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Simple, XOR based, Image Edge Detection Study on Natural Grayscale Images

Adrian-Viorel DIACONU IT&C Department

Lumina – The University of South-East Europe Bucharest, Romania

adrian.diaconu@lumina.org

Valeriu IONESCU FECC

University of Piteşti Piteşti, Romania

valeriu.ionescu@upit.ro

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).

Fig. 1. Bit-planes study over “Peppers”, 8-bit, grayscale, standard test image

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:

(i) For q = 1 : 4, for i = 1 : m, a. compute image’s most significant bit-planes

)1(),( 0 qIbitgetIq = b. compute q bit-plane’s edges

)2()1(:,)(:,)(:,:),1(:),(:),(

+⊕=+⊕=iIiIiI

iIiIiI

qqqVE

qqqHE

(ii) For q = 1 : 4, for i = 1 : m, for j = 1 : m, a. unify q bit-plane’s edges

)3(),(),(),( jiIjiIjiIqqq HVHEHVE ∨=

b. unify bit-plane’s (compute edged image) )4(),(),(),( jiIjiIjiI

qHVEHVEHVE ∨=

or )5(2),(),(),( 8 q

HVEHVEHVE jiIjiIjiIq

−⋅+=

Steps (i÷ii) will modify the matrix I0, generating a newly one denoted IHVE (i.e. representing the pixels values of the edged image).

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.

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.

a) b) 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)

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).

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.

a) b) 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.

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

a) b) c)

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. COMPARATIVE QUALITATIVE MEASURES BETWEEN DIFFERENT EDGE DETECTION OPERATORS OVER GRAYSCALE NATURAL IMAGES

Reference operator Measures “Lena” “Peppers” “Cameraman”

SXOR – 1st SXOR – 2nd SXOR – 1st SXOR – 2nd SXOR – 1st SXOR – 2nd

Canny MAE 0.1224 0.1090 0.0922 0.0867 0.1156 0.1092 MSE 0.3498 0.3302 0.3036 0.2944 0.3400 0.3305 PSNR 57.2540 57.7548 58.4854 58.7521 57.5018 57.7481

Sobel MAE 0.0833 0.0691 0.0587 0.0525 0.0994 0.0876 MSE 0.2886 0.2629 0.2422 0.2292 0.3152 0.2959 PSNR 58.9239 59.7349 60.4475 60.9281 58.1590 58.7065

Prewitt MAE 0.0834 0.0692 0.0588 0.0527 0.0999 0.0880 MSE 0.2888 0.2630 0.2424 0.2295 0.3160 0.2967 PSNR 58.9179 59.7320 60.4390 60.9155 58.1362 58.6848

IV. 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).

REFERENCES [1] B. Ahirwal, M. Khadtare, and R. Mehta, “FPGA based systen for color

space transformation RGB to YIQ and YCbCr”, Int. Conf. on Intelligent and Advanced Systems, ICIAS’07 IEEE Int. Conf., Kuala Lampur, Malaysia, 25÷28 November, 2007, pp. 1345÷1349.

[2] A.-V. Diaconu, and I. Sima, “Simple, XOR based, image edge detection. Study on black and white / grayscale synthetic images”, Int. Conf. on Electronics, Computers and Artificial Intelligence, ECAI’13 IEEE Int. Conf., Piteşti, Romania, 27÷29 June, 2013. [unpublished].

[3] M. Sharifi, M. Fathy, and M.T. Mahmoudi, “A classified and comparative study of edge detection algorithms”, Int. Conf. on Information Technology: Coding and Computing, ITCC’02 IEEE Int. Conf., Nevada: Las Vegas, USA, 8÷10 April, 2002, pp. 117÷120.

[4] N.M. Hussein, and A. Barriga, “Hardware implementation of a soft computing technique for edge detection”, Proc. of the World Congress on Engineering 2008 Vol. No. 1, WCE’08, London, U.K., 2÷4 July, 2008, pp. 659÷664.

[5] M. Sharifi, M. Fathy, and M.T. Mahmoudi, “A classified and comparative study of edge detection algorithms”, Int. Conf. on Information Technology: Coding and Computing, ITCC’02 IEEE Int. Conf., Nevada: Las Vegas, USA, 8÷10 April, 2002, pp. 117÷120.

[6] Alan C. Bovik, “Handbook of Image & Video Processing”, 2nd Ed., Elsevier Academic Press, 2005.

[7] Q.H. Zhang, S. Gao, and T.D. Bui, “Edge detection models”, Lecture Notes in Computer Science, Vol. No. 32, Iss. No. 4, 2005, pp. 133÷140.

[8] E. Nadernejad, S. Sharifzadeh, and H. Hassanpour, “Edge detection techniques: evaluations and comparisons”, Applied Mathematical Sciences, Vol. No. 2, 2008, pp. 1507÷1520.

[9] L. Bin, and M.S. Yeganeh, “Comparison for image edge detection algorithms”, IOSR Journal of Computer Engineering, Vol. No. 2, Iss. No. 6, 2012, pp. 1÷4.

[10] G.T. Shirvakshan, and C. Chandrasekar, “A comparison of various edge detection techniques used in image processing”, International Jorunal of Computer Science Issues, Vol. No. 9, Iss. No. 5/1, 2012, pp. 269÷276.