Feature Extraction

Three vein pattern based techniques, which aim to extract the vein pattern from the background resulting in a binary image (vein pattern based methods) followed by a comparison of these binary images using a correlation measure and a general purpose key-point based technique were used, which are all algorithms well-established finger vein recognition algorithms.

**Maximum Curvature** (MC [49]) is a curvature based approach which is insensitive to varying vein widths as it aims to emphasise only the centre lines of the veins. At first the centre positions of the veins are extracted by determining the local maximum curvature in cross-sectional profiles obtained by calculating the first and second derivatives in four directions—horizontal, vertical and the two oblique directions. Each profile is classified as either being concave or convex. Vein lines are indicated by local maxima in concave profiles, hence only the concave ones are used. A score is assigned to each centre position which corresponds to the width and curvature of the maxima region. Afterwards, the centre positions of the veins are connected using a filtering operation in all four directions taking the 8-neighbourhood of pixels into account to account for misclassifications at the first step due to noise and other imperfections in the images. The output feature vector is essentially a binary image which is obtained by thresholding the recorded score values using the median of all scores as a threshold.

**Principal Curvature** (PC [50]) is another curvature based approach, which is not based on the derivates but on the gradient field of the image. Hence, the first step is the calculation of the gradient field. Hard thresholding to filter out small gradients by setting their values to zero is performed to prevent amplification of small noise components. Afterwards the normalised gradient field is obtained by normalising the magnitude to 1 at each pixel, which is then smoothed by applying a Gaussian filter. The actual principal curvature calculation is then done based on this smoothed normalised gradient field by computing the Eigenvalues of the Hessian matrix at each pixel. The two Eigenvalues are the principal curvatures and the corresponding Eigenvectors of the Hessian matrix represent the directions of the maximum and minimum curvature. The bigger Eigenvalue corresponds to the maximum curvature among all directions and is recorded and further used. The final step is again a threshold-based binarisation of the principal curvature values to obtain the output feature vector which is essentially a binary vein image.

**Gabor Filter** (GF [4]) is a Gaussian kernel function modulated by a sinusoidal plane wave. Gabor filters are inspired by the human visual system's multichannel processing of visual information. Several 2D even symmetric Gabor filters with different orientations (in *<sup>π</sup> <sup>k</sup>* steps where *k* is the number of orientations) form a filter bank. The image is filtered using this filter band to extract *k* different feature vectors. The single feature vectors from the previous step are fused and thresholded to get a resulting feature vector. To remove small noise components, this vector is further post-processed using morphological operations, resulting in the final output feature vector, which is again a binary image.

**Scale Invariant Feature Transform** (SIFT [51]) is a key-point based technique. In contrast to the three vein pattern based ones, key-point based techniques use information from the most discriminative points as well as consider the neighbourhood and context information around these points. This is achieved by extracting key-point locations at stable and distinct points in the image and then assigning a descriptor to each detected key-point location. The approach we used is based on the general purpose SIFT descriptor in combination with additional key-point filtering along the finger boundaries. This filtering is done to suppress information originating from the finger shape (outside boundary) instead of the vascular pattern. We originally presented this additional key-point filtering in Reference [52].
