SURF: Speeded Up Robust Features: Difference between revisions
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Our features will be regions in the image where the determinant of the Hessian are local maxima. | Our features will be regions in the image where the determinant of the Hessian are local maxima. | ||
[[File:surf_fig_1.png | thumb | 500px | Figure 1 from the paper. Each region can be computed using a summed area table/integral image.]] | |||
* The Hessian matrix: | * The Hessian matrix: | ||
<math>\mathcal{H}(\mathbf{x}, \sigma) | <math>\mathcal{H}(\mathbf{x}, \sigma) | ||
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\end{bmatrix}</math> | \end{bmatrix}</math> | ||
* Each entry is a convolution of a the Gaussian second order derivative with the image at <math>\mathbf{x}</math> | * Each entry is a convolution of a the Gaussian second order derivative with the image at <math>\mathbf{x}</math> | ||
* These convolutions are approximated using box filters on an integral image. | * These convolutions are approximated using box filters on an integral image (Fig 1). | ||
*: The approximations are denoted as <math>D_{xx}, D_{yy}, D_{xy}</math> | *: The approximations are denoted as <math>D_{xx}, D_{yy}, D_{xy}</math> | ||
* The determinant of the hessian is then <math>D_{xx}D_{yy} - (0.9*D_{xy})^2</math> | * The determinant of the hessian is then <math>D_{xx}D_{yy} - (0.9*D_{xy})^2</math> | ||