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Information capacity: a measure of potential image quality of a digital camera Frédéric Cao 1, Frédéric Guichard, Hervé Hornung DxO Labs, 3 rue Nationale, 92100 Boulogne Billancourt, FRANCE ABSTRACT The aim of the paper is to define an objective measurement for evaluating the performance of a digital camera. The challenge is to mix different flaws involving geometry (as distortion or lateral chromatic aberrations), light (as luminance and color shading), or statistical phenomena (as noise). We introduce the concept of information capacity that accounts for all the main defects than can be observed in digital images, and that can be due either to the optics or to the sensor. The information capacity describes the potential of the camera to produce good images. In particular, digital processing can correct some flaws (like distortion). Our definition of information takes possible correction into account and the fact that processing can neither retrieve lost information nor create some. This paper extends some of our previous work where the information capacity was only defined for RAW sensors. The concept is extended for cameras with optical defects as distortion, lateral and longitudinal chromatic aberration or lens shading. Keywords: digital photography, image quality evaluation, optical aberration, information capacity, camera performance database 1. INTRODUCTION The evaluation of a digital camera is a key factor for customers, whether they are vendors or final customers. It relies on many different factors as the presence or not of some functionalities, ergonomic, price, or image quality. Each separate criterion is itself quite complex to evaluate, and depends on many different factors. The case of image quality is a good illustration of this topic. A digital camera is invariably composed of three subsystems: an optic, a sensor and digital processing. Optics all have their particular design, sensors have different size and pixel count, digital processing can be parameterized on the camera, or even be achieved by third party software. Every part of the system has qualities and defects. Devising methods and protocols to measure these individual performance is already a big issue. This is only halfway to the customer request, who basically wants to know what the best camera is. Therefore, a huge amount of information has to be synthesized in a few or even a single number. Standards organizations have been working on the topics for many years. Characterization of many parts of a camera has been described in ISO standards. More recently, the I3A Camera Phone Image Quality1 (CPIQ) has been working on the objective characterization of cameras and its relation to subjective image quality. In this paper, we will adopt a different point of view. A camera aims to capture light and its spatial distribution and reproduce it on a plane. A good camera should allow this capture with a good accuracy, that is to say with as many details as possible and unbiased. In other terms, it should capture a large amount of "good" information. A series of measurement results on about 80 cameras has been published on DxOMark.com2. Results are essentially related to sensor noise. On the other hand, resolution is not completely factored; there is only a normalization of noise measurement that reduces the resolution of sensors to a relatively low resolution in order to make comparisons. In this case, it turns out that noise is essentially dependent on sensor size. This paper aims to complete the analysis by properly 1 [email protected] Frédéric Cao, Frédéric Guichard and Hervé Hornung, "Information capacity: a measure of potential image quality of a digital camera", Proc. SPIE 7537, 75370F (2010); doi:10.1117/12.838903 Copyright 2010 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. introducing resolution. In this case, we cannot ignore the influence of lens either, with all the possible defects3. In this article, we propose the information capacity as an objective measurement that takes into account sensor noise, spectral responses and optical aberrations at the same time. On the other hand, the information capacity we propose deals with RAW images. One of the main reasons is that, for DSLR, raw converter is the user's choice, between many competitive solutions on the market. Also, raw converters evolve quite fast, at least faster than camera bodies and lenses, because they still benefit from the exponential growth of computing power. A raw converter cannot create information but only lose some or change the organization of information. Computing the RAW information capacity removes the bias of the raw converter, and also permits to anticipate the fact that some aberrations can be digitally corrected. To illustrate this point, consider the example of geometric distortion. A distorted image contains "bad" information in the sense that the spatial organization is not as expected on a perfect (pinhole) camera. However distortion correction methods have been used for a long time in computer vision, in particular 3D reconstruction. Some raw converters or other software integrate this kind of correction, and some camera manufacturers also embed such corrections on the camera chip. Therefore, we can consider that the geometrical effect of distortion can be cancelled out by digital processing. However, this correction is not priceless in terms of image: there is a local loss of resolution. This is well known for very wide-angle lenses, for which field of view is traded against distortion and resolution on the image border. The general point is that a correction algorithm can organize the information contained in the raw image differently, but cannot (or should not) create new information. Of course, distortion in an image damages the subjective quality. We consider that a correction algorithm can be designed so that the image quality attribute related to the defect can be optimal. Therefore, what we are interested in is the amount of information that has been lost due to the defect, and cannot be recovered from the image itself. The outline of the papers is as follows. In Sect. 2, we introduce the notion of local information capacity as the product of local resolution and local dynamic. We then review the main characteristics of a camera, in terms of sensor and optics aberrations and how they individually influence the local information capacity in Sect. 3 and 4. We present how to gather local contribution in Sect. 5, leading to a global definition of information capacity accounting for sensor and optics characteristics. In Sect. 6, we show some measurements and comparisons on real cameras before concluding. 2. INFORMATION CAPACITY 2.1 Definition We choose to represent the performance of a camera by measuring the amount of information it is able to capture. This amount of information has to be understood as in Shannon's work4, that is the size of the channel that is necessary to transmit the image. Image information is completely determined by resolution and dynamic. The first one is related to the details that a camera can spatially render and the second one to the level of contrast that the camera can capture. This contrast can be related to two different notions: the dynamic range which is the maximal contrast that the camera can measure without saturation, and the SNR that can be related to the smallest level of contrast that can be discriminated from noise. Resolution can be defined as a number of pixels, giving the number of elementary elements used to describe the spatial organization of the image. It is well known that even though the number of pixels of the sensor should be related to the resolution of the camera, this notion is actually more complex. Indeed, it should also account for loss due to the fact that the optical system cannot be perfect. Both the optics and the sensor introduce a certain amount of blur, which has to be integrated in the definition of resolution. Similarly, the bit depth of the sensor (which is the number of bits used to encode gray levels) is only a first rough estimate of the real photograph dynamic. For instance, noise whatever its sources) has to be taken into account. Dynamic is better measured in a logarithmic scale. This is both compliant with perception since the eye does not have a linear response to illumination and to information theory since the number of bits that are need to encode a value is proportional to the logarithm of this value. Moreover, photographers also measure light in Exposure Value (EV) which is a base 2 logarithm. Therefore a general definition of the information capacity of a camera is The main difficulty is to properly define resolution and dynamic, both as simply as possible, and as completely as possible, that is by taking all the properties of the camera into account. In previous works5,6,7, we were interested only in sensor performance. Therefore, resolution only integrated pixel blur (sensor MTF) and lens diffraction limit, and sensor noise through its color sensitivity. 2.2 Local resolution and local dynamic The main goal of this paper is to extend this model, by incorporating real lens characteristics. Most of optical aberrations are field dependent. Therefore, their influence on resolution and dynamic shall be described locally. Information capacity can also be expressed as a local quantity. The global information capacity of the camera is obtained by summing these local contributions. At each spatial position , we will define the local resolution and the local dynamic . Each aberration contributes as a loss to either resolution or dynamic.
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