Abstract
A great number of Artificial Intelligence applications are based on features extracted from signals or images. Feature extraction often requires differentiation of discrete signals and/or images in one or more dimensions. In this work we provide two Theorems for the construction of finite length (finite impulse response -FIR) masks for signal and image differentiation of any order, using central differences of any required length. Moreover, we present a very efficient algorithm for implementing the compact (implicit) differentiation of discrete signals and images, as infinite impulse response (IIR) filters. The differentiator operators are assessed in terms of their spectral properties, as well as in terms of the performance of corner detection in gray scale images, achieving higher sensitivity than standard operators. These features are considered very important for computer vision systems. The computational complexity for the centered and the explicit derivatives is also provided.
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Harris, C., Stephens, M.: A combined corner and edge detector. In: ALVEV Vision Conference, pp. 147–151 (1988)
Lindeberg, T., Garding, J.: Shape-adapted smoothing in estimation of 3-D shape cues from affine deformations of local 2-D brightness structure. Image and Vision Computing 15(6), 415–434 (1997)
Mikolajczyk, K., Schmid, C.: Scale and affine invariant interest point detectors. International Journal of Computer Vision 1(60), 63–86 (2004)
Bay, H., Ess, A., Tuytelaars, T., Gool van, L.: Speeded-up robust features (SURF). International Journal on Computer Vision and Image Understanding 110(3), 346–359 (2008)
Lowe, D.: Distinctive Image Features from Scale-Invariant Keypoints. International Journal of Computer Vision 60(2), 91–110 (2004)
Keller, H.B., Pereyra, V.: Symbolic Generation of Finite Difference Formulas. Mathematics of Computation 32(144), 955–971 (1978)
Lele, S.K.: Compact difference Schemes with Spectral-like Resolution. Journal of Computational Physics 103, 16–42 (1992)
Belyaev, A.: On implicit image derivatives and their applications. In: Hoey, J., McKenna, S., Trucco, E. (eds.) BMVC 2011, Dundee, Scotland, UK (2011)
Unser, M., Aldroubi, A., Eden, M.: B-spline signal processing: Part II - Efficient Design and Applications. IEEE Trans. Sighal Process 41(2), 834–848 (1993)
Benkert, K., Fischer, R.: An Efficient Implementation of the Thomas-Algorithm for Block Penta-diagonal Systems on Vector Computers. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007, Part I. LNCS, vol. 4487, pp. 144–151. Springer, Heidelberg (2007)
MATLAB and Octave Functions for Computer Vision and Image Processing, http://www.csse.uwa.edu.au/~pk/research/matlabfns/
Farid, H., Simoncelli, E.: Differentiation of Discrete Multi-Dimensional Signals. IEEE Trans. Image Processing 13(4), 496–508 (2004)
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Delibasis, K.K., Kechriniotis, A., Maglogiannis, I. (2013). On Centered and Compact Signal and Image Derivatives for Feature Extraction. In: Papadopoulos, H., Andreou, A.S., Iliadis, L., Maglogiannis, I. (eds) Artificial Intelligence Applications and Innovations. AIAI 2013. IFIP Advances in Information and Communication Technology, vol 412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41142-7_33
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DOI: https://doi.org/10.1007/978-3-642-41142-7_33
Publisher Name: Springer, Berlin, Heidelberg
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