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Publication# A Model of Retinal Local Adaptation for the Tone Mapping of Color Filter Array Images

Résumé

We present a tone mapping algorithm that is derived from a model of retinal processing. Our approach has two major improvements over existing methods. First, tone mapping is applied directly on the mosaic image captured by the sensor, analogue to the human visual system that applies a non-linearity on the color signals captured by the cone mosaic. This reduces the number of necessary operations by a factor three. Second, we introduce a variation of the center/surround class of local tone mapping algorithms, which are known to increase the local contrast of images but tend to create artifacts. Our method gives a good improvement in contrast while avoiding halos and maintaining good global appearance. Like traditional center/surround algorithms, our method uses a weighted average of surrounding pixel values. Instead of using it directly, the weighted average result serves as a variable in the Naka-Rushton equation, which models the photoreceptor non-linearity. Our algorithm provides pleasing results on various images with different scene content, key, and dynamic range.

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Tone mapping is an essential step for the reproduction of "nice looking" images. It provides the mapping between the luminances of the original scene to the output device's display values. When the dynamic range of the captured scene is smaller or larger than that of the display device, tone mapping expands or compresses the luminance ratios. We address the problem of tone mapping high dynamic range (HDR) images to standard displays (CRT, LCD) and to HDR displays. With standard displays, the dynamic range of the captured HDR scene must be compressed significantly, which can induce a loss of contrast resulting in a loss of detail visibility. Local tone mapping operators can be used in addition to the global compression to increase the local contrast and thus improve detail visibility, but this tends to create artifacts. We developed a local tone mapping method that solves the problems generally encountered by local tone mapping algorithms. Namely, it does not create halo artifacts, nor graying-out of low contrast areas, and provides good color rendition. We then investigated specifically the rendition of color and confirmed that local tone mapping algorithms must be applied to the luminance channel only. We showed that the correlation between luminance and chrominance plays a role in the appearance of the final image but a perfect decorrelation is not necessary. Recently developed HDR monitors enable the display of HDR images with hardly any compression of their dynamic range. The arrival of these displays on the market create the need for new tone mapping algorithms. In particular, legacy images that were mapped to SDR displays must be re-rendered to HDR displays, taking best advantage of the increase in dynamic range. This operation can be seen as the reverse of the tone mapping to SDR. We propose a piecewise linear tone scale function that enhances the brightness of specular highlights so that the sensation of naturalness is improved. Our tone scale algorithm is based on the segmentation of the image into its diffuse and specular components as well as on the range of display luminance that is allocated to the specular component and the diffuse component, respectively. We performed a psychovisual experiment to validate the benefit of our tone scale. The results showed that, with HDR displays, allocating more luminance range to the specular component than what was allocated in the image rendered to SDR displays provides more natural looking images.

The trends in the design of image sensors are to build sensors with low noise, high sensitivity, high dynamic range, and small pixel size. How can we benefit from pixels with small size and high sensitivity? In this dissertation, we study a new image sensor that is reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. The response function of the image sensor is non-linear and similar to a logarithmic function, which makes the sensor suitable for high dynamic range imaging. We first formulate the oversampled binary sensing scheme as a parameter estimation problem based on quantized Poisson statistics. We show that, with a single-photon quantization threshold and large oversampling factors, the Cramér-Rao lower bound (CRLB) of the estimation variance approaches that of an ideal unquantized sensor, that is, as if there were no quantization in the sensor measurements. Furthermore, the CRLB is shown to be asymptotically achievable by the maximum likelihood estimator (MLE). By showing that the log-likelihood function is concave, we guarantee the global optimality of iterative algorithms in finding the MLE. We study the performance of the oversampled binary sensing scheme in presence of dark current noise. The noise model is an additive Bernoulli noise with a known parameter, and the noise only flips the binary output from "0" to "1". We show that the binary sensor is quite robust with respect to noise and its dynamic range is only slightly reduced. The binary sensor first benefits from the increasing of the oversampling factor and then suffers in term of dynamic range. We again use the MLE to estimate the light intensity. When the threshold is a single photon, we show that the log-likelihood function is still concave. Thus, the global optimality can be achieved. But for thresholds larger than "1", this property does not hold true. By proving that when the light intensity is piecewise-constant, the likelihood function is a strictly pseudoconcave function, we guarantee to find the optimal solution of the MLE using iterative algorithms for arbitrary thresholds. For the general linear light field model, the log-likelihood function is not even quasiconcave when thresholds are larger than "1". In this circumstance, we find an initial solution by approximating the light intensity field with a piecewise-constant model, and then we use Newton's method to refine the estimation using the exact model. We then examine one of the most important parameters in the binary sensor, i.e., the threshold used to generate binary values. We prove the intuitive result that large thresholds achieve better estimation performance for strong light intensities, while small thresholds work better for low light intensities. To make a binary sensor that works in a larger range of light intensities, we propose to design a threshold array containing multiple thresholds instead of a single threshold for the binary sensing. The criterion is to minimize the average CRLB which is a good approximation of the mean squared error (MSE). The performance analysis on the new binary sensor verifies the effectiveness of our design. Again, the MLE is used for reconstructing the light intensity field from the binary measurements. By showing that the log-likelihood function is concave for arbitrary threshold arrays, we ensure that the iterative algorithms can find the optimal solution of the MLE. Finally, we study the reconstruction problem for the binary image sensor under a generalized piecewise-constant light intensity field model, which is quite useful when parameters like oversampling factors are unknown. We directly estimate light exposure values, i.e., the number of photons hitting on each pixel. We assume that the light exposure values are piecewise-constant and we use the MLE for the reconstruction. This optimization problem is solved by iteratively working out two subproblems. The first one is to find the optimal light exposure value for each segment, given the optimal segmentation of the binary measurements. The second one is to find the optimal segmentation of the binary measurements given the optimal light exposure values for each segment. Several algorithms are provided for solving this optimization problem. Dynamic programming can obtain the optimal solution for 1-D signals, but the computation is quite heavy. To reduce the burden of computation, we propose a greedy algorithm and a method based on pruning of binary trees or quadtrees.