Computer Graphics (CS 4300) 2010S: Lecture 5

Today

• update to HW2 and HW3: may work in pairs
• review midpoint algorithm
• introduce sampling and antialiasing
• color perception, color spaces

Sampling and Antialiasing

• “a pixel is not a little square”
  • rather, it is a sampling point, typically at the center of the “little square”
• taking this perspective, revisit line drawing
• assume desired line is a 1-pixel wide rectangle (there we go assuming pixels are little squares) centered on the line
• sampling perspective: check if the sampling point corresponding to each screen pixel is inside the rectangle
  • if so, the line is “on” the pixel
    
  • resulting set of pixels is the same as would be computed by the midpoint algorithm
  • could literally implement this sampling, but naieve implementation would require checking all pixels on screen for every line
  • midpoint algorithm is much faster
• “jaggies” of a line rendered by turning pixels fully on or off are an example of aliasing
• aliasing is a general property of any kind of sampling, where a continuous object (in this case the rectangle representing the line) is represented by a finite set of discrete samples
  • because some information is generally lost by sampling, the samples may not exactly reconstruct the original continuous object
  • in some cases, the same set of sample values can result from two very different original continuous objects (this is the origin of the word aliasing)
• we can make line rasterization look better by using gray levels rather than just on/off: antialiasing
• one way is supersampling
  • divide each original pixel into four subpixels (this is 2x supersampling, can divide further for additional quality)
  • now re-sample the same rectangle representing the line with the finer grid of sample points
  • finally, average the four subpixels for each original pixel to arrive at a gray level of 0.0, 0.25, 0.5, 0.75, or 1.0
    
  • in practice, still need to find a fast way to compute an equivalent result

What is Color?

• from physics, we know that the wavelength of a photon (typically measured in nanometers, or billionths of a meter) determines its apparent color
• we cannot see all wavelengths, but only the visible spectrum from around 380 to 750 nm
• but where are the following colors: “brown”, “pink”, “white”, …?
• clearly, the color spectrum does not actually contain all colors; i.e. some colors are non-spectral
• generally, a large number of photons with different wavelengths are simultaneosly impinging on any given location of your retina
• the actual incident light is not of a single wavelength, but can be described by a spectral histogram
  
  • the histogram represents the relative quantity of photons of each wavelength
• the human eye cannot determine the exact histogram
  • in fact just representing a complete spectral histogram exactly would require an infinite amount of space because it’s a continous quantity
  • the biological solution is another form of sampling
  • three types of cone cells respond (with the equivalent of a single number each) to the degree to which the actual incident histogram is similar to response histograms with peaks near red, green, and blue
  • so the original continous histogram impinging on one location of your retina is reduced to three measurements
  • (actually, there is a fourth rod cell type, which is mainly active in low light conditions)
  • color blindness is typically caused by anomalies in the types of cone cells
  • other animals also have different cone cells
• because we have again converted a continuous object into a set of discrete samples, we have to consider aliasing
  • different incident histograms, called metamers, may be mapped to the same set of cone cell responses
  • how many distinct colors can be seen?
  • one way to think about it is to know that each cone cell type can distinguish between about 100 intensity levels of the associated response curve, and then to take a constructive approach
  • there are =1M ways to combine cone cell responses, so avg human can distinguish roughly that many colors
• the biology of human cone cells is the not only the reason we often use RGB to represent color; in fact, it defines color. Color is not an intrinsic property of light, but rather a result of the interaction between human cone cells and histograms of incident light.

Color Spaces

• we can make an abstract color space by assigning one color to each axis in a 3D Cartesian space
• the other vertices of the cube correspond to mixes of colors: “cyan”, “magenta”, “yellow”, “white”, and “black”
• sometimes RGB are considered “additive” colors because they form a basis for the color space relative to black
• CMY can similarly be considered “subtractive” colors because, effectively
  • cyan+red = white
  • magenta+green = white
  • yellow+blue = white
  • additive colors typically used when light is generated by an output device (e.g. CRT, LCD)
  • subtractive colors typically used when printing on white paper
• sometimes RGB and CMY are considered distinct color spaces
• another common and useful color space is HSV
  • hue: the basic color, or chromaticity
  • saturation: how “deep” the color is (vs “pastel”)
  • value: the brightness of the color
• HSV is again a 3 dimensional space, but it is typically considered to use cylindrical coordinates
  • this is mainly a construction to decompose the three dimensional color space in a way that is more useful to human designers
  • also often useful in machine vision algorithms, which simulate our theories of (aspects of) human vision
  • can visualize HSV space as a “morph” of RGB space
    • “stretch” the white and black vertices up and down
    • “line up” the remaining six vertices along a common horizontal plane
    • for HSV, put the white vertex back onto plane (a variation, HSL, keeps white and black symetrically above and below )
  • hue is the radial angle “around” the cylinder
  • saturation is the radial distance “out” from the center of the cylinder
  • lightness is the “height” from the bottom to the top of the cylinder
  • a common color picker uses the HSV model, with a rotating triangle inscribed inside a “hue circle”

Next Time

• images: compression, alpha blending, image scaling
• reading on website

this page subject to change  |  last updated Mon Apr 19 13:06:55 EDT 2010  |  course homepage