Simple, XOR based, Image Edge Detection

ECAI 2013 - International Conference – 5th Edition
Electronics, Computers and Artificial Intelligence
27 June - 29 June, 2013, Piteşti, ROMÂNIA
Simple, XOR based, Image Edge Detection
Study on Natural Grayscale Images
Adrian-Viorel DIACONU
Valeriu IONESCU
IT&C Department
Lumina – The University of South-East Europe
Bucharest, Romania
[email protected]
FECC
University of Piteşti
Piteşti, Romania
[email protected]
Abstract – SXOR’s study on natural grayscale images is
carried on, as a continuation of previous investigation of
its performances over black and white / 8-bit grayscale
synthetic images.
Keywords – XOR; edge detection; noise; digital image
processing; bit-plane separation
I.
INTRODUCTION
Edge detection techniques tend to highlight sudden
changes in the image intensity, generally produced by
the boundaries of objects within the image (different
objects are usually different colored or tinted and this
causes the image intensity to change as we move from
one object to another [1]).
In this paper, we take advantage of results enforced
in one of our previous research article [2] (i.e. SXOR’s
performances assessment, when operating over binary
and 8-bit grayscale synthetic images, emphasizing on
strengths, weaknesses and small artifacts to counteract
its undesirable effects) in order to carry on the study,
over 8-bit grayscale natural images.
Compared to [3], [4] and other logical operators
based algorithms, SXOR takes the advantage of not
using thresholding stages and/or mask matrices; more
than that, due to its original underlying concept (i.e.
applying the bitwise XOR logical operator between all
pixels on image’s successive pairs of rows/columns)
SXOR is much faster and highly parallelizable (i.e. in
term of computational implementation).
The rest of this paper is organized as follows: the
2nd section presents the design of SXOR image edge
detection algorithm (namely an approach to grayscale
natural images); the 3rd section makes a detailed and
comprehensive assessment on the proposed scheme,
while making comparative analysis of the achieved
results; and the 4th section concludes carried-out work.
II.
SXOR IMAGE EDGE DETECTION ALGORITHM
In the designing of SXOR’s scheme, to operate on
8-bit grayscale images, 2nd artifact introduced in the
original algorithm (namely the elimination of the four
least significant bit-planes of the input plain-image)
has been considered.
Aforementioned consideration was reinforced by
the analysis of bit-planes, performed on each of the
chosen 8-bit grayscale standard test images, which has
revealed the following general observation: on lower
bit-planes of any plain-image details are ‘hidden’ and
whereas their representation resembles noise, they are
not likely to feature existing edges within the image so
that they can be removed from the scheme. To support
claims made Fig. 1 is presented (i.e. showing contents
of each bit-plane, within “Peppers” image).
Figure 1. Bit-planes study over “Peppers”, 8-bit, grayscale, standard test image
Adrian-Viorel DIACONU, Valeriu IONESCU
2
Therefore, with I0 representing the pixels values
matrix of an 8-bit grayscale image of size m x m, the
steps of SXOR algorithm are as follows:
Steps (i÷ii) will modify the matrix I0, generating a
newly one denoted IHVE (i.e. representing the pixels
values of the edged image).
(i) For q = 1 : 4, for i = 1 : m,
a. compute image’s most significant bit-planes
2nd step of SXOR’s algorithm, designed for 8-bit,
grayscale, natural images can suffer another approach
consisting of replacing OR function in (3) and (4) with
XOR.
I q = bitget ( I 0 , q ) (1)
b. compute q bit-plane’s edges
I HE q (i, :) = I q (i, :) ⊕ I q (i + 1, :)
( 2)
IVE q (:, i ) = I q (:, i ) ⊕ I q (:, i + 1)
(ii) For q = 1 : 4, for i = 1 : m, for j = 1 : m,
a. unify q bit-plane’s edges
I HVEq (i, j ) = I HEq (i, j ) ∨ I HVq (i, j ) (3)
b. unify bit-plane’s (compute edged image)
I HVE (i, j ) = I HVE (i, j ) ∨ I HVEq (i, j ) (4)
or
I HVE (i, j ) = I HVE (i, j ) + I HVEq (i, j ) ⋅ 28− q
a)
b)
III.
EXPERIMENTAL RESULTS AND COMMENTS
The evaluation and validation of performances of
the proposed scheme (i.e. SXOR algorithm) is made,
in comparison with other classic operators (e.g. Sobel,
Prewitt, and Canny [5÷10]), working over “Peppers”,
“Cameraman” and “Lena” 8-bit grayscale standard test
images.
Fig. 2 to 4 shows the input plain-images along with
their versions, resulting after applying aforementioned
operators.
(5)
c)
d)
Figure 2. “Lena” Grayscale Standard Test Image
a) – plain-image, b) – Sobel operator output on (a), c) – Prewitt operator output on (a), d) – Canny operator output on (a)
a)
b)
c)
d)
Figure 3. “Peppers” Grayscale Standard Test Image
a) – plain-image, b) – Sobel operator output on (a), c) – Prewitt operator output on (a), d) – Canny operator output on (a)
a)
b)
c)
d)
Figure 4. “Cameraman” Grayscale Standard Test Image
a) – plain-image, b) – Sobel operator output on (a), c) – Prewitt operator output on (a), d) – Canny operator output on (a)
Simple, XOR based, Image Edge Detection.
Study on Grayscale Natural Images
Fig. 5.a) ÷ b) to Fig. 7.a) ÷ b) show 8-bit grayscale
standard test images edged using SXOR’s 1st approach
(i.e. OR function is used in the unification stages of
bit-planes, namely (3) and (4)), while Fig. 5.c) ÷ d) to
Fig. 7.c) ÷ d) show same images edged using SXOR’s
2nd approach (i.e. XORing horizontally and vertically
edged bit-planes, respectively XORing all bit-planes
between them).
a)
b)
3
Analyzing binary weighted representation of edged
images (namely Fig. 5.b) and d), Fig. 6.b) and d),
respectively Fig. 7.b) and d)) one can notice that it’s
enough to apply SXOR (i.e. step (i) and (ii).a) only on
the most significant bit-plane of each test image, in
order to achieve performances comparable with those
of classic operators.
c)
d)
Figure 5. “Lena” Grayscale Standard Test Image
a) – SXOR’s output – 1st approach, b) – binary weighted representation of (a)
c) – SXOR’s output – 2nd approach, d) – binary weighted representation of (c)
a)
b)
c)
d)
Figure 6. “Peppers” Grayscale Standard Test Image
a) – SXOR’s output – 1st approach, b) – binary weighted representation of (a)
c) – SXOR’s output – 2nd approach, d) – binary weighted representation of (c)
a)
b)
c)
d)
Figure 7. “Cameraman” Grayscale Standard Test Image
a) – SXOR’s output – 1st approach, b) – binary weighted representation of (a)
c) – SXOR’s output – 2nd approach, d) – binary weighted representation of (c)
Thus, to support aforementioned idea (i.e. same
performances, as classical operators, can be achieved
applying SXOR only over image’s most significant bit
plane), Fig. 8.a) ÷ c) and Fig. 9.a) ÷ c) are presented.
SXOR’s performances are assessed, in an objective
manner, by computing MAE (Mean Absolute Error),
PSNR (Peak Signal – to – Noise) and MSE (Mean
Squared Error) measures, between classical operator’s
output images and those of the proposed scheme, as
shown in Table 1.
Adrian-Viorel DIACONU, Valeriu IONESCU
4
a)
b)
c)
a)
b)
c)
Figure 8. SXOR applied only over the most significant bit-plane of the 8-bit grayscale standard test images – 1st approach
a) – “Lena” SXOR edged, b) – “Cameraman” SXOR edged, c) – “Peppers” SXOR edged
Figure 9. SXOR applied only over the most significant bit-plane of the 8-bit grayscale standard test images – 2nd approach
a) – “Lena” SXOR edged, b) – “Cameraman” SXOR edged, c) – “Peppers” SXOR edged
TABLE I.
Reference
operator
Canny
Sobel
Prewitt
COMPARATIVE QUALITATIVE MEASURES BETWEEN DIFFERENT EDGE DETECTION OPERATORS
OVER GRAYSCALE NATURAL IMAGES
Measures
MAE
MSE
PSNR
MAE
MSE
PSNR
MAE
MSE
PSNR
IV.
“Lena”
SXOR – 1st
SXOR – 2nd
0.1224
0.1090
0.3498
0.3302
57.2540
57.7548
0.0833
0.0691
0.2886
0.2629
58.9239
59.7349
0.0834
0.0692
0.2888
0.2630
58.9179
59.7320
CONCLUSIONS
The conducted work developed a simple, valid and
effective image edge detection scheme, based on XOR
logical operator.
Pragmatic, comprehensive, experimental tests have
been carried out (on various 8-bit, grayscale natural
images) and numerical analysis showed comparable
performances of the proposed SXOR scheme, relative
to several others.
Another feature worthy to be considered, derived
from SXOR’s procedure, is its high level of computing
parallelism. Thus, as future work, an actual attempt of
implementation is concerned (e.g. on a FPGA, focused
on the optimization of proposed scheme, for parallel
computing).
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