A Hitherto Unnoticed Singularity of Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Proceedings of the 4th international conference on Scale space methods in computer vision
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Content based image retrieval using multiscale top points a feasibility study
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
The hierarchical structure of images
IEEE Transactions on Image Processing
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Blurring an image with a Gaussian of width σ and considering σ as an extra dimension, extends the image to an Gaussian scale space ($\mathcal{GSS}$) image. In this $\mathcal{GSS}$-image the iso-intensity manifolds behave in an nicely pre-determined manner. As a result of that, the $\mathcal{GSS}$-image directly generates a hierarchy in the form of a binary ordered rooted tree, that can be used for segmentation, indexing, recognition and retrieval. Understanding the geometry of the manifolds allows fast methods to derive the hierarchy. In this paper we discuss the relevant geometric properties of $\mathcal{GSS}$ images, as well as their implications for algorithms used for the tree extraction. Examples show the applicability and increased speed of the proposed method compared to traditional ones.