The Hotelling Transform Sample Clauses

The Hotelling Transform. This transform, also known as Principle Component Analysis, can be used to take a matrix of data to be transformed A and select a standard orientation for it. This means that all images of the same covariance will be orientated in the same manner. To perform this transform, the covariance (formed as a circle in Figure 5.4, but normally an ellipse) undergoes Eigenvector and Eigenvalue decomposition, to form a ranked Eigenvector and ranked Eigenvalue matrix. The height and width of the transformed image space is now equal to ⌈ EValue ⌉σ , where EValue represents the largest Eigenvalue and σ represents a sigma capturing the desired number of standard deviations, for example, 3 or 4. To transform the space: Y = AEVector (5.18) In this equation, Y is the resultant image transform that takes the original image to the correct orientation based on the Eigenvectors, A is a matrix formed by taking the data to be transformed and subtracting the mean of the data set from each value. More formally, A= x−Mx  , where x is a data point within the set and Mx is the mean of the data set. Due to the effect of multiplying the A matrix with the Eigenvectors, the transform will now send the data to a patch of unit size. To scale this new Y matrix to a set size, a scalar representing the required size must now be post multiplied with the Y matrix values. Once this is done, a patch normalised for rotation and scale is available.
Sample 1
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Related to The Hotelling Transform

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