Optimal Exposure Detection Function for Digital and

2012 IEEE International Conference on Consumer Electronics (ICCE)

Optimal Exposure Detection Function for Digital and Smart-Phone Camera Applications S. Yousefi1, H. R. Rabiee2, P. Mianjy2, 1 University of Texas at Dallas 2 Sharif University of Technology

Abstract — Auto-Exposure detection is a key feature in digital cameras and smart-phones. The image information can be used to detect scene over and under exposure passively. This paper introduces an effective optimal exposure detection function based on joint probability density function of the pixels in the scene. Index Terms — Passive Auto-Exposure, Digital Cameras, Image Analysis, Probability Density Function.

I. INTRODUCTION Nowadays, most digital cameras and smart-phones possess a passive auto-exposure (AE) feature. Always accompanied by auto focus (AF), AE modes are divided to two main categories, shutter priority and aperture priority. The equation that relates the exposure value (EV), aperture f-number f and exposure duration t is as follows [1]: (

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The primary purpose of AE is to select a proper exposure value regardless of the scene lighting condition. One of the key features used in the literature for this purpose is the brightness of the scene. The brightness value (BV) and EV are related to each other by the relation provided below [1] ( ) where and denote the optimum and current exposure of the scene, respectively. Different AE functions have been reported in the literature [2-6]. Most of the methods presented in the literature are based on analysis of the brightness of the captures scene. The recently introduced method presented in [7] is based on analyzing the entropy of the scene to capture the optimal exposure. Here, we introduce a new brightness approach to detect the optimum exposure value based on joint probability density function (pdf) of the scene (image) pixels. This method is shown to be simple and computationally efficient that has a potential to be utilized in digital cameras and cell phones. The pdf of the image can be computed by a one pass over the pixels of the image and creating the joint histogram of two pixels. Even to save more computation, it is feasible to select a portion of the scene and applying the process just to that area. The rest of this paper is organized as follows. In section II, our introduced AE function and its properties are explained. The experiment and comparison results in terms of accuracy are then presented in section III. Finally, the conclusions are stated in Section IV.

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II. THE OPTIMAL EXPOSURE DETECTION FUNCTION Let denote the scene (image) of size . The pixels composing this scene are essentially random variables (RV). The joint pdf of these RVs has some useful properties that can be used to detect optimum exposure value of a scene. In the next section we show that the spread of this joint pdf changes with different lighting conditions. Let denote the joint pdf of a specific pixel in the scene and its immediate right (one of the immediate neighbors) neighbor pixel. Essentially, can be represented by a matrix, where indicates the number of gray levels in the scene. The spread of the values in this matrix also have some useful properties. For example, large values appear concentrated around its diagonal since images contain mostly uniform intensity areas. Figure 1 displays a sample scene and the joint pdf function of two immediate neighboring pixels in this scene. For better visibility, the matrix is shown as binary indicating value versus no-value. As can be seen from Fig. 1, most of the values are concentrated around the diagonal of the joint pdf matrix. The other property of joint pdf matrix is that values concentrated around the corners of this matrix mainly correspond to dark area and bright areas of the scene. Figure 2 shows a scene at three different lighting conditions (top under exposure, middle normal exposure and bottom over exposure). The joint histogram of a pixel and its right neighbor of these scenes are depicted with a color bar here for better visibility.

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Fig. 1. Sample scene and the joint pdf matrix of two immediate neighboring pixels of the scene.

Fig. 2. The same scene at different lighting conditions and the joint histogram matrix (joint pdf of two pixels) of the scene.

As can be seen from this figure, the values concentrated in top-left corner of the joint pdf matrix start moving towards bottom-right corner as the scene gets brighter. We define the variation in the area under function confined between two threshold values as an indication of different exposure values. Thus our AE function is defined as: ∑ where x and y indicate the row and column indices of the f matrix, and and correspond to the area the summation is computed. In Fig. 2, one can see what happens to the function when the scene undergo over and under exposure. The elements move towards top-left corner upon under exposure while they move towards bottom-right corner in case of over exposure.

Fig. 3. The AE value for three different sequences under different lighting conditions based on introduced AE function.

results for 3 different real scenes captures using the settings mentioned before. The red ellipse in plots indicate the exposure value taken using auto-mode (ground truth) of the camera that is used here as a comparison to what the camera with its own auto-exposure function selects and what our AE function achieves. As is visually clear, the new introduced AE function almost achieves the optimal exposure value as what the auto-exposure mode in the camera acheives. IV. CONCLUSION A new function for achieving passive auto exposure in digital still cameras and cell-phones was introduced. It was shown that this function performs pretty well in comparison with the existing algorithms in commercial cameras in automode and has the potential to be utilized in new devices.

III. IMPLEMENTATION RESULTS The introduced AE function was heavily examined by using simulated over and under exposure images as well as by using real image sequences captured by commercial digital cameras. Ten different scenes were captures using manual mode of a digital camera using different shutter speeds. As an example for one of the sequences we used ISO as 400, apperture fnumber f was set to 2.8 and exposure duration time t was set to 1/2000, 1/1600, 1/1250, 1/1000, 1/800, 1/640, 1/500, 1/400, 1/320, 1/250, 1/200, 1/160, 1/125, 1/100, 1/80, 1/60, 1/50, 1/40, 1/30, 1/25, 1/20, and 1/15 seconds. In other sequences, different f-number was used. For capturing the right exposure value as a ground truth for comparison purpose, the camera was set on auto-mode and a picture from the same scene was captured. Figure 3 shows the

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