What Can Be Known about the Radiometric Response from Images?
Brightness values of pixels in an image are related to image irradiance by a non-linear function, called the radiometric response function. Recovery of this function is important since many algorithms in computer vision and image processing use image irradiance. Several investigators have described methods for recovery of the radiometric response, without using charts, from multiple exposures of the same scene. All these recovery methods are based solely on the correspondence of gray-levels in one exposure to gray-levels in another exposure. This correspondence can be described by a function we call the brightness transfer function. We show that brightness transfer functions, and thus images themselves, do not uniquely determine the radiometric response function, nor the ratios of exposure between the images. We completely determine the ambiguity associated with the recovery of the response function and the exposure ratios. We show that all previous methods break these ambiguities only by making assumptions on the form of the response function. While iterative schemes which may not converge were used previously to find the exposure ratio, we show when it can be recovered directly from the brightness transfer function. We present a novel method to recover the brightness transfer function between images from only their brightness histograms. This allows us to determine the brightness transfer function between images of different scenes whenever the change in the distribution of scene radiances is small enough. We show an example of recovery of the response function from an image sequence with scene motion by constraining the form of the response function to break the ambiguities.
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