Efficient tree construction for multiscale image representation and processing

Abstract

With the continuous growth of sensor performances, image analysis and processing algorithms have to cope with larger and larger data volumes. Besides, the informative components of an image might not be the pixels themselves, but rather the objects they belong to. This has led to a wide range of successful multiscale techniques in image analysis and computer vision. Hierarchical representations are thus of first importance, and require efficient algorithms to be computed in order to address real-life applications. Among these hierarchical models, we focus on morphological trees (e.g., min/max-tree, tree of shape, binary partition tree, αtree) that come with interesting properties and already led to appropriate techniques for image processing and analysis, with a growing interest from the image processing community. More precisely, we build upon two recent algorithms for efficient α-tree computation and introduce several improvements to achieve higher performance. We also discuss the impact of the data structure underlying the tree representation, and provide for the sake of illustration several applications where efficient multiscale image representation leads to fast but accurate techniques, e.g. in remote sensing image analysis or video segmentation.

Efficient Algorithms for Hierarchical Graph-Based Segmentation Relying on the Felzenszwalb–Huttenlocher Dissimilarity

“…20 and on Ref. 15, respectively. Even if the worst-case complexities of these two algorithms are comparable, the running times of the HGB method are signi¯cantly decreased when the incremental algorithm is used instead of the nonincremental one.…”

“…We can adapt these algorithms (in particular Algorithm 6 in Ref. 15) into an incremental quasi-°at zone update algorithm. At each iteration of Line 2 in Method 1, the weight of the edge u is decreased from its initial value maxf 2 Eg to its¯nal value resulting from the minimization of Eq.…”

“…We can adapt the algorithm proposed by Ref. 15, in order to merge these disjoint parts of the tree and update the tree only on the components containing x and y, thus avoiding the need to recompute the whole hierarchy at every iteration of Method 1.…”

Partition and Inclusion Hierarchies of Images: A Comprehensive Survey

“…The α-tree construction algorithm relies on its equivalence with a Min-tree defined on the edges valued with pixel intensity differences [44,69], and can use any Min-tree algorithm. Extending the idea, Havel et al [110,111] calculate the α-tree directly using a modification of Tarjan's union-find [104], presenting an algorithm suited for multithreading applications.…”

GEOBIA at the Terapixel Scale: Toward Efficient Mapping of Small Woody Features from Heterogeneous VHR Scenes

“…This framework embeds the different (nested) objects in a structure called a morphological tree, with no need of parameter tuning. Computation of such a stack of segmentations benefits from some recent scalable implementations that make realistic their very fast extraction from image datasets covering large areas (>1 million km 2 ) [4,5]. In order to avoid confusion in the term "tree" in this document.…”