Temporal anti-aliasing
Encyclopedia
Temporal anti-aliasing seeks to reduce or remove the effects of temporal aliasing
. Temporal aliasing is caused by the sampling
rate (i.e. number of frames per second) of a scene being too low compared to the transformation speed of objects inside of the scene; this causes objects to appear to jump or appear at a location instead of giving the impression of smoothly moving towards them. To avoid aliasing artifacts altogether, the sampling rate of a scene must be at least twice as high as the fastest moving object. The shutter behavior of the sampling system (typically a camera) strongly influences aliasing, as the overall shape of the exposure over time determines the band-limiting of the system before sampling, an important factor in aliasing. A temporal anti-aliasing filter can be applied to a camera to achieve better band-limiting. A common example of temporal aliasing in film is the appearance of vehicle wheels travelling backwards, the so-called wagon-wheel effect
.
, animators can either add motion lines
or create an object trail to give the impression of movement. To solve the wagon-wheel effect without changing the sampling rate or wheel speed, animators could add a broken or discolored spoke to force viewer's visual system to make the correct connections between frames.
One approach used is to derive a high resolution (i.e. larger than the output image)
temporal intensity function from object attributes which can then be convolved
with
an averaging filter to compute the final anti-aliased image.
In this approach, there are two methods available for computing the temporal intensity function.
The first method being to compute the position of each object as a continuous function and then
using the function to determine which pixels are covered by this object in the scene. The second
method can use traditional rendering techniques to supersample the moving scene and determine a
discrete approximation of object position.
One algorithm proposed for computing the temporal intensity function is:
Note: The "temporal transformation function" in the above algorithm is simply the function mapping the change of a dynamic attribute (for example, the position of an object moving over the time of a frame).
In the cases where either object attributes (shape, color, position, etc) are
either not explicity defined or are too complex for efficient analysis,
interpolation between the sampled values may be used. To obtain results closest to the source data,
B-spline
s can be used to interpolate the attributes. In cases where speed is a major
concern, linear interpolation
may be a better choice.
Temporal anti-aliasing can be applied in image space for simple objects (such as a circle or disk) but more complex polygons could require some or all calculations for the above algorithm to be performed in object space.
In spatial anti-aliasing it is possible to determine the image intensity function by supersampling
.
Supersampling is also a valid approach to use in temporal anti-aliasing; the animation system can generate multiple (instead of just one) pixel intensity buffers for a single output frame.
The primary advantage of supersampling is that it will work with any image, independent of what objects are displayed or rendering system is used.
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...
. Temporal aliasing is caused by the sampling
Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....
rate (i.e. number of frames per second) of a scene being too low compared to the transformation speed of objects inside of the scene; this causes objects to appear to jump or appear at a location instead of giving the impression of smoothly moving towards them. To avoid aliasing artifacts altogether, the sampling rate of a scene must be at least twice as high as the fastest moving object. The shutter behavior of the sampling system (typically a camera) strongly influences aliasing, as the overall shape of the exposure over time determines the band-limiting of the system before sampling, an important factor in aliasing. A temporal anti-aliasing filter can be applied to a camera to achieve better band-limiting. A common example of temporal aliasing in film is the appearance of vehicle wheels travelling backwards, the so-called wagon-wheel effect
Wagon-wheel effect
The wagon-wheel effect is an optical illusion in which a spoked wheel appears to rotate differently from its true rotation. The wheel can appear to rotate more slowly than the true rotation, it can appear stationary, or it can appear to rotate in the opposite direction from the true rotation...
.
In cel animation
In cel animationTraditional animation
Traditional animation, is an animation technique where each frame is drawn by hand...
, animators can either add motion lines
Motion lines
In comics, motion lines is a term that refers to the abstract lines that appear behind a moving object or person to make them look like they're moving quickly....
or create an object trail to give the impression of movement. To solve the wagon-wheel effect without changing the sampling rate or wheel speed, animators could add a broken or discolored spoke to force viewer's visual system to make the correct connections between frames.
In computer generated imagery
To perform anti-aliasing in computer graphics, the anti-aliasing system requires a key piece of information: which objects cover specific pixels at any given time in the animation.One approach used is to derive a high resolution (i.e. larger than the output image)
temporal intensity function from object attributes which can then be convolved
Convolution
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation...
with
an averaging filter to compute the final anti-aliased image.
In this approach, there are two methods available for computing the temporal intensity function.
The first method being to compute the position of each object as a continuous function and then
using the function to determine which pixels are covered by this object in the scene. The second
method can use traditional rendering techniques to supersample the moving scene and determine a
discrete approximation of object position.
One algorithm proposed for computing the temporal intensity function is:
For each image frame:
For each object in the frame:
Calculate the temporal transformation function for each dynamic attribute
Determine the areas the object covers during the filtered interval
For each pixel:
Determine which objects are covering this pixel at some time in the sampled interval
Determine the subintervals of time during which each object projects onto this pixel
Perform hidden surface removal by removing subintervals of occuluded objects
Determine pixel intensity function based on the remaining subintervals and the object's temporal transformation function
Filter resulting pixel intensity function
Note: The "temporal transformation function" in the above algorithm is simply the function mapping the change of a dynamic attribute (for example, the position of an object moving over the time of a frame).
In the cases where either object attributes (shape, color, position, etc) are
either not explicity defined or are too complex for efficient analysis,
interpolation between the sampled values may be used. To obtain results closest to the source data,
B-spline
B-spline
In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky...
s can be used to interpolate the attributes. In cases where speed is a major
concern, linear interpolation
Linear interpolation
Linear interpolation is a method of curve fitting using linear polynomials. Lerp is an abbreviation for linear interpolation, which can also be used as a verb .-Linear interpolation between two known points:...
may be a better choice.
Temporal anti-aliasing can be applied in image space for simple objects (such as a circle or disk) but more complex polygons could require some or all calculations for the above algorithm to be performed in object space.
In spatial anti-aliasing it is possible to determine the image intensity function by supersampling
Supersampling
Supersampling is an antialiasing technique, the process of eliminating jagged and pixelated edges . It is a method of smoothing images rendered in computer games or other programs that generate imagery.-Overview:...
.
Supersampling is also a valid approach to use in temporal anti-aliasing; the animation system can generate multiple (instead of just one) pixel intensity buffers for a single output frame.
The primary advantage of supersampling is that it will work with any image, independent of what objects are displayed or rendering system is used.
See also
- Motion blurMotion blurMotion blur is the apparent streaking of rapidly moving objects in a still image or a sequence of images such as a movie or animation. It results when the image being recorded changes during the recording of a single frame, either due to rapid movement or long exposure.- Photography :When a camera...
- Anti-aliasingAnti-aliasingIn digital signal processing, spatial anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution...
- Exposure (photography)Exposure (photography)In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...
- Temporal posterization