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Imatest Documentation Canon EOS-10D Canon EOS-1Ds Kodak DCS-14n 2048x3072 (6.3) 1325 1341 221 100 4.01 2.30 0.66 2704x4064 (11) 1447 1880 184 100 7.18 4.01 1.02 Little built-in sharpening. 3000x4500 (13.5) 2102 2207 272 100? 10.0 5.92 1.90 Nikon D100 2000x3008 (6) 1224 1264 148 200? 3.43 1.85 0.40 Nikon D70 2000x3008 (6) 1749 1692 139 ? 4.53 2.42 0.50 Sigma SD10 1512x2268 (3.4) 1363 1381 288 100 3.20 1.9 0.63 No anti-aliasing filter. Strong noise reduction. Strikingly different response from D100. Less aggressive anti-aliasing. Foveon sensor. No anti-aliasing filter. Very high MTF50C and response at Nyquist. Canon G5 1944x2592 (5) 1451 1361 94 ? 2.89 1.43 0.20 Strongly oversharpened. Sony DSC-F828 2448x3264 (8) 1688 1618 134 64 4.67 2.47 0.49 Performance measurements were taken from the edge located about 16% above the center of the image. Compact 8 MP digital with excellent lens. S/N and C are expected to degrade at high ISO. Here are some additional examples, illustrating unusual noise spectra. The Kodak DCS-14n shows a steep rolloff indicative of extreme noise reduction. This is reflected in the unusually high Shannon capacity at 1% contrast. The Olympus E-1 has an unusual noise spectrum, with a spike at Nyquist. I don't know what to make of it. Summary Here is a summary of the key points. Shannon capacity C has long been used as a measure of the goodness of electronic communication channels. Imatest calculates the Shannon capacity C for the Y (luminance) channel of digital images. The calculation of C is an approximation: it is not absolutely precise, but it is sufficient for comparing the performance of digital cameras (or scanned film images). We hypothesize that C is closely related to overall image quality; that it provides a fair basis for comparing cameras with different pixel counts, sharpening, and noise levels. 62 of 451
Imatest Documentation We display values of C that correspond to three signal levels, 100%, 10% and 1%, representing moderately contrasty images, low contrast images, and smooth areas. Shannon capacity has not been used to characterize photographic images because it was difficult to calculate and interpret. But now it can be calculated easily, its relationship to photographic image quality is open for study. We stress that C is still an expreimental metric for image quality. Much work needs to be done to demonstrate its validity. Noise reduction and sharpening can distort its measurement. Imatest results for C should therefore be regarded with a degree of skepticism; they should not be accepted uncritically as "the truth." Further considerations and calculations Since Imatest displays S and N as voltage rather than power or energy (both of which are proportional to the square of voltage), the equation used to evaluate Shannon capacity per pixel is CP = W log2((S/N) 2 +1), where W is measured in cycles per pixel. The total capacity is C = CP* number of pixels. Imatest calculates Shannon capacity C for the luminance channel (Y = 0.3*R + 0.6*G + 0.1*B), which represents the eye's sensitivity to the three primary colors and best represents how the eye detects information in typical scenes. C could be calculated separately for each of the channels (R, G, and B), but this would cause unnecessary confusion. The channel must be linearized before C is calculated, i.e., an appropriate gamma correction (signal = pixel level gamma , where gamma ~= 2) must be applied to obtain correct values of S and N. The value of gamma (close to 2) is determined from runs of Imatest Q-13 and Colorcheck. Digital cameras apply varying degrees of noise reduction, which may make an image look "prettier," but removes low contrast signals (which represent real information) at high spatial frequencies. Noise reduction makes the Shannon capacity appear better than it really is, but it results in a loss of information— especially in low contrast textures— resulting in images where textures look "plasticy" or "waxy." (Some people like this effect enough to take it beyond the virtual realm— to plastic (cosmetic) surgery.) The exact amount of noise reduction cannot be determined with a simple slanted-edge target; Imatest is developing more sophisticated targets for this purpose. Noise reduction results in an unusually rapid dropoff the noise spectrum— which is evident when several cameras are compared. Its effects can be examined with RAW conversion software. For example, Capture One has allow larges DSLR noise reduction to be set to one of four levels in its Preferences— Develop settings. Because of a number of factors (noise reduction, the use of MTF50C to approximate W, the arbitrary nature of S, etc.) the Shannon capacity calculated by Imatest is an approximation. But it can be useful for comparing different cameras. Calculating Shannon capacity The measurement of Shannon capacity is complicated by two factors. 1. 2. The voltage in the image sensor is proportional to the energy (the number of photons) striking it. Since Shannon's equations apply to electrical signals, I've stuck to that domain. The pixel level of standard digital image files is proportional to the sensor voltage raised to approximately the 1/2 power. This is the gamma encoding, Green is for geeks. Do you get excited by a good equation? Were you passionate about your college math classes? Then you're probably a math geek— a member of a maligned and misunderstood but highly elite fellowship. The text in green is for you. If you're normal or mathematically challenged, you may skip these sections. You'll never know what you missed. designed to produce a pleasing image when the luminance of an output device is proportional to the pixel level raised to a power of 2.2 (1.8 for Macintosh). This exponent is called the gamma of the device or the image file designed to work with the device. Gamma = 2.2 for the widely-used sRBG and Adobe RGB (1998) color spaces. Since I need to linearize the file (by raising the pixel levels to a power of 2) to obtain a correct MTF calculation, I use the linearized values for calculating Shannon capacity, C. The correct, detailed equation for Shannon capacity was presented in Shannon's second paper in information theory, "Communication in the Presence of Noise," Proc. IRE, vol. 37, pp. 10-21, Jan. 1949. W is maximum bandwidth, P(f) is the signal power spectrum (the square of the MTF) andN( f ) is the noise power spectrum. There are a number of difficulties in evaluating this integral. Because P and N are calculated by different means, they are scaled differently. P( f ) is derived from the Fourier transform of the derivative of the edge signal, while N( f ) is derived from the Fourier transform of the signal itself. And noise reduction removes information while reducing N( f ) at high spatial 63 of 451
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