Digital system of invariant correlation to position and scale using adaptive ring masks and unidimensional signatures
Selene Solorza*a, Josué Álvarez-Borrego†b a Facultad de Ciencias, UABC, Km. 103 Carretera Tijuana-Ensenada, Ensenada, B.C., México, C.P. 22860; b División de Física Aplicada, Departamento de Óptica, CICESE, Carretera Ensenada-Tijuana No. 3918, Fraccionamiento Zona Playitas, Ensenada, B.C., México, C.P. 22860. ABSTRACT Digital systems of invariant non-linear correlation to position and scale based on adaptive binary mask of concentric rings and unidimensional signatures are useful tool in pattern recognition. With the modulus of the Fourier transform of the image we obtain the invariance to translation. Using the Scale transformation and adaptive binary ring masks the scale invariant is calculated. The discrimination between objects is done by non-linear correlation of the unidimensional signatures assigned to the problem image and the target. In addition, working with unidimensional signatures reduce the computational time considerably, achieving a step toward the ultimate goal, which is developing a simple digital system that accomplishes recognition in real time at low cost. Keywords: Image processing, pattern recognition, unidimensional signatures, binary ring mask, non-linear correlation.
1. INTRODUCTION Since the computer's evolution in the middle of last century, pattern recognition of digital images based on correlations has been applied in science as well as technology areas1,2. Their applications are broad and varied. The techniques developed are used to identify micro- and macro- objects3-8, for example, automobiles, bone structures, fingerprints, virus inclusion bodies, bacteria, etc. So, the invariant correlation digital system to position and scale is a useful tool in the classification of micro- and macro- structures, independently of the translation and scale in which the object appears. Such invariants are made by the Fourier and Scale transforms9 in conjunction with some linear filters. In addition with the linear filters there are other kind of filters, the non-linear ( -law filter), which have more capacity in the discrimination between objects10,11. Other relevant aspect to be considered when we use a digital system is the leak of information. In the methodology presented in this work the signature assigned at each image was obtained using binary masks of concentric rings12,13. When the mask is applied to an image, this plays the role of a filter; hence, there is leak of information. Then, an efficient digital system in pattern recognition will use masks that drop only the irrelevant information. Here, a technique is presented to build a mask using an image to be recognized; in this form it is adapted to the problem avoiding important information leak. Because of the mask changes with the problem, it is called adaptive mask. This work presents an analysis of a digital correlation system to position and scale invariant using an adaptive mask, the Scale transform of the unidimensional signature and non-linear correlation. Also, the efficiency of such system is tested in the classification of black and white image of some Arial letters.
2. THE DIGITAL SYSTEM CORRELATION INVARIANCE TO POSITION AND SCALE Figure 1 shows the algorithm used in this work. Steps (a) and (b) selects the target and the problem image (PI), respectively. To explain the algorithm graphically, the E letter was selected as the target and its 5% scaled images as the problem image (Figure 2a and 2e, respectively). Next, the real part of the Fourier Transform ( ) of both * †
[email protected] [email protected] 22nd Congress of the International Commission for Optics: Light for the Development of the World, edited by Ramón Rodríguez-Vera, Rufino Díaz-Uribe, Proc. of SPIE Vol. 8011, 801172 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.902008 Proc. of SPIE Vol. 8011 801172-1
images are obtained (Figure 1c). In Figure 1d the binary mask of concentric rings for the target (Figure 2b) and the PI (Figure 2f) are built (in section 3 is presented the explanation to construct the mask of the image).
/A problem ima,,/' (P1)
(a)
(b)
ReaI(FT) (c)
t Binary mask of concentric circular rings (e)
(d)
Signature of the images: Sum of the IFTI values on each ring (f)
V ID(c)I of the signature for the target and the P1
I
Non-linear correlation (h)
Max Icorrelationi (i)
Figure 1. The digital system of invariant correlation to position and scale. The asterisk means the point to point multiplication of both images.
Then, the modulus of the Fourier Transform ( | | ) of both images are calculated in Figure 1e. Figure 2c and 2g, shows the | | of E letter and E scaled 5%, respectively. The binary mask is applied to each | | and, Figure 2d and 2h show the results for selected target and PI, respectively. Next, the | | values for each ring are summed and the result is assigned to the corresponding ring (counting them from inside to outside), thus, the signature of each image is obtained (Figure 1f and Figure 2i). Because the signature of the image depends upon the number of rings in the mask and the | | values the form of the signature changes when the target or the PI changes (Figure 2i).
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In order to determine if the PI is the scaled target or another image, in Figure 1g is obtained the modulus of the Scale |) and the problem image (| |). The Scale transform9 is given by transform for the signature of the target (| /
,
√
where is the signature of the image and √ 1. Then, in Figure 1h the | |), named , to recognize or not the target using the non-linear correlation ( (| |
,
|
(1) |, called , is compared with the ),
|
|
(2)
and are the phases of the Fourier transform of the problem image and the target, where means correlation, respectively, and is the non-linearity factor which is bounded as 0 1. To compute the correlation, the vectors of the modulus of the Scale transform for the target and the problem image need to have the same length. Because of the use of different ring masks this does not happen in all the cases (Figure 2j), then, zeros are added to the shorter length vector to match the length of both vectors. Finally, if the maximum value for the magnitude of the correlation is significant (Figure 1i) the PI contains the target, otherwise has a different image of the target.
3. THE ADAPTIVE BINARY MASK The mask of a selected image , for example Figure 3a, is built by taking the real part of its 2D-Fourier transform (step b). Then, a cross-section cut of the graph along the 129-axes in the -direction is taken, that is the function 129, showing in step (c). Next, we built the one-dimensional function 1, 0,
129, 0, otherwise.
(2)
Next, taking the 129-vertical axis as the rotation axis for the graph of (step d) and rotating it 360 deg, we obtained concentric cylinders of height one, different widths and centered in (129, 129). Finally, mapping those cylinders in two dimensions we built the binary ring mask (step e) associated to image in step a.
4. RESULTS In the present work, the digital system described in Figure 1 was applied to the 256 256 pixels, black and white images with Arial font letters B, E, F and H, each of them scaled 5% as the PI and the E letter as the target. Figure 4 | of the images. The non-linear correlation shows the maximum of the absolute values of the correlation for the | factor ( ) used was 0.3. The target autocorrelation is presented as a squared. The figure shows that the digital system works excellently in the identification of the E letter and its scaled images.
5. CONCLUSIONS In this work was presented a simple and efficient non-linear correlation digital system invariant to position and scale. The invariance to translation was achieved using the properties of the modulus of the Fourier transform of a function. The scale invariant was obtained by the Scale transform applied to the signature of the images. Those signatures were determined by the binary concentric ring mask. Moreover, the masks were constructed based on the given image; hence, the mask is adapted to problem avoiding in this form the information leak. Because the signatures of the images are vectors, the computational time cost was reduced considerably compared to those systems that use bi-dimensional signatures (matrices).
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Figure 2. Digital system algorithm example. The asterisk means the point to point multiplication of both images. Only for visualization purposes the (c), (d), (g) and (h) figures are shown in ln scale.
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Figure 3. The binary mask of concentric rings for E letter image.
ACKNOWLEDGMENTS This work was partially supported by CONACyT with grant No. 102007. The authors thank to Professors De Sena A. and Rocchesso D. by the Matlab routines to calculate the unidimensional scale transform. The critical review of the manuscript by Lic. Magdalena I. Calderón Guillén is greatly appreciated.
REFERENCES [1] Casasent, D. and Psaltis, D., ``Position, rotation, and scale invariant optical correlation,” Appl. Opt. 15, 1795–1799 (1976). [2] Mersereau, K. and Morris, G.M., ``Scale, rotation, and shift invariant image recognition,” Appl. Opt. 25, 2338-2342 (1986). [3] Álvarez-Borrego, J. and Chávez-Sánchez, M.C, [Introducción a la identificación automática de organismos y estructuras microscópicas y macroscópicas], Ediciones de la Noche, Guadalajara, México, (2008).
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[4] Solorza, S. and Álvarez-Borrego, J., ``System of digital invariant correlation to rotation applied to identify car models,” Digital Scientific and Technological Journal, e-Gnosis, on line (2009). [5] Lerma-Aragón, J.R. and Álvarez-Borrego, J., ``Character recognition based on vectorial signatures,” Digital Scientific and Technological Journal, e-Gnosis, on line (2009). [6] Padilla-Ramírez, A.A. and Álvarez-Borrego, J., ``Automatic recognition system of objects,” Digital Scientific and Technological Journal, e-Gnosis, on line (2009). [7] Lerma-Aragón, J.R. and Álvarez-Borrego, J., ``Vectorial signatures for invariant recognition of position, rotation and scale pattern recognition,” J. Mod. Opt. 56(14), 1598 –1606 (2009). [8] Coronel-Beltrán, A. and Álvarez-Borrego, J., ``Comparative analysis between different font types and styles letters using a nonlinear invariant digital correlation,” J. Mod. Opt. 57(1), 58-64 (2010). [9] De Sena, A. and Rocchesso, D., ``A study on using the Mellin transform for vowel recognition,” Proc. of the 7th Int. Conference on Digital Audio Effects (DAFx’04), 5-8 (2004). [10] Guerrero-Moreno, R.E. and Álvarez-Borrego, J., ``Nonlinear composite filter performance,” Opt. Eng. 48, 067201 (2009). [11] Bueno-Ibarra, M.A., Chávez-Sánchez M.C. and Álvarez-Borrego, J., ``K-law spectral signature correlation algorithm to identify white spot syndrome virus in shrimp tissues,” Aquaculture, (2011). In press. [12] Solorza, S. and Álvarez-Borrego, J., ``Digital system of invariant correlation to position and rotation,” Opt. Com. 283(19), 3613-3630 (2010). [13] Álvarez-Borrego, J. and Solorza, S., ``Comparative analysis of several digital methods to recognize diatoms,” Hidrobiologica 20(2), 158-170 (2010).
Target E 1200
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I 1
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ann E
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Figure 4. The result of the maximum values of the correlation for the |D c | vectors. Each images were scaled 5%.
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