21-08-2013, 04:01 PM
Performance Analysis of Edge Detection Methods on Hexagonal Sampling Grid
Performance Analysis .pdf (Size: 435.96 KB / Downloads: 56)
Abstract
Hexagonal sampling grid offers less storage time, less computation time,
increased coding efficiency, less quantization error, equidistant property and
consistent connectivity, etc., Edge detection is one of the important
preprocessing steps in many of the image processing applications. Various
edge detection techniques are available for images on rectangular grids such as
classical operators, CLAP algorithm based edge detection, wavelet based edge
detection etc. Wavelet based edge detection is found to be a better technique
for specific application such as iris recognition system, 3D vertebrae shape
recognition, infrared target recognition etc. These techniques are not suitable
for hexagonal domain. For these we need to choose proper addressing scheme.
In this paper, (i) Edge detection using masks on hexagonal grid (using spiral
addressing scheme) is performed (ii) CLAP algorithm is performed on
rectangular domain and hexagonal domain (using alternate pixel suppressal
and half-pixel shift method ) (iii) Wavelet based edge detection was performed
on rectangular domain. For hexagonal domain, we need to choose proper
directional wavelet. Gabor wavelet based edge detection is proposed for the
hexagonal grid and we were able to get good results. For performance
evaluation we are considering Mean Square Error, Peak Signal to Noise Ratio
and ratio of edge pixels to size of image. For all operations, edge detection on
hexagonal domain gives better results and better visual appeal of images
compared to edge detection on rectangular domain.
Introduction
Edge detection is the most common approach for detecting meaningful discontinuities
in gray level. An edge is a set of connected pixels that lie on the boundary between
two regions. Edge is a ‘local’ concept [1]. In hexagonal domain the edge detection
operations were performed on the hexagonally sampled image. Resampling is the
process of transforming a discrete image which is defined at one set of coordinate
locations to a new set of coordinate points [2] i.e, converting from rectangular to
hexagonal grid.
Many classical edge detectors have been developed over time. They are based on
the principle of matching local image segments with specific edge patterns. The edge
detection is realized by the convolution with a set of directional derivative masks.
Classical edge detection operators like Roberts, Sobel, Prewitt and Laplacian are
defined on a 3 X 3 pattern grid, so they are efficient and easy to apply. In hexagonal
domain we can use hexagonal operators for edge detection. These hexagonal masks
are applied on the images which is represented using spiral addressing scheme.
Operator Based Edge detection
Various classical operators used for rectangular grid are Prewitt, Laplacian of
Gaussian, Canny edge detector, etc., These operators are applicable exclusively for
spiral addressing scheme representation of hexagonal grid. Sheridan [6] proposed a
one-dimensional addressing system, as well as two operations as addition and
multiplication based on this addressing system, for hexagonal structure. This system
is called Spiral Architecture (Figure.2). It is inspired from anatomical consideration of
the primate’s vision system. Middleton and Sivaswamy [7] also proposed a single-
index system for pixel addressing by modifying the Generalized Balanced Ternary
system. Neighborhood operations are often used in image processing. Finding the
neighbor in a hexagonal image makes use of the spiral addition operation. In a seven-
pixel cluster, the neighborhood relation can be determined by spiral addition . One
can find out the spiral address of any hexagonal pixel with centre on a certain
hexagonal pixel whose spiral address is known.
Wavelet based edge detection
Different methods were proposed for edge detection on rectangular grid [9-13] in
which wavelets can be directly used for edge detection. But for hexagonal domain,
due to the three axis of symmetry, we have to consider the directionality of wavelets.
We have to choose better wavelet which is having the property of directionality. To
reflect the local and global direction of the image transform, the directional wavelet
transform is applied using Daubachies 6 wavelet.
Performance Evaluation
In this work, the performances of edge detection on rectangular and hexagonal grids
are computed using operators, CLAP algorithm and Wavelets. The performance was
compared based on the parameters Mean Square Error (MSE), Peak Signal-to-Noise
Ratio (PSNR), Computation time and mean square error.
Conclusions
In this work various edge detection techniques like operator based edge detection and
CLAP algorithm based edge detection were implemented on both rectangular lattice
and hexagonal lattice. Performance comparison shows improved results for edge
detection on hexagonal lattice based on both subjective analysis and objective
analysis. Gabor wavelet is found to be suitable wavelet for hexagonal domain because
of its directional selectivity. Due to non-availability of hexagonal displays, we used
software based approach by converting rectangular lattice into hexagonal lattice
which is a limitation of our work.