Introduction to algorithms
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
Tree Representation and Implicit Tree Matching for a Coarse to Fine Image Matching Algorithm
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Tree Representation for Image Matching and Object Recognition
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Parallel Algorithm for Concurrent Computation of Connected Component Tree
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Segmentation of Complex Images Based on Component-Trees: Methodological Tools
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Component-Trees and Multi-value Images: A Comparative Study
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Efficient computation of new extinction values from extended component tree
Pattern Recognition Letters
Selection of relevant nodes from component-trees in linear time
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Interactive segmentation based on component-trees
Pattern Recognition
Component-Trees and Multivalued Images: Structural Properties
Journal of Mathematical Imaging and Vision
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The aim of this paper is to present a new algorithm to calculate the confinement tree of an image - also known as component tree or dendrone - for which we can prove that its worst-case complexity is O(n log n) where n is the number of pixels. More precisely, in a first part, we present an algorithm which separates the different kinds of operations - which we call scanning, fusion, propagation, and attribute operations - such that we can separately apply complexity analysis on them and such that all operations except propagation stay in O(n). The implementation of the propagation operations is presented in a second part, first in O(nn2), where nn is the number of nodes in the tree (nn ≤ n). This is sufficient if the number of pixels is much larger than the number of nodes (nn ≪ n). Else, we show how to obtain O(nn lognn) complexity for propagation. We construct two example images to investigate the behavior of two known algorithms for which we can show worst-case complexity of O(n2 log n) and O(n2), respectively, and we compare it to our algorithm. Finally, a practical evaluation will be opposed to the theoretical results. Several variations of the implementation will show which operations are time consuming in practice.