A Hybrid Shared-Memory Parallel Max-Tree Algorithm for Extreme Dynamic-Range Images

Abstract

Max-trees, or component trees, are graph structures that represent the connected components of an image in a hierarchical way. Nowadays, many application fields rely on images with high-dynamic range or floating point values. Efficient sequential algorithms exist to build trees and compute attributes for images of any bit depth. However, we show that the current parallel algorithms perform poorly already with integers at bit depths higher than 16 bits per pixel. We propose a parallel method combining the two worlds of flooding and merging max-tree algorithms. First, a pilot max-tree of a quantized version of the image is built in parallel using a flooding method. Later, this structure is used in a parallel leaf-to-root approach to compute efficiently the final max-tree and to drive the merging of the sub-trees computed by the threads. We present an analysis of the performance both on simulated and actual 2D images and 3D volumes. Execution times are about better than the fastest sequential algorithm and speed-up goes up to on 64 threads.

Partition and Inclusion Hierarchies of Images: A Comprehensive Survey

“…The merge-based approaches are mainly used for parallelism, and are not further discussed here (for a recent parallel implementation of Max-tree combining the merge-based and flooding approach, cf. e.g., [102]). …”

Parallel Computation of Component Trees on Distributed Memory Machines

“…The algorithms are grouped into three main classes: immersion-, floodingand merge-based. Algorithms that belong to the immersion and flooding class, may also be referred to as leaf-to-root merging and root-to-leaf flooding methods, respectively [32]. Since this section is not intended to repeat the review, Fig.…”

“…For the Naples dataset, experiments are performed only using the first channel [52]. For the ESO, the RGB image is simplified to a singular luminance channel, similarly to how it was done by Moschini et al [32] in order to obtain similar conditions for benchmarking the proposed algorithm. The luminance image is obtained through weighing and summing the channels, so that L ¼ 0:2126Rþ 0:7152G þ 0:0722B.…”

Distributed Component Forests in 2-D: Hierarchical Image Representations Suitable for Tera-Scale Images

“…27 The computational complexity of algorithms to construct these tree structures is also modest: either OðGNÞ, with G the number of gray levels in the regular 8-16 bit per pixel case or ðN log NÞ in the 32-bit or more integer or°oating point case. 2,15 Furthermore, shared-memory parallel algorithms for computation of these trees, 14,29 and subsequent postprocessing have been developed. 30,31 On fairly modest compute servers they can handle images up to a few gigapixel at most.…”

“…In practice, in parallel computation we pre-allocate this maximum, both because it can simplify the algorithm, and because it avoids the need for (locking) memory allocation during tree construction. 14,29 Given that many imaging modalities routinely acquire images in the order of tens or hundreds of gigapixels, and tera-scale images occur in both remote sensing and astronomy, there is a need for a representation capable of handling these hierarchies in a distributed manner. Very recently, such a method has been developed in the form of distributed component forests (DCFs).…”