A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels
Pattern Recognition Letters
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Recursive Implementation of Erosions and Dilations Along Discrete Lines at Arbitrary Angles
IEEE Transactions on Pattern Analysis and Machine Intelligence
Periodic lines: Definition, cascades, and application to granulometries
Pattern Recognition Letters
An application of mathematical morphology to road network extraction on SAR images
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Directional Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Image Structure Orientation Using Mathematical Morphology
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Basic morphological operations, band-limited images and sampling
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Constrained and dimensionality-independent path openings
IEEE Transactions on Image Processing
Spatially-variant structuring elements inspired by the neurogeometry of the visual cortex
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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When performing measurements in digitized images, the pixel pitch does not necessarily limit the attainable accuracy. Proper sampling of a band-limited continuous-domain image preserves all information present in the image prior to digitization. It is therefore (theoretically) possible to obtain measurements from the digitized image that are identical to measurements made in the continuous domain. Such measurements are sampling invariant, since they are independent of the chosen sampling grid. It is impossible to attain strict sampling invariance for filters in mathematical morphology due to their nonlinearity, but it is possible to approximate sampling invariance with arbitrary accuracy at the expense of additional computational cost. In this paper, we study morphological filters with line segments as structuring elements. We present a comparison of three known and three new methods to implement these filters. The method that yields a good compromise between accuracy and computational cost employs a (subpixel) skew to the image, followed by filtering along the grid axes using a discrete line segment, followed by an inverse skew. The staircase approximations to line segments under random orientations can be modeled by skewing a horizontal or vertical line segment. Rather than skewing the binary line segment we skew the image data, which substantially reduces quantization error. We proceed to determine the optimal number of orientations to use when measuring the length of line segments with unknown orientation.