- Research
- Open Access
Analysis and processing of pixel binning for color image sensor
- Xiaodan Jin1 and
- Keigo Hirakawa1Email author
https://doi.org/10.1186/1687-6180-2012-125
© Jin and Hirakawa; licensee Springer. 2012
- Received: 11 October 2011
- Accepted: 29 May 2012
- Published: 21 June 2012
Abstract
Pixel binning refers to the concept of combining the electrical charges of neighboring pixels together to form a superpixel. The main benefit of this technique is that the combined charges would overcome the read noise at the sacrifice of spatial resolution. Binning in color image sensors results in superpixel Bayer pattern data, and subsequent demosaicking yields the final, lower resolution, less noisy image. It is common knowledge among the practitioners and camera manufacturers, however, that binning introduces severe artifacts. The in-depth analysis in this article proves that these artifacts are far worse than the ones stemming from loss of resolution or demosaicking, and therefore it cannot be eliminated simply by increasing the sensor resolution. By accurately characterizing the sensor data that has been binned, we propose a post-capture binning data processing solution that succeeds in suppressing noise and preserving image details. We verify experimentally that the proposed method outperforms the existing alternatives by a substantial margin.
Keywords
- Aliasing
- Neighboring Pixel
- High Dynamic Range Imaging
- Sensor Resolution
- Color Filter Array
1 Introduction
Recent progress on digital camera technology has had extraordinary impact on numerous electronic industries, including mobile phones, security, vehicle, bioengineering, and computer vision systems. In many applications, sensor resolution has exceeded the optical resolution, meaning that the additional hardware complexity to increase pixel density would not necessarily result in large image quality gains. The significant improvement in sensor sensitivity has allowed cameras to operate in lighting conditions that were unthinkable with film cameras.
Despite increased sensitivity, however, noise remains a serious problem in modern image sensors. Available technologies for reducing noise in hardware include backside illuminated architecture [1, 2], color filters with higher transmittance [3, 4], and pixel binning [5–7]. Processing techniques at our disposal include image denoising [8–10], joint denoising and demosaicking [11–14], image deblurring [15, 16] (long shutter to compensate for light), and single-shot high dynamic range imaging [17].
Commonly used binning schemes. Binning refers to the concept of combining the electrical charges of neighboring pixels together to form a superpixel. (a–b) The numbers over the high resolution Bayer pattern indicate which pixels are combined together. (c) The resultant superpixel Bayer pattern, where the numbers indicate the relative locations of the combined pixels (for [7] and [5]).
Binning vs. no binning. Compared to no binning, binning succeeds in reducing noise. However, the pixelization and zippering artifacts deteriorate the image quality. (a) Reconstruction from full resolution CFA; (b) reconstruction from Kodak PIXELUX scheme of Figure 1a; (c) reconstruction from PhaseOne scheme of Figure 1b.
The remainder of this article is organized as follows. We begin by briefly reviewing CFA sampling and demosaicking in Section 2. Section 3. provides a rigorous analysis of binning. A novel binning-aware demosaicking technique is developed in Section 4. We experimentally verify its effectiveness in 5. before making concluding remarks in Section 6.
2 Background
2.1 CFA sampling
where denotes the translucency of CFA at location n. The advantage to the representation is that the difference images x α =x r −x g and x β =x b −x g enjoy rapid spectral decay and can serve as a proxy for chrominance. On the other hand, the “baseband” green image x g can be taken to approximate luminance. As our eventual image recovery task will be to approximate the true color image triple x(n) from acquired sensor data y(n), note that recovering either representations ({x r x g x b }or {x g x α x β }) are equivalent. Moreover, the representation of (1) allows us to re-cast the pure-color sampling structure in terms of sampling structures c α and c β associated with the difference channels x α and x β . For more extensive investigation on the bandlimitedness assumptions of {x g x α x β }, see [18–20].
Idealized spectral support of a color image acquired under the Bayer pattern. In each figure, the horizontal and vertical axes span [−Π,Π)2of Fourier index, and the DC is located at the center of the figure. Solid lines indicate the baseband signals, while replicated spectra with the dashed lines arises as a result of CFA sampling. Black and red lines correspond to the support of luminance and chrominance images, respectively. Alias-inducing chrominance replications are shown with (a) Radially symmetric luminance, (b) vertical feature luminance, (c) horizontal feature luminance.
2.2 Demosaicking
Most demosaicking algorithms described in the literature make use (either implicitly or explicitly) of correlation structure in the spatial frequency domain, often in the form of local sparsity or directional filtering [14, 19, 21–23]. As noted in our earlier discussion, the set of carrier frequencies induced by c α and c β include Π,0] T and [0,Π T , locations that are particularly susceptible to aliasing by horizontal and vertical edges. Figures 3b,c indicates these scenarios, respectively; it may be seen that in contrast to the radially symmetric baseband spectrum of Figure 3a, chrominance–luminance aliasing occurs along one of either the horizontal or vertical axes. However, successful reconstruction can still occur if a noncorrupted copy of this chrominance information is recovered, thereby explaining the popularity of (nonlinear) directional filtering steps [19, 21–23]. We can, therefore, view the CFA design problem as one of spatial-frequency multiplexing, and the CFA demosaicking problem as one of demultiplexing to recover subcarriers, with spectral aliasing given the interpretation of “cross talk” [19].
where d(·,·) is some distance metric and εis a tolerance parameter.
3 Analysis of binning
Let us rigorously analyze the effects that binning has on the acquired sensor data. We begin in Section 3.1 with a brief review of the signal-to-noise ratio (SNR) gains that binning is expected to improve [24]—the main motivation behind binning. An in-depth analysis in Section 3.2 will prove that a combination of binning and demosaicking results in a loss of resolution that is far worse than commonly believed. Section 3.3 offers an alternative perspective that paves a path towards recovering artifact-free images.
3.1 Signal measurement uncertainty
where t is the exposure time, Q is the quantum efficiency constant, D is the dark current constant, and N is the read noise power.
SNR as a function of signal intensity. Here, M=4, Q=0.70, t=1/100s, D=0.1electrons/pixel/second, and N=10electrons rms/pixel [24]. See (5-7).
3.2 Binning “sampling”
Due to the fact that binning combines M electric charges of neighboring pixels, each pixel cannot be shared by more than one superpixel. Moreover, the charges can be combined by summation only (i.e. no fractional combinations). As such, the options for binning schemes are fairly limited. Furthermore, the superpixels produced by pixel binning in color image sensors form a Bayer pattern that requires the additional step of demosaicking to recover the full color low resolution image. We will show that superpixel Bayer pattern suffers from many problems that the pixel-level Bayer pattern does not, leading to the conclusion that combining pixel binning and demosaicking is the wrong approach.
Consider Kodak PIXELUX, the most widely used binning scheme illustrated in Figure 1a,c [7]. It combines four neighboring pixel values together to form one superpixel. This process of combining neighboring pixels to form a single superpixel is equivalent to applying a convolution operator followed by downsampling:
-
filtering: let hbindenote the filter coefficients(8)where Δ(·)denotes the Kronecker delta function. Then the charge summation in PIXELUX is
-
downsampling: to yield the superpixel Bayer pattern data s, do(9)
Idealized spectral support of binning sampled data S ( ω )in (10), corresponding to Figure 1. As before, solid lines indicate the baseband signals, while spectra with the dashed lines arises as a result of CFA sampling. Black and red lines correspond to the support of luminance and chrominance images, respectively. The blue box represents the original sampling rate.
The main advantage of binning in (9) over (2) is that the signal strength of the baseband X g and the chrominance components X α and X β are boosted by four times—consistent with the SNR analysis in the previous section. As evidenced by Figure 5a, the Fourier support of (9) closely resembles the Bayer pattern of Figure 3a. Superpixel Bayer pattern data in (10) is far from an ideal Bayer pattern representation of the true image x(n) we hope to recover from s(n), however. One distortion we see is the unwanted filtering term that degrades the baseband luminance/green signal X g (ω). Another complication is that the antialiasing is only partially effective, allowing aliasing to corrupt the baseband X g (ω) near .
Contrary to the popular belief that Kodak PIXELUX binning results in 2×2reduction in resolution, the main conclusion we draw from (9) is that the “Nyquist rate” of this binning scheme is Π/4due to high risk of aliasing—implying that the actual resolution loss is 4×4, far worse than the presumed 2×2. Even if this Nyquist rate did not cause problems (e.g. increase sensor resolution), s does not escape the unwanted filtering term in (9)—this cannot be eliminated simply by increasing sensor resolution. Hence when a demosaicking algorithm is applied to the superpixel Bayer pattern data s, what is expected is a filtered and aliased image that we have already seen in Figure 2.
3.2 Binning “subsampling”
Binning subsampling is an alternative interpretation to the binning sampling in Figure 1. (a) Subsampled data t(n)in (11) equivalent to the superpixel Bayer pattern of Figure 1c. (b) Idealized spectral support of binning subsampled data T(ω)in (12). The baseband signal X g is free of aliasing in the shaded region. As before, solid lines indicate the baseband signals, while spectra with the dashed lines arises as a result of CFA sampling. Black and red lines correspond to the support of luminance and chrominance images, respectively.
-
filtering: The charge summation in PIXELUX is
-
subsampling: to yield the binning subsampling data t, do(11)
Fourier transform of.
4 Binning-aware demosaicking
Motivated by the analysis of pixel binning subsampling in (12), we now present a novel binning-aware demosaicking aimed at recovering full-color image xwithout introducing binning artifacts. We accomplish this in three stages.
Step 1: Chrominance estimation
Idealized spectral support of binning subsampled data, at various stages of binning-aware demosaicking. Shaded regions denote filter support. See text.
where (·) † denotes a pseudo inverse matrix and h0 is a lowpass filter whose passbands matches the support of X α and X β . The reconstruction of vertically oriented image feature (denoted ) is same as (13) but with 90° rotation.
Step 2: Luminance filtering
As illustrated in Figure 8c,d, the modulation by f(n)not only shifts the spectrums, but also creates additional aliasing copies. Hence, the filter h2is needed to attenuate them. The same procedure can be used to find the green image based on and .
Step 3: Directional selection
Once and are found, they must be combined to yield the final estimate, via the convex combination (3). As already mentioned, the directional selection variable τ has received considerable attention in research and many techniques are available. However, these studies often lack analysis under noise—although binning reduces noise considerably, most directional selection variables are nevertheless sensitive to random perturbations.
where and are as defined in (3) and (4), respectively. Contrast this to the original AHD formulation which selected either or (i.e. τ∈{0,1} instead of τ∈[0,1]) as the final output . The modified strategy of (16) behaves similarly to the original AHD near the edges of an image, but encourages averaging in the flat regions of the image. It was found empirically to be far more robust to directional selection under noise.
5 Experimental validation
5.1 Setup
Example of images used in experiment (zoomed).
Reconstruction performance in PSNR with various noise levels
Noise (σ n ) | Color | LR-CFA | HR-CFA | HR-CFA + binning | ||
---|---|---|---|---|---|---|
[19] | [19] + DS | PO + [19] | K + [19] | K + Proposed | ||
0.000 | R | 48.1787 | 51.4671 | 45.2485 | 45.3275 | 47.8061 |
G | 51.8147 | 54.7110 | 46.5344 | 47.1429 | 48.6259 | |
B | 46.5116 | 50.9532 | 43.6715 | 44.5752 | 45.5689 | |
0.005 | R | 47.1788 | 46.5149 | 44.6596 | 44.7572 | 46.8994 |
G | 50.1223 | 48.5953 | 46.3633 | 41.5903 | 47.6607 | |
B | 45.6221 | 45.2237 | 43.1426 | 43.9331 | 44.6091 | |
0.010 | R | 45.4430 | 42.1931 | 43.4914 | 43.5929 | 45.2686 |
G | 47.6553 | 43.9223 | 44.5383 | 44.9318 | 45.9540 | |
B | 44.0420 | 40.7293 | 42.0733 | 42.7001 | 42.9732 | |
0.015 | R | 43.7677 | 39.1858 | 42.2368 | 42.3349 | 43.6632 |
G | 45.5264 | 40.7919 | 4.18183 | 43.4857 | 44.3119 | |
B | 42.4968 | 37.6716 | 40.9172 | 41.4211 | 41.3987 | |
0.020 | R | 42.2672 | 36.9118 | 41.0434 | 41.1293 | 42.2202 |
G | 43.7388 | 38.4621 | 41.9128 | 42.1503 | 42.8488 | |
B | 41.0955 | 35.3795 | 39.8064 | 40,2189 | 39.9910 | |
0.025 | R | 40.9430 | 35.0944 | 39.9375 | 40.0160 | 40.9391 |
G | 42.2200 | 36.6133 | 40.7530 | 40.9454 | 41.5568 | |
B | 39.8450 | 33.5524 | 38.7712 | 39.1164 | 38.7417 | |
0.030 | R | 39.7693 | 33.5816 | 38.9267 | 38.9959 | 39.7997 |
G | 40.9107 | 35.0803.9327 | 39.7008 | 39.8595 | 40.4102 | |
B | 38.7310 | 32.0235.3426 | 37.8168 | 38.1076 | 37.6279 |
The linear images used in this simulation study are a part of the collection of [25, 26], examples of which are shown in Figure 9. Numerical scores in Table 1 and Figure 13 were obtained by averaging performance over 84 images. Noise is simulated by adding pseudorandom white Gaussian noise to the CFA data y(n), the superpixel CFA data s(n) and p(n), and the lower resolution CFA data y ′ (n). In the experiments, the 12 bit image data in [25, 26] were renormalized to ranges 0–1—meaning noise standard deviation σ n =0.01 correspond to standard deviation of 40.96 in a 12 bit camera processing pipeline, etc. Considering the noise models in (57), one may ask if such a simplified noise model is appropriate. As evidenced by the analysis in (7), however, the difference between SNR and SNRsumis M (the number of pixels combined together); and the difference between SNRsum and SNRbin is the read noise power N. Hence the SNR gains in binning is attributed only to the signal-independent portion of the noise, and not on the signal dependent portion. Furthermore, the read noise dominates in the low light regime. Hence simulated additive white Gaussian noise suffices for experimental verification. The binning subsample signal t(n) represents the same data as s(n) and is computed by upsampling s(n)(insert zeros where necessary).
5.2 Results
Example outputs from four different methods () are shown in Figures 10, 11 and 12. As expected, demosaicking applied to a full resolution CFA () has a noisy appearance due to low SNR of individual pixels. However, edges and image features are clearly defined even after downsampling thanks to the full resolution description. Demosaicking applied to superpixel CFAs (), on the other hand, yields the opposite qualities—the noise is significantly reduced owing to high SNR of binning, but the image suffers from severe artifacts stemming from aliasing in (10). More specifically, the aliasing in Kodak PIXELUX binning manifests itself as a pixelization artifact, while PhaseOne binning results in zippering artifacts. However, one may argue that the aliasing artifacts in become less bothersome at the highest level of noise because the zippering and noise become less distinguishable. By contrast, the proposed binning-aware demosaicking method () succeeds in suppressing noise while preserving the image features. Of particular interest is the comparison between and , since they both use Kodak PIXELUX binning but the proposed method yield drastically improved outcomes. Overall, the proposed method has better visual quality than and for σ n <0.03; but proposed has a slightly noisier appearance at the highest level of noise (σ n =0.03). Finally, the output from the low resolution camera is both robust to noise and aliasing. This is expected, as lower resolution CFA data y ′ (n) does not share the problems that superpixel CFAs p(n),s(n),t(n) have. However, has superior reconstruction over without noise (σ n =0). Figure 12 shows an example where none of the reconstruction methods produced a satisfactory output (except for under no noise).
The performance is evaluated also in terms of peak SNR, using the downsampled version of the ideal lowpassed (antialiased) image x ′ in (18) as their reference. The results are summarized in Table 1. When there is no noise (σ n =0), ordinary demosaicking reconstruction and lower resolution sensor yields the best results, as expected. However, the proposed is a very close third, yielding comparably satisfactory results. Binning result is worst by far due to binning artifacts.
When noise is taken into consideration, the quality of suffers greatly as expected. Even with noise variance as little as σ n =0.005, the performance of deteriorates significantly, while performance of , , , and in terms of PSNR are far less sensitive to noise. With moderate noise levels (σ n <0.03) the proposed binning-aware demosaicking clearly outperforms the artifact-plagued demosaicking of superpixels. With the largest noise level considered (σ n =0.03), PSNR performances of , , and are closer to each other because deteriorations in output images are dominated by noise (rather than by artifacts).
The analysis in Figures 10, 11, 12, 13 and Table 1 sheds a light on the decades-old debate about resolution versus noise. On one hand, the lower resolution sensor delivers consistent performance under noise (). However, Figure 11 shows that under no noise, extra sensor resolution is still desirable. Consider Figure 13. The comparison between green (low resolution) and red (high resolution) curves is consitent with the image quality of Figures 10 and 11. With the availability of pixel binning, we would compare the green curve with the “max function” over the red and blue (binning) curves in Figure 13. Hence one can think of binning as a way to narrow the gap between the red and green curves in noise, without making sacrifices to the advantages of higher spatial resolution.
6 Conclusion
In this article, we proved via a rigorous analysis of binning sampling that Kodak PIXELUX binning scheme results in 4×4reduction in image resolution—contrary to the popular belief that binning of four pixels should result in 2×2reduction in resolution. We proposed a binning-aware demosaicking algorithm based on the Fourier analysis of binning subsampling to combine unaliased copies of the Fourier spectra together via the demodulation. The resultant method succeeds in reconstructing the color image with only 2×2 resolution loss—or increasing the resolution by 2×2over the traditional approach of applying demosaicking to superpixels. The binning-aware demosaicking also succeeds in suppressing noise and preserving image details. We verified experimentally that the binning-aware demosaicking outperforms the alternatives.
Appendix 1: Proof of Fourier Representation of binning subsampling
where we used the fact that Hbin(0)=4.
The Fourier support of T(ω) is illustrated in Figure 6b. Note that the summation over λsuggests that binning subsampling will result in 16 modulations. However, is 0 for many values of λ, as shown in Figure 7. As a result, there are only nine actual modulations.
Appendix 2: Proof of Fourier representation of binning sampling
7 Endnote
aFilter hbin is a combination of highpass and lowpass. However, binning takes advantage of the fact that the sensor resolution exceeds optical resolution, meaning hbin is taken to be a lowpass/antialiasing filter on x g .
Declarations
Acknowledgement
This work was funded in part by Texas Instruments.
Authors’ Affiliations
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