Spaghetti Labeling: Directed Acyclic Graphs for Block-Based Connected Components Labeling

Abstract

Connected Components Labeling is an essential step of many Image Processing and Computer Vision tasks. Since the first proposal of a labeling algorithm, which dates back to the sixties, many approaches have optimized the computational load needed to label an image. In particular, the use of decision forests and state prediction have recently appeared as valuable strategies to improve performance. However, due to the overhead of the manual construction of prediction states and the size of the resulting machine code, the application of these strategies has been restricted to small masks, thus ignoring the benefit of using a block-based approach. In this paper, we combine a block-based mask with state prediction and code compression: the resulting algorithm is modeled as a Directed Rooted Acyclic Graph with multiple entry points, which is automatically generated without manual intervention. When tested on synthetic and real datasets, in comparison with optimized implementations of state-of-the-art algorithms, the proposed approach shows superior performance, surpassing the results obtained by all compared approaches in all settings.

One DAG to Rule Them All

“…that integrates all the proposed algorithmic solutions, and allows to automatically generate optimized code for the selected task. 3) An improvement to the compression strategy of trees and forests described in [30]. 4) New GRAPHGEN-generated binary image processing algorithms, which significantly improve stateof-the-art on 2D and 3D CCL, Thinning and Chain-Code, both in CPU and GPU environments.…”

“…With respect to previous proposals [30], [40], our approach is a dynamic programming algorithm which guarantees to reach the optimal compression. In order to save computation time, we use a memoization technique that consists of a compact representation of trees in string form.…”

“…In [41], the conversion of a decision tree into a Directed Rooted Acyclic Graph (DRAG) has proved to be an effective technique to reduce the machine code footprint and lessen its impact on the instruction cache when considering large neighborhoods. Finally, the application of the state prediction approach to the 2×2 mask (Spaghetti) [30] further improved performance, setting the state-of-the-art on CCL.…”

A Heuristic-Based Decision Tree for Connected Components Labeling of 3D Volumes: Implementation and Reproducibility Notes

“…Among them, some of the most promising techniques that led to major breakthroughs in the field consist in the usage of Decision Trees (DTrees), combined with the 2 × 2 block-based approach. A detailed description of the algorithms based on these paradigms is provided in [7]. Moreover, algorithmic solutions relying on DTrees have demonstrated their effectiveness even when applied, with the necessary variations, to parallel architectures [4,12].…”

A Warp Speed Chain-Code Algorithm Based on Binary Decision Trees

“…With this paper, we introduce different optimizations of the algorithm proposed by Cederberg [13]. The use of decision trees, already proven to be a winning strategy for improving the performance of image processing algorithms [15], [16], [17], [18], [19], [20], has shown the best performance on this task: our proposals are able to significantly outperform current software implementations of chain-code algorithms. In Section IV, a thorough evaluation of different variations of our algorithm (presented in Section III) is performed also in comparison with state-of-the-art implementations.…”