Application of SURF method in access control systems based on biometric technologies
The Speeded Up Robust Features (SURF) method has positively proven itself in the tasks of finding objects in images, 3D reconstruction, when comparing images. Consider the use of this method in biometric systems that authenticate by vascular hand drawing.
The SURF method solves two problems - the search for special points of the image and the creation of their descriptors (descriptive element, invariant to change the scale and rotation). In addition, the search for key points itself must also have invariance, i.e. The rotated object of the scene must have the same set of cue points as the sample.
The method searches for singular points using the Hesse matrix. The determinant of the Hessian matrix (the so-called Hessian) reaches an extremum at the points of the maximum change in the brightness gradient. For a two-dimensional function, its determinant is defined as follows:
')
where H is the Hesse matrix,
f (x, y) - the function of changing the brightness gradient.
Hessian is invariant with respect to rotation. But not scale invariant. Therefore, the SURF method uses multi-scale filters to find the Hessians. For each key point is considered a gradient and scale. The point gradient is calculated using Haar filters. The filter size is taken equal to 4s (where s is the scale of the singular point). The view of the Haar filters is shown in fig. one.
Fig. 1. Haar filters. (black areas have values “-1”, white “+1”)
After finding the key points, the SURF method generates their descriptors. A descriptor is a set of 64 (or 128) numbers for each key point. These numbers represent gradient fluctuations around a key point. Since the key point is the maximum of the Hessian, it is thus guaranteed that there should be areas with different gradients in the vicinity of the point. Thus, the variance (difference) of the descriptors for different key points is ensured, due to which the invariance of the descriptor with respect to rotation is achieved. The size of the area on which the descriptor is considered is determined by the scale of the Hessian matrix, which ensures scale invariance.
In fig. Figures 2-5 show a set of test images obtained as a result of using the SURF method in biometric systems that authenticate using a vascular palm pattern.
Fig. 2. On the left is the sample, on the right is the scene. Localized.
Fig. 3. The sample has a larger scale than the stage. Localized.
Fig. 4. The sample is rotated 45 degrees. Localized.
Fig. 5. There is no sample on stage. The algorithm did not find localization.
In general, the method copes with the task of recognizing the patterns of a vascular palm pattern. The smaller the area, the less large-scale distortion affects it. So, if the object as a whole, is subject to the effect of perspective (the near edge of the object has a larger visible size than the distant one), for a small part of it, the perspective phenomenon can be neglected, replacing with scaling. Similarly, a small rotation of the object around the axis can greatly change the image of the object as a whole, but small areas will change slightly. In addition, in the case when a part of the object extends beyond the edge of the image or is obscured, small areas around a part of the key points are visible in their entirety, which also allows them to be identified. In the case when small areas lie entirely inside the desired object, background objects have no effect on them. On the other hand, the area around the key point should not be too small. Very small areas carry insufficient information about the image and are more likely to coincide randomly with each other.
The SURF method solves two problems - the search for special points of the image and the creation of their descriptors (descriptive element, invariant to change the scale and rotation). In addition, the search for key points itself must also have invariance, i.e. The rotated object of the scene must have the same set of cue points as the sample.
The method searches for singular points using the Hesse matrix. The determinant of the Hessian matrix (the so-called Hessian) reaches an extremum at the points of the maximum change in the brightness gradient. For a two-dimensional function, its determinant is defined as follows:
')
where H is the Hesse matrix,
f (x, y) - the function of changing the brightness gradient.
Hessian is invariant with respect to rotation. But not scale invariant. Therefore, the SURF method uses multi-scale filters to find the Hessians. For each key point is considered a gradient and scale. The point gradient is calculated using Haar filters. The filter size is taken equal to 4s (where s is the scale of the singular point). The view of the Haar filters is shown in fig. one.
Fig. 1. Haar filters. (black areas have values “-1”, white “+1”)
After finding the key points, the SURF method generates their descriptors. A descriptor is a set of 64 (or 128) numbers for each key point. These numbers represent gradient fluctuations around a key point. Since the key point is the maximum of the Hessian, it is thus guaranteed that there should be areas with different gradients in the vicinity of the point. Thus, the variance (difference) of the descriptors for different key points is ensured, due to which the invariance of the descriptor with respect to rotation is achieved. The size of the area on which the descriptor is considered is determined by the scale of the Hessian matrix, which ensures scale invariance.
In fig. Figures 2-5 show a set of test images obtained as a result of using the SURF method in biometric systems that authenticate using a vascular palm pattern.
Fig. 2. On the left is the sample, on the right is the scene. Localized.
Fig. 3. The sample has a larger scale than the stage. Localized.
Fig. 4. The sample is rotated 45 degrees. Localized.
Fig. 5. There is no sample on stage. The algorithm did not find localization.
In general, the method copes with the task of recognizing the patterns of a vascular palm pattern. The smaller the area, the less large-scale distortion affects it. So, if the object as a whole, is subject to the effect of perspective (the near edge of the object has a larger visible size than the distant one), for a small part of it, the perspective phenomenon can be neglected, replacing with scaling. Similarly, a small rotation of the object around the axis can greatly change the image of the object as a whole, but small areas will change slightly. In addition, in the case when a part of the object extends beyond the edge of the image or is obscured, small areas around a part of the key points are visible in their entirety, which also allows them to be identified. In the case when small areas lie entirely inside the desired object, background objects have no effect on them. On the other hand, the area around the key point should not be too small. Very small areas carry insufficient information about the image and are more likely to coincide randomly with each other.
Source: https://habr.com/ru/post/152679/
All Articles