Threshold Superposition in Morphological Image Analysis Systems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Single viewpoint catadioptric cameras
Panoramic vision
Catadioptric Projective Geometry
International Journal of Computer Vision
Grey-Scale Morphology Based on Fuzzy Logic
Journal of Mathematical Imaging and Vision
Image Processing in Catadioptric Planes: Spatiotemporal Derivatives and Optical Flow Computation
OMNIVIS '02 Proceedings of the Third Workshop on Omnidirectional Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
IEEE Transactions on Fuzzy Systems
On optimal linear filtering for edge detection
IEEE Transactions on Image Processing
Spherical Edge Detector: Application to Omnidirectional Imaging
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Level-dependent Sugeno integral
IEEE Transactions on Fuzzy Systems
Edge Detection by Maximum Entropy: Application to Omnidirectional and Perspective Images
International Journal of Computer Vision and Image Processing
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Morphological tools can provide transformations suitable for real projective images, but the camera and objects to be analyzed have to be positioned in such a manner that a regular mesh on the objects projects a regular mesh on the image. A morphological modification of the image is thus the projection of an equivalent operation on the object. Otherwise, due to perspective effects, a morphological operation on the image is not the projection of an equivalent operation on the objects to be analyzed. With catadioptric omnidirectional images, it is almost impossible to place the sensor such that a regular mesh on the scene projects a regular mesh on the image. Nevertheless, with proper calibration of a central catadioptric system, the projection of a regular structuring element in a scene can be determined for each point on the image. The aim of this paper is to present new morphological operators that use this projective property. These operators make use of a structuring element of varying shape. Since this varying shape cannot be represented as a binary union of pixels, we propose to use a fuzzy extension of the classical gray-level morphology to account for this phenomenon. This fuzzy extension is performed via fuzzy integrals.