Errata

Errata: Stereo image reconstruction using regularized adaptive disparity estimation

[+] Author Affiliations
Kyung-Hoon Bae

Samsung Thales Co., Ltd., San 14-1, Giheung-gu, Yongin-city, Gyeonggi-do, 446-712, Korea

Jung-Hwan Ko, Jung-Suk Lee

Inha Technical College, Department of Mechatronics, Incheon, Korea 402-752

J. Electron. Imaging. 17(3), 039801 (September 16, 2008). doi:10.1117/1.2976106
History: Published September 16, 2008
Text Size: A A A

Open Access Open Access

This article was originally published online on 9 March 2007 [J. Electron. Imag.16, 013013 (Jan.–Mar. 2007)]. The following errors were discovered by the authors after publication.

In the first lines of both the abstract and conclusion, the text originally read, “In this paper, stereo image reconstruction using regularized adaptive disparity estimation is proposed.” The text should read: “In this paper, natural stereo image reconstruction using regularized adaptive disparity estimation with a median filter is proposed.”

On page 2, Fig. 1 should be replaced with the figure shown here.

Graphic Jump LocationF1 :

Overall flowchart of the proposed algorithm.

On page 3, Fig. 4 should be replaced with the figure shown here.

Graphic Jump LocationF4 :

Sample “Man” sequence for finding the correspondence point: (a) left image, (b) residual image, and (c) right image.

References 26 through 28 should be added.

Furthermore, Sec. 2f of the original paper is insufficient and contains errors. Therefore, in these errata, Sec. 2f is upgraded and the error is corrected in its entirety. Section 2f is revised as follows:

Stereo Image Reconstruction
Disparity regularization

Some regions in each image have similar disparity vectors, but in the matching process, though vertical vector similarity exists, only the similarity in horizontal direction has been considered. So, considering the vertical vector similarity, we can remove the false disparity vectors. Therefore, the disparity vectors of these regions are substituted with the mean values of the disparity vectors of the nearby regions. The best method for disparity regularization is vector smoothing inside the segmented object in the image. But image segmentation is not very reliable and requires high computational loads, so instead we use the spatial smoothing filter in a vertical direction. Figure 5 are examples of the “Man” and “Fichier” sequences of disparity maps applying to disparity regularization.

Graphic Jump LocationF5 :

Examples “Man” and “Fichier” applyed to disparity regularization with (a) median filtering, (d) disparity map, (b) and (e) regularization, and (c) and (f) median filtering.

In this paper, a new adaptive disparity estimation algorithm employing a neighborhood averaging-based regularization scheme is used for alleviating the problems of matching window overlapping and misallocation occurring in the conventional disparity estimation.19 Here the regularized pixel g(x,y) is defined by Eq. 6:Display Formula

6g(x,y)=1M(i,j)Sf(i,j),
where M and S are the number and set of neighborhood pixel (i×j), respectively.

In this paper, we used Eq. 7 to preserve edge value in an edge region:Display Formula

7g(x,y)={1M(i,j)Sf(i,j)iff(x,y)1M(i,j)Sf(i,j)<T,f(x,y)otherwise.}

That is, if the difference between the regularized and original pixel value f(x,y) is smaller than the predetermined threshold, the original pixel value is replaced with the regularized one. Otherwise, by using the original pixel value, problems of over-regularization can be solved. Here, the threshold value used in this algorithm is determined by finding edges through the Laplacian operation and choosing the points whose disparity gradients were larger than a certain threshold.21,22

Accordingly, in this paper, the disparity is estimated through the adaptive matching process using an edge-preserving regularization scheme with a threshold, in which matching windows are adaptively selected in accordance with the magnitudes of the extracted feature values from the input stereo images pair. But adaptive selection of matching windows might cause overlapping and disallocation of the disparity vectors in some areas, so that in the proposed method disparity vectors of those regions are regularized with the mean values of disparity vectors of the nearby region. With this regularization process, the predicted stereo images expect to be more effectively reconstructed.

Median filtering

The mean filter is a spatial filter that replaces the center value in the window with the average of all the pixel values in the window.26 Examples of mean filtering in a 3×3 window are shown Fig. 5. Median filtering is a simple and very effective noise removal filtering process. Its performance is particularly good for removing shot noise. Median filtering is similar to using an averaging filter, in that each output pixel is set to an average of the pixel values in the neighborhood of the corresponding input pixel.27 However, with median filtering, the value of an output pixel is determined by the median of the neighborhood pixels, rather than the mean. The median is much less sensitive than the mean to extreme values (called outliers). Median filtering is therefore better able to remove these outliers without reducing the sharpness of the image. Figure 5 is shows the process of median filtering.

Graphic Jump LocationF5-1 :

Process of median filtering.

Reconstructed image

During the stereo image reconstruction process, some occluded regions might occur where one of the stereo cameras sees while the other does not, as shown in Fig. 5.

Because the disparity vector is not allocated to this occluded region, an average value of the disparities of the nearby regions is assigned through the process of disparity stability.23,24 If the viewpoint is not occluded then, the disparity is defined as the distance between the image points in both images. Equation 8 shows the disparity in the horizontal direction and the relationship between the right image Ir and the left image Il25,28:Display Formula

8Ir=[irjr]=[il+DV(il,jl)jl]=Il+[DV(il,jl)0].

References

Gonzalez  R. C., and Woods  R. E.,  Digital Image Processing. , 2nd ed.,  Prentice Hall  ((2002)).
Sun  T., and Neuvo  Y., “ Detail-preserving median based filters in image processing. ,” Pattern Recogn. Lett..  0167-8655 15, , 341–347  ((1994)).
Bae  K. H., , Ko  J. H., , and Kim  E. S., “ Regularized stereo matching scheme using adaptive disparity estimation. ,” Jpn. J. Appl. Phys..  0021-4922 45, (5A ), 4107–4114  ((2006)).
© 2008 SPIE and IS&T

Citation

Kyung-Hoon Bae ; Jung-Hwan Ko and Jung-Suk Lee
"Errata: Stereo image reconstruction using regularized adaptive disparity estimation", J. Electron. Imaging. 17(3), 039801 (September 16, 2008). ; http://dx.doi.org/10.1117/1.2976106


Figures

Graphic Jump LocationF1 :

Overall flowchart of the proposed algorithm.

Graphic Jump LocationF4 :

Sample “Man” sequence for finding the correspondence point: (a) left image, (b) residual image, and (c) right image.

Graphic Jump LocationF5 :

Examples “Man” and “Fichier” applyed to disparity regularization with (a) median filtering, (d) disparity map, (b) and (e) regularization, and (c) and (f) median filtering.

Graphic Jump LocationF5-1 :

Process of median filtering.

Tables

References

Gonzalez  R. C., and Woods  R. E.,  Digital Image Processing. , 2nd ed.,  Prentice Hall  ((2002)).
Sun  T., and Neuvo  Y., “ Detail-preserving median based filters in image processing. ,” Pattern Recogn. Lett..  0167-8655 15, , 341–347  ((1994)).
Bae  K. H., , Ko  J. H., , and Kim  E. S., “ Regularized stereo matching scheme using adaptive disparity estimation. ,” Jpn. J. Appl. Phys..  0021-4922 45, (5A ), 4107–4114  ((2006)).

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