Errata

Errata: Computer-based integrated imaging using normalized cross-correlation for resolution enhancement

[+] Author Affiliations
Kyung-Hoon Bae

Samsung Thales Company, Limited, San 14-1, Giheung-Gu, Yongin-City, Gyeonggi-Do, 446-712, Korea

Jungjoon Lee

Information and Communication University, 119 Mujiro, Yuseong-gu, Daejeon 305-732, Korea

Changhan Park

Samsung Electronics Company, Limited, San 14-1, Giheung-Gu, Yongin-City, Gyeonggi-Do, 446-712, Korea

J. Electron. Imaging. 16(4), 049801 (November 08, 2007). doi:10.1117/1.2803892
History: Published November 08, 2007
Text Size: A A A

Open Access Open Access

This article was originally published online on 6 August 2007 [J. Electron. Imag.16, 033010 (Jul.–Sep. 2007)]. The following errors were discovered by the authors after publication.

In Sec. 1, on page 1, column 2, and lines 1–3, the text should be replaced as follows: “Recently, the concept of computer-based II has been proposed by D. H. Shin et al. and they introduced a good application of 3-D optical correlation.7

Also, Ref. 7 should be replaced as follows: “7. J. S. Park, D. C. Hwang, D. H. Shin and E. S. Kim, “Resolution-enhanced 3D image correlator using computationally reconstructed integral images,” Opt. Commun.276, 72–79 (2007).”

In Sec. 1, on page 2, column 1, lines 41–45, the text should be replaced as follows:

“The cross correlation between two signals is an approach that is widely used in location and recognition of some designated features or specific patterns. The correlation coefficient eliminated difficulties by normalizing the image and feature to unit length. If C(u,v), T(x,y), and R(x,y) are, respectively, the output image, target image, and reference image that is to be matched with the reference image, Eq. 1 means the general formula of normalized cross correlation (NCC)19:Display Formula

1C(u,v)=x,y[T(x,y)t(u,v)][R(xu,yu)r]{x,y[T(x,y)t(u,v)]2x,y[R(xu,yu)r]2}2
where t(u,v) is the mean of T(x,y) in the region under the feature and r is the mean of the reference image.

Therefore, from the NCC between the focused reference and object plane images sharp correlation peaks can be expected, from which the location data of the target object in space can be extracted.”

The original Eq. 1 is replaced as follows:Display Formula

2C(x,y,z)=PR(xr,yr,zr)PO(xo,yo,z).

Reference 19 should be added as follows: “19. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Addison-Wesley, Reading, Massachusetts (1992).”

Section 3, Experiment and Result, of the original paper is insufficient and has some errors. Therefore, in this errata, the Experiment and Result section is upgraded, and the error is corrected in its entirety. Section 3 is revised as follows:

Experiment and Result

To show the usefulness of our proposed CIIS-based 3-D correlation scheme, some experiments on recognition of 3-D object in a scene were performed. To show the feasibility of the proposed scheme we simplified the experimental conditions. That is, we used plain objects existing in 3-D space. For test reference objects, a 3-D object consisted of three 2-D patterns, target 1, target 2, and target 3. That is, target 1, target 2, and target 3 patterns are used for reference objects, and they are located at z1=12mm, z2=24, and z3=36mm, and their center positions are given by (0mm, 0mm, 12mm), (0mm, 0mm, 24mm), and (0mm, 0mm, 36mm), respectively. On the other hand, we placed the test target objects in space, as shown in Fig. 2, and then we verified the lateral positions in each target object.

Graphic Jump LocationF2 :

Target object with target 1, target 2, and target 3.

Here, EI of the test target and reference objects are picked up by use of a computer-generated (CG) pickup method for simplicity.14 We assumed that the lenslet array has 34×25 lenslets and its diameter is 1.08mm and the pixel pitch of the display panel is 36μm. Therefore, we obtained EI that have 1020×750 pixels. The picked-up EI for each reference object are shown in Figs. 3. On the other hand, the target object is generated by randomly positioning target 1, target 2, and target 3 patterns in space, and its EI are picked up. Figure 3 shows the picked-up EI of a 3-D object consisting of three target patterns.

Graphic Jump LocationF3 :

Picked-up EI: (a) target 1, (b) target 2, (c) target 3, and (d) all targets.

With the picked-up EI of the reference and target objects, plane images are reconstructed at the output plane using the conventional CIIS technique.13 First, the reference plane images (RPI) of target 1, target 2, and target 3 are reconstructed at distances of z=12mm, z=24, and z=36mm, as shown in Fig. 4.

Graphic Jump LocationF4 :

Reconstructed plane images of the reference and target objects: (a) z=12mm for target 1, (b) z=24mm for target 2, and (c) z=36mm for target 3.

Next, the target plane images (TPIs) of the target objects are reconstructed at every distance with an increase of 3mm from z=9mm to z=39mm, as shown in Fig. 5.

Graphic Jump LocationF5 :

Reconstructed TPIs at (a), (b), and (c) z=9 to 15mm, (c), (d), and (e) z=21 to 27mm, (f), (g), and (h) z=33 to 39mm.

Through normalized cross-correlation between these reconstructed plane images of the reference and target objects, the target object can be recognized and its lateral and longitudinal location coordinates in 3-D space can be detected. That is, Fig. 6 shows some results of normalized cross-correlations between the targets and TPIs. From these calculations we obtained the highest correlation peak value of 0.8902 at the output plane of z=12mm, which means that a target object of target 1 must exist at the output plane of z=12mm. On the other hand, another target object of target 2 can be also detected from the cross-correlations between the reconstructed reference plane image of target 2 and the reconstructed target plane images. We obtained a highest correlation peak value of 0.7865 at the output plane of z=24mm, where the target object of target 2 was located. The target object of target 3 can also be detected from the cross-correlations between the reconstructed reference plane image of target 3 and the reconstructed target plane images. We obtained a highest correlation peak value of 0.8872 at the output plane of z=36mm, where the target object of target 3 was located. That is, at the output plane of z=36mm a clearly focused target image can be reconstructed.

Graphic Jump LocationF6 :

Results of normalized cross-correlations between RPI and TPIs: (a) target 1, (b) target 2, and (c) target 3.

As a result of our confirmation of the reference object position in the input signal using a graphic tool, the detected location was accurate, and the proposed correlation scheme provides good discrimination and detection performance for 3-D object recognition.

© 2007 SPIE and IS&T

Citation

Kyung-Hoon Bae ; Jungjoon Lee and Changhan Park
"Errata: Computer-based integrated imaging using normalized cross-correlation for resolution enhancement", J. Electron. Imaging. 16(4), 049801 (November 08, 2007). ; http://dx.doi.org/10.1117/1.2803892


Figures

Graphic Jump LocationF2 :

Target object with target 1, target 2, and target 3.

Graphic Jump LocationF3 :

Picked-up EI: (a) target 1, (b) target 2, (c) target 3, and (d) all targets.

Graphic Jump LocationF4 :

Reconstructed plane images of the reference and target objects: (a) z=12mm for target 1, (b) z=24mm for target 2, and (c) z=36mm for target 3.

Graphic Jump LocationF5 :

Reconstructed TPIs at (a), (b), and (c) z=9 to 15mm, (c), (d), and (e) z=21 to 27mm, (f), (g), and (h) z=33 to 39mm.

Graphic Jump LocationF6 :

Results of normalized cross-correlations between RPI and TPIs: (a) target 1, (b) target 2, and (c) target 3.

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