CS 248: Midterm Solutions

Question 3 [This was actually worth 21 points]

3A [4 points]

Intensity refers to the amount of light "energy." A linear intensity space means that amount of energy is linearly related to the intensity value.

Brightness refers to the perception of light. If the perceived brightness of a light is twice that of another, then its brightness value is twice that of the other.

Brightness is related to intensity by the power law: B = I^(1/3). Just stating this without describing what intensity, brightness, and linearity means was worth only 3 points. No points were taken off for not having this formula in your answer.

3B [4 points]

For 2 points each, here are some of the advantages of a linear perceptual brightness space::

• Equal steps in brightness are uniformly space, leading to a better distribution of values.
• If this space is quantized, better compression results because the perceptual error is minimizied.
• Brightness values are less sensitive to noise, again because noise causes less perceptual error.
• If you are displaying an image on a CRT, then there is no need to do gamma correction. This can be interpreted as an advantage (no hardware for gamma correction required), although just barely.

I also accepted answers of the form that this space is better if you want to encode images in perceptual space. I did not accept the answer that this space is more intuitive for 3B or 3C because both spaces are intuitive, but in different ways. I also didn't accept as a reason any arithmetic operation (such as the answer addition or multiplication) because arithmetic may easily be done in either space.

3C [4 points]

For two points each, here are some operations that need to be done in a linear intensity space:

• Dithering and halftoning.
• Compositing and blending.
• Filtering including its use in reconstruction, interpolation and antialiasing.
• Lighting and shading calculations (although we haven't talked about them yet).

Gamma correction is not an operation in linear intensity space; it produces a linear intensity space.

3D [5 points]

Color matching is used to compare a mixture of three primary colors, e.g. a red, green and blue lasers, to a given color. The intensities of the primaries are adjusted until the two colors are perceived to be the same; that is, match. The intensities of the lasers are the color coordinates of the given color. I gave 3 points for this part of the answer.

To say that color matching is linear means that if I determine the color coordinates of two colors C1 and C2, then the color coordinates of the combined color C1 + C2 equal (R1+R2, G1+G2, B1+B2). This was worth 2 points.

3E [4 points]

Here are the answers:

• RGB - Y (linear)
• HSV - N (non-linear)
• CMY - Y (linear)
• CMYK - N (non-linear)

RGB is the color matching space, and thus it is linear. HSV is a non-linear transformation from RGB (since it involves if statements and various other non-linear functions of R, G and B), thus colors in this space are not linear. Whether CMY and CMYK are linear is tricker and requires more thought. CMY is actually 1-(RGB) which is a linear transformation from RGB, thus that space is linear. CMYK involves multiplying K times C, M and Y; this double multiply makes the space non-linear.