Difference between revisions of "Procedural Image"
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{{Image Description Ready | {{Image Description Ready | ||
|ImageName=Procedural Image | |ImageName=Procedural Image | ||
− | |Image= | + | |Image=Vase2.jpg |
|ImageIntro=A procedural image is an image generated by a series of mathematical functions | |ImageIntro=A procedural image is an image generated by a series of mathematical functions | ||
|ImageDescElem=Procedural images can be created by combining a wide variety of mathematical functions into a single expression. | |ImageDescElem=Procedural images can be created by combining a wide variety of mathematical functions into a single expression. | ||
|ImageDesc=Consider a simple example of creating a checkerboard texture for a binary image. Let <math>I(x,y)</math> be our output image. To create a checkerboard image let's defined our image as | |ImageDesc=Consider a simple example of creating a checkerboard texture for a binary image. Let <math>I(x,y)</math> be our output image. To create a checkerboard image let's defined our image as | ||
− | <math>I_{1}(x,y) \equiv \left( \frac{x}{w} \pmod{2} + \frac{y}{h} \pmod{2} \right) \pmod{2} \equiv \frac{x}{w} + \frac{y}{h} \pmod{2}</math> where w is the width of the checker and h is it's height | + | <math>I_{1}(x,y) \equiv \left( \frac{x}{w} \pmod{2} + \frac{y}{h} \pmod{2} \right) \pmod{2} \equiv \frac{x}{w} + \frac{y}{h} \pmod{2}</math> where w is the width of the checker and h is it's height. |
− | Let <math>I_{2}(x,y) = ( 1 - I_{1}(x,y) ) c_{0} + I_{1}(x,y) c_{1} </math> where <math>c_{1}</math> is the color of a checker and <math>c_{0}</math> is the other color. | + | This function simply returns 1 when on a checker and 0 when not on a checker. Let's extend our example to three channel RGB images. |
+ | |||
+ | Let <math>I_{2}(x,y) = ( 1 - I_{1}(x,y) ) c_{0} + I_{1}(x,y) c_{1} </math> | ||
+ | where <math>c_{1}</math> is a dimension 3 vector representing the color of a checker and <math>c_{0}</math> is the other color. | ||
+ | |||
+ | Imagine that we want to add a bit of monochrome noise to our checkerboard image. | ||
+ | |||
+ | <math>I_{3}(x,y) = I_{2}(x,y) + r(x,y) \left[ \begin{array}{c} 1 \\ 1 \\ 1 \end{array} \right]</math> | ||
+ | where r(x,y) is a random number generator | ||
+ | |||
+ | Additionally we can add two images together: | ||
+ | <math>I_{4}(x,y) = \frac{1}{2} I_{2}(x,y) + \frac{1}{2} I_{3}(x,y)</math> | ||
|Field=Computer Graphics | |Field=Computer Graphics | ||
|InProgress=No | |InProgress=No | ||
}} | }} |
Revision as of 13:06, 26 August 2009
Procedural Image |
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Procedural Image
- A procedural image is an image generated by a series of mathematical functions
Basic Description
Procedural images can be created by combining a wide variety of mathematical functions into a single expression.
A More Mathematical Explanation
Consider a simple example of creating a checkerboard texture for a binary image. Let '"`UNIQ--math-0 [...]
Consider a simple example of creating a checkerboard texture for a binary image. Let be our output image. To create a checkerboard image let's defined our image as
where w is the width of the checker and h is it's height.
This function simply returns 1 when on a checker and 0 when not on a checker. Let's extend our example to three channel RGB images.
Let where is a dimension 3 vector representing the color of a checker and is the other color.
Imagine that we want to add a bit of monochrome noise to our checkerboard image.
where r(x,y) is a random number generator
Additionally we can add two images together:
Teaching Materials
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Leave a message on the discussion page by clicking the 'discussion' tab at the top of this image page.
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