Computing Geometric Properties of Images Represented by Linear Quadtrees

Samet, Hanan; Tamminen, Markku

doi:10.1109/tpami.1985.4767646

Cited by 99 publications

(40 citation statements)

References 22 publications

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“…So, there is a contradiction, and as such the 9th entry cannot occur after the 3rd entry. Similarly, it can be shown that the pairs (3,15), (9,15), (2,8), (2,14) and (8,14) cannot occur at consecutive time instances. h…”

Section: Adder Design and Time Complexitymentioning

confidence: 89%

“…The Euler number computation based on the quad-tree [14,15] involves computing the quad-tree from the pixel entries followed by a traversal on the quad-tree. The time complexity T(n) for formation of the quad-tree involves the following recurrence:…”

Section: Space and Time Complexitymentioning

confidence: 99%

“…Now, traversal of a quad-tree for computing the Euler number takes linear time in the number of leaf nodes in the quad-tree [14,15]. The number of leaf nodes can be N 2 .…”

Section: Space and Time Complexitymentioning

confidence: 99%

“…We show that certain properties of runs and neighboring runs and their distributions in the pixel matrix can be exploited to compute the Euler number of a binary image very efficiently. Performance analysis of the algorithm indicates that the proposed technique outperforms significantly in speed, the existing bit-quad counting and quadtree based methods [2,11,[13][14][15]. Experimental results on a logo database show very favorable results.…”

Section: Introductionmentioning

confidence: 98%

“…Computation of these parameters needs counting of specific types of bit-quads in the image namely, [14] proposed an algorithm to compute the Euler number of an image represented by a quad-tree. Samet and Tamminen [15] improved the algorithm further by using a new staircase type of data structure to represent the blocks that have already been processed. Juan et al [16] considered a skeletonized version of the binary image and computed Euler number in terms of the number of terminal points T p , and the number of threeedge points TE p , as (T p À TE p )/2.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Bishnu

Bhattacharya

Kundu

et al. 2005

Journal of Systems Architecture

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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.

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Section: Adder Design and Time Complexitymentioning

confidence: 89%

Section: Space and Time Complexitymentioning

confidence: 99%

“…Now, traversal of a quad-tree for computing the Euler number takes linear time in the number of leaf nodes in the quad-tree [14,15]. The number of leaf nodes can be N 2 .…”

Section: Space and Time Complexitymentioning

confidence: 99%