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This article presents a novel scale- and rotation-invariant detector and descriptor, coined SURF (Speeded-Up Robust Features). SURF approximates or even outperforms previously proposed schemes with respect to repeatability, distinctiveness, and robustness, yet can be computed and compared much faster. This is achieved by relying on integral images for image convolutions; by building on the strengths of the leading existing detectors and descriptors (specifically, using a Hessian matrix-based measure for the detector, and a distribution-based descriptor); and by simplifying these methods to the essential. This leads to a combination of novel detection, description, and matching steps. The paper encompasses a detailed description of the detector and descriptor and then explores the effects of the most important parameters. We conclude the article with SURF's application to two challenging, yet converse goals: camera calibration as a special case of image registration, and object recognition. Our experiments underline SURF's usefulness in a broad range of topics in computer vision.
The authors develop and describe a novel method for detecting, describing and matching interest points in images. Comparison with various state of art techniques show the novel descriptor, SURF, outperforms them. In addition to higher quality matching, the new technique is also simpler and faster to both compute and match.
SURF Detector:
Interest points are defined as local maxima in scale space of the determinant of the Hessian over a neighborhood. In practice the Hessian is computed over the image using a box-filter to approximate second order derivative of Gaussians. By using integral images the image response to the box filters can be computed quickly in time independent of the filter size. Multiple scales are approximated by up-sampling the box-filter, instead of down-sampling the image. This eliminates aliasing effects and leads to faster performance, but at the same time can introduce spurious responses from high-frequency elements.
The final location of the interest points is determined by applying 3D local-maxima suppression and interpolating through scale space.
SURF Descriptor:
Rotational invariance can be added by setting a dominant orientation to the interest point. First Haar wavelet responses (dx and dy box filters) are computed around the interest point, weighted by a Gaussian of size 2s (Where s is the scale at which the point is detected). The responses are represented as 2d points (2D histogram of gradients). A sliding orientation window with angle pi/3 is rotated around the histogram, and the responses of all points falling within the window are summed to generate a direction vector. The orientation at which the length of the direction vector is maximized is defines the dominant orientation.
The descriptor is defined as the sum of Haar wavelet responses around the interest point, summed across locally defined bins as aligned with the dominant orientation. The support region is of size 20s. The region is divided into 4X4 equal sub-regions, for each sub-region Haar wavelet responses are computed (Using filter size of 2s) at 5X5 regularly spaced sample points. These are weighted by a Gaussian window with size 3.3s.
For each sub-region the descriptor consists of 4 values, the sum of reponses in x and y directions, and the sum of absolute responses in x and y directions v = (sum dx, sum dy, sum |dx|, sum |dy|). This yields a final descriptor of length 64.
The final vector is normalized to unit length to account for illumination invariance.
Speed-up is achieved by using integral images to compute responses to the Haar wavelet. Also, instead of rotating the image by the dominant orientation to calculate the descriptor Haar wavelet responses are calculated on the original image and interpolated to account for the dominant orientation.
SURF Matching:
In addition to the descriptor mentioned earlier, each SURF feature also includes the sign of the Laplacian at the interest point (The trace of the Hessian matrix computed earlier). This is used during matching to quickly eliminate a large portion of the query space. Note that the sign of the Laplacian defines whether the interest point is centered around a dark blob on a brighter background or vice-versa.
After filtering with the sign of the Laplacian, matches are found using a standard distance measurement.
The speed-up here is a result of the Laplacian sign and due to the fact that the descriptor is only a 64 length vector.
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- 2009-09-17 21:23:07
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