Tag Archives: gradient

Deconvolution, Sharpening, unsharp mask, USM

The Richardson-Lucy Algorithm

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Deconvolution by the Richardson-Lucy algorithm is achieved by minimizing the convex loss function derived in the last article

(1)   \begin{equation*} J(O) = \sum \bigg (O**PSF - I\cdot ln(O**PSF) \bigg) \end{equation*}

with

  • J, the scalar quantity to minimize, function of ideal image O(x,y)
  • I(x,y), linear captured image intensity laid out in M rows and N columns, corrupted by Poisson noise and blurring by the PSF
  • PSF(x,y), the known two-dimensional Point Spread Function that should be deconvolved out of I
  • O(x,y), the output image resulting from deconvolution, ideally without shot noise and blurring introduced by the PSF
  • **   two-dimensional convolution
  • \cdot   element-wise product
  • ln, element-wise natural logarithm

In what follows indices x and y, from zero to M-1 and N-1 respectively, are dropped for readability.  Articles about algorithms are by definition dry so continue at your own peril.

So, given captured raw image I blurred by known function PSF, how do we find the minimum value of J yielding the deconvolved image O that we are after?

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Banding, Information Science, IQ, Perceptual, Posterization, Quantization

Smooth Gradients and the Weber-Fechner Fraction

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Whether the human visual system perceives a displayed slow changing gradient of tones, such as a vast expanse of sky, as smooth or posterized depends mainly on two well known variables: the Weber-Fechner Fraction of the ‘steps’ in the reflected/produced light intensity (the subject of this article); and spatial dithering of the light intensity as a result of noise (the subject of a future one).

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Information Science, IQ, Quantization, Sensors

How Many Bits to Fully Encode My Image

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My camera sports a 14 stop Engineering Dynamic Range.  What bit depth do I need to safely fully encode all of the captured tones from the scene with a linear sensor?  As we will see the answer is not 14 bits because that’s the eDR, but it’s not too far from that either – for other reasons, as information science will show us in this article.

When photographers talk about grayscale ‘tones’ they typically refer to the number of distinct gray levels present in a displayed image.  They don’t want to see distinct levels in a natural slow changing gradient like a dark sky: if it’s smooth they want to perceive it as smooth when looking at their photograph.  So they want to make sure that all possible tonal  information from the scene has been captured and stored in the raw data by their imaging system.

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