Comparative Study and Proof of Single-Pass Connected Components Algorithms

Zig-Zag Based Single-Pass Connected Components Analysis

“…Compared to [23,25] approximately 20% more memory bits are required, primarily from the merger table and other auxiliary data structures. The active tag is larger than that of [6] to detect object completion at the earliest possible time; this matches the timing of [25]. The advantage over [23] is merger handling using on-chip memories, rather than a large multiplexed shift register, which is a more efficient use of resources.…”

“…Similarly, there can also be no conflict between a merger and a two lookup stale label because the merger would require L C to be non-zero, so the following pixel cannot be the first in a run. However, there can be conflicts between a new label and a two lookup stale label (scenario 6 in Figure 14b), and also between a merger and changed label in a run (scenario 7 ).…”

“…Two clock cycles later, when the neighbourhood window is centred on pixel (4, 3), component segments associated with labels 1 and 2 merge, with MT[2] ← 1 in the following cycle. Meanwhile, label 3 is read from RB [6], and requires two lookups in MT. The second lookup occurs in the same clock cycle that the merger is being written to MT, so the second lookup would actually return the old label (2), shown in red in Figure 15, and is not recognised as a stale label.…”

“…As the algorithm by Jeong et al [23] uses registers to realise the row buffer, both registers used as memory and on-chip memory (RAM blocks) are considered in the comparison of memory resources. Table 1 compares the on-chip memory and register requirements for the algorithms presented in [6,20,21,23,25] for an image of size W × H. The number of labels required, N L , defines the number of connected components that are stored at any one time inside an architecture before their feature vectors are ultimately output. N L is, therefore, the key factor for all architectures, as it defines the lower bound of the depth and the width for the memories of the examined CCA architectures.…”

Union-Retire: A New Paradigm for Single-Pass Connected Component Analysis

“…Most CCL and CCA algorithms are based on some form of Union-Find data structure and algorithm [ 11 , 19 ]. Typical CCL algorithms require two raster-scan passes through the image.…”