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Imatest Documentation Sharpening Why standardized sharpening is needed for comparing cameras Introduction to sharpening Sharpening is an important part of digital image processing. It restores some of the sharpness lost in the lens and image sensor. Virtually every digitized image needs to be sharpened at some point in its workflow— in the camera, the RAW conversion software, and/or the image editor. Almost every digital camera sharpens images to some degree. Some models sharpen images much more than others— often more than appropriate for large prints. This makes it difficult to compare cameras and determine their intrinsic sharpness. Imatest has developed an approach to solving the problem— standardized sharpening. Before we proceed, we need to describe the elementary sharpening process. Sharpening on a line and edge A simple sharpening algorithm subtracts a fraction of two neighboring pixels from each pixel, as illustrated on the right. The thin black curve is the input to the sharpening function: it is the camera's response to a point or sharp line (called the line or point spread function). The two thin dashed blue curves are replicas of the input multiplied by -ksharp/2 and shifted by distances of ±2 pixels (typical of the sharpening applied to compact digital cameras). This distance is called the sharpening radius. The thin red curve the impulse response after sharpening— the sum of the black curve and the two blue curves. The thick black and red curves (shown above the thin curves) are the corresponding edge responses, unsharpened and sharpened. Sharpening increases image contrast at boundaries by reducing the rise distance. It can cause an edge overshoot. (A small overshoot is illustrated in the upper red curve.) Small overshoots enhance the perception of sharpness, but large overshoots cause "halos" near boundaries that can become glaringly obvious at high magnifications, detracting from image quality. Sharpening also boosts MTF50 and MTF50P (the frequencies where MTF is 50% of its low frequency and peak values, respectively), which are indicators of perceived sharpness. But sharpening also boosts noise, which is not so good. 26 of 451
Imatest Documentation The formula for the simple sharpening algorithm is, Lsharp(x) = [ L(x) - (ksharp /2) * (L(x-V) + L(x+V)) ] / (1- ksharp ) L(x) is the input pixel level and Lsharp(x) is the sharpened pixel level. ksharp is the sharpening constant (related to the slider setting scanning or editing program). V is the shift used for sharpening. V = R/dscan where R is the sharpening radius (the number of pixels between original image and shifted replicas) in pixels. dscan is the scan rate in pixels per distance. 1/dscan is the spacing between pixels. The sharpening algorithm has its own MTF (the Fourier transform of Lsharp(x) / L(x)). MTFsharp( f ) = (1- ksharp cos(2π f V ))/(1- ksharp ) This equation boosts response at high spatial frequencies with a maximum where cos(2π f V ) = cos(π) = -1, or f = 1/(2V ) = dscan/(2R). This is equal to the Nyquist frequency, fN = dscan/2, for R = 1 and lower for R > 1. Actual sharpening is a two dimensional operation. Standardized sharpening The degree of sharpening performed by digital cameras varies greatly. Some cameras and many RAW converters allow you to change the amount of sharpening from the default value. If an image is undersharpened, the photographer will need to apply additional sharpening during the image editing process for best results. Many compact digital cameras oversharpen images, resulting in severe peaks or "halos" near boundaries. This makes small prints (4x6 or 5x7 inches) look good straight out of the camera, but it doesn't truly enhance image quality: halos can get ugly in big enlargements and noise can become objectionable. Sharpening increases the 50% MTF frequency (MTF50). A camera with extreme oversharpening may have an impressive MTF50 but poor image quality. A camera with little sharpening will have an MTF50 that doesn't indicate its potential. For these reasons, comparisons between cameras based on simple MTF50 measurements have little meaning. Raw MTF50 is a poor measure of a camera's intrinsic sharpness, even though it correlates strongly with perceived image sharpness. MTF50P, the frequency where MTF drops to half its peak value, is equal to MTF for weak to moderate sharpening but lower for strong sharpening. Hence it is a somewhat better indicator of perceived sharpness and image quality. Imatest displays MTF50P when standardized sharpening is not displayed (is unchecked in the input dialog box). It is also available as a secondary readout. To obtain a good measure of a camera's sharpness— to compare different cameras on a fair basis, the differences in sharpening must be removed from the analysis. The best way to accomplish this is to set the sharpening of all cameras to a standard amount. This means sharpening undersharpened images and de-sharpening (blurring) oversharpened images. The algorithm for standardized sharpening takes advantage of the observation that most compact digital cameras sharpen with a radius R of about 2 pixels (though R can be as low as 1 for DSLRs). This has been the case for several cameras I've analyzed using data from dpreview.com and imaging-resource.com. The algorithm for standardized sharpening is as follows. 1. 2. Apply sharpening (or de-sharpening) with a default radius of 2 to make the MTF at feql = 0.3 times the Nyquist frequency (feql = 0.3 fN = 0.15 dscan; a relatively low spatial frequency) equal to 1 (100%), which the MTF at very low spatial frequencies. MTF at higher spatial depends on lens and imager quality. The sharpening radius is adjustable in Imatest; 2 is the default. Linearize the phase of the pulse by removing the imaginary part of the MTF. This results in an antisymmetrical pulse with a small overshoot (halo) near edges— typical of what you would get with carefully-done manual sharpening. If the edge is seriously blurred (MTF50 < 0.2 fN ), so that there is very little energy at feql = 0.3 fN , the sharpening radius is increased and the equalization frequency is decreased to feql = 0.6 MTF50. The sharpening radius is not increased if Fixed sharpening radius in the Settings menu of the Imatest main window has been checked. The formula for standardized sharpening with radius R is, MTFstandard( f ) = MTF( f ) (1- ksharp cos(2πR f/dscan)) / (1- ksharp ) where sharpening constant ksharp is set so MTFstandard( feql ) = MTF(0) = 1. fN = dscan/2 is the Nyquist frequency; feql = 0.3 fN ; feql = 0.6 MTF50 for seriously blurred edges where MTF50 < 0.2 fN . 27 of 451
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