Optimized Regression for Efficient Function Evaluation

Garcia, Eric K.; Arora, Raman; Gupta, Manisha

doi:10.1109/tip.2012.2200902

Cited by 20 publications

(14 citation statements)

References 23 publications

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“…For both types of data, we compared the performance of RPCC with the LCC and PCC up to degree of four. We also compared the above with the colour correction using the tri-linear LUT interpolation implemented as suggested in [32]. Here, we used 13×13×13 LUT and employed the Graph Hessian Regularizer also described in the above reference.…”

Section: Methodsmentioning

confidence: 99%

“…However, for all terms except the first three linear, the individual variables are in the fractional powers. The rootpolynomials are also related to the multi-linear polynomials, which arise in a multi-linear LUT interpolation [32]. However, the latter do not have the desired property of degree 1 and hence will not demonstrate the aforementioned exposure invariance.…”

Section: B Related Workmentioning

confidence: 99%

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Color Correction Using Root-Polynomial Regression

Finlayson

Mackiewicz

Hurlbert

2015

IEEE Trans. on Image Process.

172

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Cameras record three color responses (RG B) which are device dependent. Camera coordinates are mapped to a standard color space, such as XYZ-useful for color measurement-by a mapping function, e.g., the simple 3×3 linear transform (usually derived through regression). This mapping, which we will refer to as linear color correction (LCC), has been demonstrated to work well in the number of studies. However, it can map RG Bs to XYZs with high error. The advantage of the LCC is that it is independent of camera exposure. An alternative and potentially more powerful method for color correction is polynomial color correction (PCC). Here, the R, G, and B values at a pixel are extended by the polynomial terms. For a given calibration training set PCC can significantly reduce the colorimetric error. However, the PCC fit depends on exposure, i.e., as exposure changes the vector of polynomial components is altered in a nonlinear way which results in hue and saturation shifts. This paper proposes a new polynomial-type regression loosely related to the idea of fractional polynomials which we call root-PCC (RPCC). Our idea is to take each term in a polynomial expansion and take its kth root of each k-degree term. It is easy to show terms defined in this way scale with exposure. RPCC is a simple (low complexity) extension of LCC. The experiments presented in this paper demonstrate that RPCC enhances color correction performance on real and synthetic data.

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Section: Methodsmentioning

confidence: 99%

Section: B Related Workmentioning

confidence: 99%

Color Correction Using Root-Polynomial Regression

Finlayson

Mackiewicz

Hurlbert

2015

IEEE Trans. on Image Process.

172

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show abstract

“…1b. Specifically, we find a 5 × 5 × 5 LUT interpolation function by using lattice regression [11] that minimizes min LUT () Σ i ||LUT(g( f (Mρ i ))) − P i || 2 where g() is a non-linear function that stretches highlights. We found empirically there was an advantage in deploying more LUT resolution in the highlight region where gamut mapping is created.…”

Section: Gamut Correction Stepmentioning

confidence: 99%

Rank-Based Radiometric Calibration

Gong¹,

Finlayson²,

Darrodi³

et al. 2018

jist

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Raw images are more useful than JPEG images for machine vision algorithms and professional photographers because raw images preserve a linear relation between pixel values and the light measured from the scene. A camera is radiometrically calibrated if there is a computational model which can predict how the raw image is mapped to the corresponding rendered image (e.g. JPEGs) and vice versa. Our method makes use of the observation that the rank order of pixel values are mostly preserved post color correction. We show that this observation is the key for getting a compact and robust radiometric calibration model. Since our method requires fewer variables, it can be solved for using less calibration data. An additional advantage is that we can derive the camera pipeline from a single pair of raw-JPEG images. Experiments demonstrate that our method delivers stateof-the-art results (especially for the most interesting conversion from JPEG to raw).

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“…1b. Specifically, we find a 5 × 5 × 5 LUT by using lattice regression [10] that minimises min LUT () Σ i ||LUT( f (Mρ i )) − P i || 2 .…”

Section: Gamut Correction Stepmentioning

confidence: 99%

“…9) to find f −1 by optimising min f −1 () Σ i || f −1 (P i ) − Mρ i ||. Finally, we solve for the backward LUT() by optimising min LUT () Σ i ||LUT(M −1 f −1 (P i )) − ρ i || where the LUT is fitted by a 5 × 5 × 5 lattice regression [10].…”

Section: Rank-based Recovery Of Rawmentioning

confidence: 99%

Concise Radiometric Calibration Using The Power of Ranking

Gong¹,

Finlayson²,

Darrodi

2017

Procedings of the British Machine Vision Conference 2017

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Compared with raw images, the more common JPEG images are less useful for machine vision algorithms and professional photographers because JPEG-sRGB does not preserve a linear relation between pixel values and the light measured from the scene. A camera is said to be radiometrically calibrated if there is a computational model which can predict how the raw linear sensor image is mapped to the corresponding rendered image (e.g. JPEGs) and vice versa. This paper begins with the observation that the rank order of pixel values are mostly preserved post colour correction. We show that this observation is the key to solving for the whole camera pipeline (colour correction, tone and gamut mapping). Our rank-based calibration method is simpler than the prior art and so is parametrised by fewer variables which, concomitantly, can be solved for using less calibration data. Another advantage is that we can derive the camera pipeline from a single pair of raw-JPEG images. Experiments demonstrate that our method delivers state-of-the-art results (especially for the most interesting case of JPEG to raw).

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Optimized Regression for Efficient Function Evaluation

Cited by 20 publications

References 23 publications

Color Correction Using Root-Polynomial Regression

Color Correction Using Root-Polynomial Regression

Rank-Based Radiometric Calibration

Concise Radiometric Calibration Using The Power of Ranking

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