledge is referred to as '''transformation-invariance'''. The mostly used transformations used in image recognition are:

* [[Translation_(geometry)|translation]];

* [[rotationRotation_(mathematics)]];

* [[skewingSkewing]];

* [[scalingScaling_(geometry)]].

Incorporating the invariance to a transformation <math>T_{\theta}: \boldsymbol{x} \mapsto T_{\theta}\boldsymbol{x}</math> parametrized in <math>\theta</math> into a classifier of output <math>f(\boldsymbol{x})</math> for an input pattern <math>\boldsymbol{x}</math> corresponds to enforce the equality