机器视觉lec05_corner_blob.pptVIP

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Scale-invariant features: Blobs Recall: Edge detection f Source: S. Seitz Edge Derivativeof Gaussian Edge = maximumof derivative Edge detection, Take 2 f Edge Second derivativeof Gaussian (Laplacian) Edge = zero crossingof second derivative Source: S. Seitz From edges to blobs Edge = ripple Blob = superposition of two ripples Spatial selection: the magnitude of the Laplacianresponse will achieve a maximum at the center ofthe blob, provided the scale of the Laplacian is“matched” to the scale of the blob maximum Scale selection We want to find the characteristic scale of the blob by convolving it with Laplacians at several scales and looking for the maximum response However, Laplacian response decays as scale increases: Why does this happen? increasing σ original signal(radius=8) Scale normalization The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases Scale normalization The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases To keep response the same (scale-invariant), must multiply Gaussian derivative by σ Laplacian is the second Gaussian derivative, so it must be multiplied by σ2 Effect of scale normalization Scale-normalized Laplacian response Unnormalized Laplacian response Original signal maximum Blob detection in 2D Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D Blob detection in 2D Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D Scale-normalized: Scale selection The 2D Laplacian is given by  Therefore, for a binary circle of radius r, the Laplacian achieves a maximum at r image Laplacian response scale (σ) (up to scale) Characteristic scale We define the characteristic scale as the scale that produces peak of Laplacian response characteristic scale T. Lindeberg (1998). Feature detection wi