SIFT Sample Clauses

SIFT. The SIFT algorithm consists of two main phases: features detection and feature description. We focus here on the most computation-intensive part, feature detection. A candidate feature (keypoint) is a pixel located at a specific image frequency scale that has either the minimum or the maximum value in relation to its neighborhood, defined by a 3x3 window located at the same scale space and at the upper and lower adjacent scales. The frequency band for each scale is obtained by using the difference of Gaussian (DoG) operation, which is computed by subtracting two identical images convolved by two different Gaussian kernels. Equation (1) defines the convolution operation for the first and the other subsequent scales, where I is the input image, K the Gaussian kernel and G the smoothed image. G0 (x, y) = K0 (x, y)* I (x, y) Gs+1 (x, y) = K s+1 (x, y)*G s+1 (x, y) (1) Equation (2) defines the difference operation (DoG), where D is the resulting image at a specific frequency scale defined by the kernel values (s). Di (x, y) = Gs+1 (x, y) − Gs (x, y) (2) Accepting a keypoint as a feature is evaluated through three functions: location refinement, contrast check and edge responses. The location refinement is performed as shown in Equation (3), where l is the pixel location vector (x; y; s) (coordinates <x;y> and scale s). This equation performs an interpolation operation with the pixels found inside of the keypoint’s neighborhood (26 pixels), with ω added to the current keypoint position in order to produce its new location. The ω offset is also used to compute the keypoint contrast. If the result is smaller than a user- defined threshold then the keypoint is rejected. ⎛ ∂ 2 D ⎞−1 ∂D ⎜ ∂ 2l ⎟ ⎠ ∂l (3) Finally, principal curvature analysis is evaluated to reject keypoints that are located at poorly defined edges, which are consequently highly unstable to noise. This is particulary necessary for the difference of Gaussian function because most of the detected keypoints are located at edges. The bigger the principal curvature, the poorer is its edge. Equation (4) shows how the principal curvature is computed (and rejected if it is above a pre-established threshold). ⎜ ⎛ ∂D ⎝ ⎜ ∂x 2 ∂D ⎞2 ⎟ ⎠ + ∂y 2 ⎟ ( ) ≤ Threshold (4) where ⎡ ∂D ∂D ⎤ ⎢ ∂x 2 ∂x∂y ⎥ H = ⎢ ∂D ∂D ⎥ (5) ⎢ ⎥ ⎢⎣ ∂y∂x ∂y 2 ⎥⎦