I think so, thatâs very helpful !, so easy to get yourself tied in knots, that you canât see the wood for the trees. BTW I am trying to fit this part of a curve before a power function is applied to the normalised values.
Thanks alan, thatâs very detailed I have been researching lift,gamma,gain.
Actually I now realise I want to apply a curve to the value from .8 to 1.2. and leave the values below .8 alone. (.8 and 1.2 are just illustrative, I would like to parametrise them)
Yes, my âpower methodâ applies a curve just to the highlights, leaving values below 0.8 (or whatever you want) untouched. It can also apply a different curve to shadows, leaving values above 0.1 (or whatever) untouched. Values between the limits are unchanged.
In Power curve for shadow, mid and highlights, I show how to get a single power curve that changes all values, giving required values at the top, bottom and somewhere between. This is pretty much the same as lift-gamma-gain.
My pages at im.snibgo.com use ImageMagick and Windows BAT scripts (yeah, I know, hawk spit), but I try to explain enough so the concepts can be applied to any platform.
I have been going through you scripts I converted the graph1d and graphline scripts to bash, that is very helpful to visualise things.
I am busy studying stepwise polynomialâs
I have two math questions that may save me a lot of timeâŚ
In the filmic tutorial the author says âGiven those points, how can we form a continuous curve between them? One option would be polynomials, but that does not work well. These changes can be pretty sharp in linear space and fitting to polynomials will sometimes have undesirable concavity changes. Instead, we are going to use power curves.â
Should I just ignore that comment, as it doesnât make all that much sense, I thought with polynomials could you can match any curve?
Am I correct in understanding that for polynomials all exponents must be positive?
In standard polynomials, yes, all exponents are positive integers. If x is the input and y is the output, a polynomial of degree 2 is:
y = ax^2 + bx + c
So three parameters (a, b, c) specify the polynomial. Beware that some people write this as:
y = a + bx + cx^2
If we have (n) known correspondences between x and y, it is true that a polynomial of degree (n-1) can be found that passes exactly through those given points. But what does the curve do between those points? Sadly, it often does stupid things, going madly beyond what a human would consider sensible or desirable.
For that reason, we often prefer a series of joined paramaterised cubic curves (or Bezier curves or B-splines, they are all variations of the same thing). Each curve starts and ends at two of the desired points but its shape is influenced by two other points. Each curve joins to the next curve at one point, and has the same slope and curvature.
Bezier curves passing through given points more closely follow what a human would draw. Gimp and other editors use them in the âcurve editorâ. (Though I donât like the Gimp curve editor because it can cause clipping.)
A power curve, in the form âŚ
y = a*x^p + b
⌠has parameters a, p and b, and these have fairly intuitive meanings (âgainâ, âgammaâ and âliftâ in some editors). They are easer to calculate than Beziers, and are better-behaved than polynomials.
Yes, okay, my statement should have said: Degree (n) means there are up to (n+1) terms, and thus (n+1) coefficients, but coefficients other than the top one can be zero.
I try not to get hung up on terminology (I donât actually care what âdegreeâ means), but I used the term so I should get it right.
I got a working simulation of negative/positive colour film camera working that is reasonably accurate/authententic. i.e. its not just negate. Using Kodak Porta 400 as a model.
You can make a colour negative of any jpeg picture.