Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale median and morphological filters for 2D pattern recognition
Proceedings of of the IEEE winter workshop on Nonlinear digital signal processing
Digital Image Processing
Openings Can Introduce Zero Crossings in Boundary Curvature
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological scale-space with application to three-dimensional object recognition
Morphological scale-space with application to three-dimensional object recognition
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Segmentation-Free Estimation of Length Distributions Using Sieves and RIA Morphology
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Data Mining and Knowledge Discovery
International Journal of Computer Vision
Improving the accuracy of isotropic granulometries
Pattern Recognition Letters
An evaluation of area morphology scale-spaces for colour images
Computer Vision and Image Understanding
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In this paper, we prove that the scale-space of a one-dimensional gray-scale signal based on morphological filterings satisfies causality (no new feature points are created as scale gets larger). For this we refine the standard definition of zero-crossing so as to allow signals with certain singularity, and use them to define feature points. This new definition of zero-crossing agrees with the standard one in the case of functions with second order derivative. In particular, the scale-space based on the Gaussian kernel G does not need this concept because a filtered signal G * f is always infinitely differentiable. Using this generalized concept of zero-crossing, we show that a morphological filtering based on opening (and, hence, also closing by duality) satisfies causality. We note that some previous works have mistakes which are corrected in this paper. Our causality results do not apply to more general two-dimensional gray scale images. Causality results on alternating sequential filter, obtained as byproduct, are also included.