OE Letters

Depth image upsampler using pixel selection based on selective weight function

[+] Author Affiliations
Soo-Yeon Shin, Jae-Won Suh

Chungbuk National University, Seowongu, Cheongju, Chungbuk, Republic of Korea

Opt. Eng. 56(4), 040503 (Apr 21, 2017). doi:10.1117/1.OE.56.4.040503
History: Received February 16, 2017; Accepted April 7, 2017
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Abstract.  We propose an image upsampling algorithm to increase the depth image resolution while preserving edge information and protecting from the texture copy problem. The proposed upsampler selectively combines the spatial, depth range, and color range weight functions for cost calculation according to the weight selection algorithm. In particular, a color range weight function is proposed to reduce the texture copy problem caused by distinct patterns in the color image. Simulation results show that the proposed algorithm outperforms other conventional upsamplers.

Figures in this Article

Resolution of a depth image captured by a three-dimensional (3-D) camera for depth sensing is generally lower than its corresponding color image for 3-D video applications. In addition, an advanced 3-D TV system transmits low-resolution depth images to make the best use of a transmission bandwidth. For practical purposes, an efficient depth image upsampling algorithm is necessary to adjust the resolution between depth and color images.

There are a number of depth image upsamplers. The bilinear interpolator and bicubic interpolator can be directly used for depth image upsampling. These interpolators generate good results in smooth regions, but make noise looked like the shape of staircase in the edge. To remove the staircase noise, some depth image upsamplers based on weight functions have been introduced.13 These studies show positive results for staircase noise, but generate the drawback of texture copy problem caused by a distinct color pattern. In this paper, we propose a depth image upsampling algorithm to overcome these problems, such as staircase noise and texture copy problem. The proposed algorithm suggests an effective weight choice method and a color weight function.

To increase the sampling rate of a depth image, Kopf et al.1 have developed a joint bilateral upsampler (JBU) by extending the idea of a joint bilateral filter based on weight functions. Suppose that there are a low-resolution depth image Dl and a high-resolution color image Ih. Let (p,q) and (p,q) denote the pixel coordinates in the low-resolution image and the high-resolution image, respectively. p is the center of the local neighborhood N(p) and q is the neighboring pixel location of p.

The depth value Dph at p in an upsampled depth image Dh is calculated by a normalized weighted sum, which is expressed as Display Formula

Dph=qN(p)fs(p,q)·fr(p,q)·DqlqN(p)fs(p,q)·fr(p,q),(1)
where fs and fr are the spatial and range weighting functions, respectively. The fs and fr are modeled by the exponential function as follows: Display Formula
fs(p,q)=exp(pq22δs2),fr(p,q)=exp(IphIqh22δr2),(2)
where · is a Euclidean distance operator. δs and δr are the smoothing parameters of fs and fr, respectively.

To get an upsampled depth image while keeping the shape of the edge without staircase noise, the previous works13 define the color weight function and take advantage of the color information under the assumption that depth and color images have similar characteristics. However, the use of color weight occasionally causes an unexpected depth in smooth areas when a distinct pattern is in the color image. This phenomenon is called texture copy problem. To reduce the texture copy problem, we propose a weight selection algorithm that selectively applies a range weight function for cost calculation: color range weight function or depth range weight function. In addition, we define a color range weight function based on Laplacian distribution to utilize the color information more effectively.

Figure 1 shows the overall flow of the proposed upsampler. First, a low-resolution depth image Dl is upsampled by a bicubic interpolation algorithm and the upsampled high-resolution depth image is denoted by Bh. Then, all pixels in the upsampled depth image Bh should be tested by weight selection algorithm whether the pixel belongs to a distinct color pattern or not. Next, the cost values between the center pixel and the surrounding pixels are calculated based on spatial and range weight functions. Finally, when the candidate pixel at qx has the minimum cost among the nine candidates, the depth value Dph at p is replaced by the depth value Bqxh at qx.

Graphic Jump Location
Fig. 1
F1 :

Overall flow of the proposed upsampler.

After obtaining the upsampled depth image Bh by the bicubic interpolation algorithm, we perform the weight selection algorithm for all pixels, as shown in Fig. 2. If we detect a distinct color pattern in a color image, we do not use the color image information to avoid the texture copy problem. To detect a distinct color pattern, we compare the mean of absolute difference (MAD) of the color image and that of the depth image. The MAD of the color image at p and the MAD of the depth image are denoted as MADpc and MADpd and calculated as Display Formula

MADpc=1NqN(p)|IphIqh|,MADpd=1NqN(p)|BphBqh|.(3)
Then we calculate the absolute difference (AD) between MADpc and MADpdDisplay Formula
ADp=|MADpcMADpd|.(4)
If the predefined difference threshold Td is bigger than ADp, we can expect that the color texture problem will not happen because there is no big differences between neighboring pixels in the color image. In this case, we use a color range weight function for cost calculation. If Td is smaller than ADp, we select a depth range weight function to remove the effects of the color image.

Graphic Jump Location
Fig. 2
F2 :

Weight selection algorithm.

Figure 3 shows the pixel position for cost calculation and weight function. The cost Cp,q at q with respect to p is calculated as Display Formula

Cp,q={RWq,r·|BphBqh|if  |BphBqh|1RWq,rotherwise,(5)
where Display Formula
RWq,r={rN(q)fφ(q,r)·fψ(q,r)if  ADp<TdrN(q)fφ(q,r)·fω(q,r)otherwise.(6)
The region weight RWq,r is a weighted sum of spatial and range weight functions between q and its neighbor rN(q). To calculate the value of the region weight, we use the result of weight selection algorithm. In the equation below , the spatial weight function fφ and the depth range weight function fω are modeled as a simplified Gaussian function Display Formula
fφ(q,r)=exp(qr2δφ),fω(q,r)=exp(BqhBrh2δω),(7)
where δφ and δω are the smoothing parameters of fφ and fω, respectively. However, unlike predefined weight functions, a color range weight function fψ is modeled as a simplified Laplacian function to reduce the effect of color information. The Laplacian function is narrower and sharper than the Gaussian function. It is also expressed by an exponential function Display Formula
fψ(q,r)=12δψexp(IqhIrhδψ),(8)
where δψ is the smoothing parameter of fψ.

Graphic Jump Location
Fig. 3
F3 :

Candidate pixels for cost calculation.

After calculating each cost of all nine candidates, we find the minimum cost among these nine candidates. Minimum cost pixel qx is represented as Display Formula

qx:min{Cp,q1,Cp,q2,,Cp,q9}.(9)
Finally, Dph is replaced with a pixel Bqxh generating the minimum cost Display Formula
Dph=Bqxh.(10)

To evaluate the performance of the depth image upsampling algorithm, we performed computer simulations on various images having ground truth depth data. To generate input 8-bit low-resolution depth images, each ground truth depth image is downsampled by a factor of 2 and 4. The performance of the proposed algorithm was compared to the JBU,1 joint trilateral upsampler (JTU),2 and fast edge preserving depth upsampler (FEDU)3 in terms of peak signal-to-noise ratio (PSNR) and subjective visual quality. In the simulation, the cost function parameters were set by q3×3, r3×3, Td=50, δφ=2, δψ=0.1, and δω=0.1.

Tables 1 and 2 show the results of PSNR comparison. When the upsampling factor is 2, the proposed upsampler has higher PSNRs by as much as about 11.11, 11.3, and 2.54 dB than JBU,1 JTU,2 and FEDU3 on average, respectively. When the upsampling factor is 4, the PSNR gains of the proposed algorithm are 6.57, 4.21, and 2.65 dB higher than JBU,1 JTU,2 and FEDU3 on average, respectively.

Table Grahic Jump Location
Table 1PSNR comparison (unit: dB and upsampling factor: 2).
Table Grahic Jump Location
Table 2PSNR comparison (unit: dB and upsampling factor: 4).

As shown in Figs. 4 and 5, the excellence of the proposed algorithm is also demonstrated by a subjective visual quality test. The first image is the color image and the region of interest is marked by a red box. (a), (b), and (c) are the results of JBU, FEDU, and the proposed algorithm, respectively. Sawtooth and art are upsampled by 4 and 2. From the result of JBU in Fig. 4(a), the staircase distortion is observed. FEDU3 reduces the staircase distortion. but there remain blurring artifacts in the sharp edge as shown in Fig. 4(b). However, the proposed algorithm generates a sharp edge without blurring artifacts. In addition, we can see the reduced texture copy problem in Fig. 5(c) compared to the result of JBU in Fig. 5(a).

Graphic Jump Location
Fig. 4
F4 :

Subjective visual quality tests of sawtooth (×4): (a) original color image, (b) JBU, (c) JTU, and (d) FEDU.

Graphic Jump Location
Fig. 5
F5 :

Subjective visual quality tests of art (×2): (a) original color image, (b) JBU, (c) JTU, and (d) FEDU.

A depth image upsampler has been proposed to preserve edge information and reduce the texture copy problem. To achieve the goal, we introduced the weight selection algorithm and the color range weight function based on a Laplacian distribution model. Computer simulations were performed on various test images to show the superiority of the proposed algorithm. The simulation results demonstrate that the proposed scheme has advantages in terms of PSNR and subjective visual quality. As a result, the increased upsampled depth image quality can lead to an improvement in the virtual view synthesis and multiview 3-D videos.

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (No. 2014R1A1A2057662) and research projects of “The Development of Security and Safety Systems based on Ubiquitous Technology for Shipping and Logistics.”

Kopf  J.  et al., “Joint bilateral upsampling,” ACM Trans. Graphics. 26, (3 ), 1 –6 (2007). 0730-0301 CrossRef
Li  Y.  et al., “Depth map super-resolution via iterative joint trilateral upsampling,” in  IEEE Conf. on Visual Communications and Image Processing , pp. 386 –389 (2014).CrossRef
Kim  S. Y., and Ho  Y. S., “Fast edge-preserving depth image upsampler,” IEEE Trans. Consum. Electron.. 58, (3 ), 971 –977 (2012). 0098-3063 CrossRef
© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Citation

Soo-Yeon Shin and Jae-Won Suh
"Depth image upsampler using pixel selection based on selective weight function", Opt. Eng. 56(4), 040503 (Apr 21, 2017). ; http://dx.doi.org/10.1117/1.OE.56.4.040503


Figures

Graphic Jump Location
Fig. 3
F3 :

Candidate pixels for cost calculation.

Graphic Jump Location
Fig. 2
F2 :

Weight selection algorithm.

Graphic Jump Location
Fig. 1
F1 :

Overall flow of the proposed upsampler.

Graphic Jump Location
Fig. 4
F4 :

Subjective visual quality tests of sawtooth (×4): (a) original color image, (b) JBU, (c) JTU, and (d) FEDU.

Graphic Jump Location
Fig. 5
F5 :

Subjective visual quality tests of art (×2): (a) original color image, (b) JBU, (c) JTU, and (d) FEDU.

Tables

Table Grahic Jump Location
Table 2PSNR comparison (unit: dB and upsampling factor: 4).
Table Grahic Jump Location
Table 1PSNR comparison (unit: dB and upsampling factor: 2).

References

Kopf  J.  et al., “Joint bilateral upsampling,” ACM Trans. Graphics. 26, (3 ), 1 –6 (2007). 0730-0301 CrossRef
Li  Y.  et al., “Depth map super-resolution via iterative joint trilateral upsampling,” in  IEEE Conf. on Visual Communications and Image Processing , pp. 386 –389 (2014).CrossRef
Kim  S. Y., and Ho  Y. S., “Fast edge-preserving depth image upsampler,” IEEE Trans. Consum. Electron.. 58, (3 ), 971 –977 (2012). 0098-3063 CrossRef

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