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 of the input pattern. This type of knowledge is referred to as transformation-invariance. The mostly used transformations used in image recognition are: translation; rotation; skewing; scaling.

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dbpprop:abstract
  • 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 of the input pattern. This type of knowledge is referred to as transformation-invariance. The mostly used transformations used in image recognition are: translation; rotation; skewing; scaling. Incorporating the invariance to a transformation T_{\theta}: \boldsymbol{x} \mapsto T_{\theta}\boldsymbol{x} parametrized in \theta into a classifier of output f(\boldsymbol{x}) for an input pattern \boldsymbol{x} corresponds to enforce the equality f(\boldsymbol{x}) = f(T_{\theta}\boldsymbol{x}), \quad \forall \boldsymbol{x}, \theta Local invariance can also be considered for a transformation centered at \theta=0, so that T_0\boldsymbol{x} = \boldsymbol{x}, by the constraint \left. \frac{\partial}{\partial \theta}\right|_{\theta=0} f(T_{\theta} \boldsymbol{x}) = 0 It must be noted that f in these Equations can be either the decision function of the classifier or its real-valued output. Another approach is to consider the class-invariance with respect to a "domain of the input space" instead of a transformation. In this case, the problem becomes finding f so that f(\boldsymbol{x}) = y_{\mathcal{P}},\ \forall \boldsymbol{x}\in \mathcal{P} where y_{\mathcal{P}} is the membership class of the region \mathcal{P} of the input space. A different type of class-invariance found in pattern recognition is the permutation-invariance, i.e. invariance of the class to a permutation of elements in a structured input. A typical application of this type of prior knowledge is a classifier invariant to permutations of rows in matrix inputs.
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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 of the input pattern. This type of knowledge is referred to as transformation-invariance. The mostly used transformations used in image recognition are: translation; rotation; skewing; scaling.
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  • Prior knowledge for pattern recognition
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