A pipeline architecture for computing the Euler number of a binary image

Abstract

Euler number of a binary image is a fundamental topological feature that remains invariant under translation, rotation, scaling, and rubber-sheet transformation of the image. In this work, a run-based method for computing Euler number is formulated and a new hardware implementation is described. Analysis of time complexity and performance measure is provided to demonstrate the efficiency of the method. The sequential version of the proposed algorithm requires significantly fewer number of pixel accesses compared to the existing methods and tools based on bit-quad counting or quad-tree, both for the worst case and the average case. A pipelined architecture is designed with a single adder tree to implement the algorithm on-chip by exploiting its inherent parallelism. The architecture uses O(N) 2-input gates and requires O(N log N) time to compute the Euler number of an N · N image. The same hardware, with minor modification, can be used to handle arbitrarily large pixel matrices. A standard cell based VLSI implementation of the architecture is also reported. As Euler number is a widely used parameter, the proposed design can be readily used to save computation time in many image processing applications.

Euler Vector for Search and Retrieval of Gray-Tone Images

“…1(b), we compute the Euler number for the four most significant bitplanes by using a run-based algorithm [6] to determine the Euler vector, which is found to be .…”

“…It is known that the Euler number of a binary image can be computed as the difference of the sum of the number of runs for all rows (or columns), and the sum of the neighboring runs between all consecutive pairs of rows (or columns) [11], [33] and can also be implemented efficiently on-chip [6]. The algorithm for computing the Euler vector of a gray-tone image is described in Fig.…”

A Further Improvement on Bit-Quad-Based Euler Number Computing Algorithm

“…Among others, there are (1) bit-quad-based algorithm proposed by Gray [12], which calculates the Euler number by counting certain 2 × 2 pixel patterns called bit-quads and is adopted by the famous commercial image processing tools MAT-LAB [13]; (2) run-based algorithm [14], which calculates the Euler number by use of the numbers of runs and the neighboring runs in the image; (3) labeling-based algorithm proposed by He, Chao and Suzuki [15], which calculates the Euler number by labeling connected components and holes in the image; (4) an improved bit-quad-based algorithm proposed [16], which reduces the number of pixels to be checked for processing a bit-quad from 4 to 2; and (5) graphbased algorithm [17], which calculates the Euler number by use of graph theory, and only needs to check 1.875 pixels for processing a bit-quad on average. For convenience, we refer the algorithms proposed in Refs.…”

“…For convenience, we refer the algorithms proposed in Refs. [12], [14]- [17] as to GRAY algorithm, RUN algorithm, HCS algorithm, I-GRAY algorithm, and GT algorithm, respectively. This paper presents a further improved bit-quad-based algorithm for computing the Euler number in a given binary image.…”

Método Automático para Morfometria de Membranas Neuronais Utilizando Perceptron de Múltiplas Camadas e Código de Cadeia Diferencial

“…O NE corresponde ao número de objetos agrupados numa imagem menos o número de buracos nesses objetos [9]. Conforme o fluxograma apresentado, objetos com NE maior que zero foram classificados como ruído visto que não apresentam nenhum buraco e, portanto, não são axônios ou são axônios incompletos (Figura 4).…”