What Can We Learn from Discrete Images about the Continuous World?
Image analysis attempts to perceive properties of the continuous real world by means of digital algorithms. Since discretization discards an infinite amount of information, it is difficult to predict if and when digital methods will produce reliable results. This paper reviews theories which establish explicit connections between the continuous and digital domains (such as Shannon’s sampling theorem and a recent geometric sampling theorem) and describes some of their consequences for image analysis. Although many problems are still open, we can already conclude that adherence to these theories leads to significantly more stable and accurate algorithms.
KeywordsPoint Spread Function Homotopy Type Sampling Theorem Discrete Image Noise Standard Deviation
- 5.Förstner, W.: Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range Images. In: Proc. Summer School on Data Analysis and the Statistical Foundations of Geomatics. Lecture Notes in Earth Science, Springer, Berlin (1999)Google Scholar
- 7.Köthe, U.: Edge and Junction Detection with an Improved Structure Tensor. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 25–32. Springer, Heidelberg (2003)Google Scholar
- 9.Pavlidis, T.: Algorithms for Graphics and Image Processing. Computer Science Press, Rockville (1982)Google Scholar
- 13.Unser, M., Aldroubi, A., Eden, M.: B-Spline Signal Processing. IEEE Trans. Signal Processing 41(2), 821–833 (part I), 834–848 (part II) (1993)Google Scholar