Connected Components Labeling on DRAGs

Abstract

In this paper we introduce a new Connected Components Labeling (CCL) algorithm which exploits a novel approach to model decision problems as Directed Acyclic Graphs with a root, which will be called Directed Rooted Acyclic Graphs (DRAGs). This structure supports the use of sets of equivalent actions, as required by CCL, and optimally leverages these equivalences to reduce the number of nodes (decision points). The advantage of this representation is that a DRAG, differently from decision trees usually exploited by the state-of-the-art algorithms, will contain only the minimum number of nodes required to reach the leaf corresponding to a set of condition values. This combines the benefits of using binary decision trees with a reduction of the machine code size. Experiments show a consistent improvement of the execution time when the model is applied to CCL.

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

“…In [19], authors noticed the existence of identical and equivalent subtrees in the optimal decision tree obtained using the algorithm by [24]. They observed that identical subtrees were merged together by the compiler optimizer, with the introduction of jumps in machine code.…”

“…While the code compression operated by the compiler optimizer is aimed at the reduction of code footprint, the compiler is only capable of recognizing identical pieces of code. In [19], this optimization is enhanced by merging not only identical subtrees, but also equivalent ones. The formal statement of the problem is as follows.…”

“…Since main and end forests described in the previous section have a very large number of nodes, we exploit the merging of equal and equivalent subtrees in order to reduce code footprint and make a better use of the instruction cache. Differently from the original work by Bolelli et al [19], however, we do not have a single tree, but three whole forests for each line case (i.e. first row, last row, and middle rows).…”

“…Similarly as described in Section II-C, if during the tree traversal, equivalent subtrees are merged together as soon as they are found, there is the risk to change the list of equivalent actions so that now it is impossible to perform another substitution of larger subtrees. The exhaustive optimal solution adopted in [19] is not applicable to our case, because the amount of equivalent forests is too large for the execution time to be reasonable. To solve the problem, we use a heuristic greedy algorithm which tries to prioritize more valuable substitutions, meaning that larger equivalent subtrees get substituted before smaller ones.…”

“…The only difference is thus the time required to obtain the result. Since 1966, many papers showed algorithms to improve the efficiency of CCL and, given the relevance of the task, this still represents a hot research topic [15], [16], [17], [18], [19], [20], [21]. The first significant improvement has been provided by Wu et al [22], who proved an optimal strategy to reduce the average number of load/store operations during the scan of the input image, driven by Rosenfeld mask (Fig.…”