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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  • Developer’s Attachment Facilities (“DAF”). Developer shall, at its expense, design, procure, construct, own and install the DAF, as set forth in Appendix A hereto.

  • Software Transfer You may permanently transfer all of your rights under this XXXX, provided you (a) retain no copies, (b) transfer all of the SOFTWARE PRODUCT (including all component parts, the media and printed materials, any upgrades, this XXXX, and, if applicable, the Certificate of Authenticity), and (c) the recipient agrees to abide by all of the terms of this XXXX. If the SOFTWARE PRODUCT is an upgrade, any transfer must include all prior versions of the SOFTWARE PRODUCT and all of your rights therein, if any.

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