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Publication# The Gigavision Camera

Abstract

We propose a new image device called gigavision camera. The main differences between a conventional and a gigavision camera are that the pixels of the gigavision camera are binary and orders of magnitude smaller. A gigavision camera can be built using standard memory chip technology, where each memory bit is designed to be light sensitive. A conventional gray level image can be obtained from the binary gigavision image by low-pass filtering and sampling. The main advantage of the gigavision camera is that its response is non-linear and similar to a logarithmic function, which makes it suitable for acquiring high dynamic range scenes. The larger the number of binary pixels considered, the higher the dynamic range of the gigavision camera will be. In addition, the binary sensor of the gigavision camera can be combined with a lens array in order to realize an extremely thin camera. Due to the small size of the pixels, this design does not require deconvolution techniques typical of similar systems based on conventional sensors.

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Pixel

In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest addressable element in a dot matrix display device. In m

High dynamic range

High dynamic range (HDR) is a dynamic range higher than usual, synonyms are wide dynamic range, extended dynamic range, expanded dynamic range.
The term is often used in discussing the dynamic range

Logarithm

In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which

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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.

Edoardo Charbon, Yue Lu, Luciano Sbaiz, Sabine Süsstrunk, Martin Vetterli, Feng Yang

We study a new image device called gigavision camera or the gigapixel digital film camera. The main differences between a conventional and a gigavision camera are that the pixels of the latter are binary and orders of magnitude smaller. A gigavision camera can be built using standard memory chip technology, where each memory bit is designed to be light sensitive. A conventional gray level image can be obtained from the binary gigavision image by low-pass filtering and sampling. The main advantage of the gigavision camera is that its response is non-linear and similar to a logarithmic function, which makes it suitable for acquiring high dynamic range scenes. The larger the number of binary pixels considered, the higher the dynamic range of the gigavision camera will be.

2010Edoardo Charbon, Luciano Sbaiz, Sabine Süsstrunk, Martin Vetterli, Feng Yang

Recently, we have proposed a new image device called gigavision camera whose most important characteristic is that pixels have binary response. The response function of a gigavision sensor is non-linear and similar to a logarithmic function, which makes the camera suitable for high dynamic range imaging. One important parameter in the gigavision camera is the threshold for generating binary pixels. Threshold T relates to the number of photo-electrons necessary for the pixel output to switch from "0" to "1". In this paper, a theoretical analysis of the threshold influence in the gigavision camera is given. If the threshold in the gigavision sensor is large, there will be a "dead zone" in the response function of a gigavision sensor. A method of adding artificial light is proposed to solve the "dead zone" problem. Through theoretical analysis and experimental results based on synthesized images, we show that for high light intensity, the gigavision camera with a large threshold and added light works better than one with unity threshold. Experimental results with a prototype camera based on a single photon avalanche diodes (SPAD) camera are also presented.

2010