In this paper, we propose a new finger biometric method. Infrared finger images are first captured, and then feature extraction is performed using a modified Gaussian high-pass filter through binarization, local binary pattern (LBP), and local derivative pattern (LDP) methods. Infrared finger images include the multimodal features of finger veins and finger geometries. Instead of extracting each feature using different methods, the modified Gaussian high-pass filter is fully convolved. Therefore, the extracted binary patterns of finger images include the multimodal features of veins and finger geometries. Experimental results show that the proposed method has an error rate of 0.13%.

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In this paper, by using q-Volkenborn integral [10], the first author [25] constructed new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. We define higher-order twisted (h, q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach to the complete sums of products of twisted (h, q)-Bernoulli polynomials and numbers. p-adic q-Volkenborn integral is used to evaluate summations of the following form:

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This study proposes a novel procedural modeling method using convolution sums of divisor functions to model a variety of natural trees in a virtual ecosystem efficiently. The basic structure of the modeling method defines the growth grammar, including the branch propagation, a growth pattern of branches and leaves, and a process of growth deformation for various tree generation. Here, the proposed procedural method for trees is to utilize convolution sums of divisor functions as a novel approach. The structure of convolution sums has branch propagation of a uniform pattern, which is controllable, so that it is efficient for real-time virtual ecosystem construction. Furthermore, it can process changes of environment factors or growth deformation for various and unique tree generation simply through the properties of divisor functions. Finally, an experiment is performed in order to evaluate our proposed modeling method whether it can generate natural and various tree models, and a real-time virtual ecosystem of a large area where a variety of trees are presented using the modeling method can be constructed efficiently.