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Contrast sensitivity is typically expressed as the reciprocal of the threshold contrast for detection of a given pattern (i.e., 1 ÷ contrast threshold). [16] Using the results of a contrast sensitivity exam, a contrast sensitivity curve can be plotted, with spatial frequency on the horizontal, and contrast threshold on the vertical axis.
The moment-independent sensitivity measures of , here denoted by , can be defined through an equation similar to variance-based indices replacing the conditional expectation with a distance, as = [(, |)], where (,) is a statistical distance [metric or divergence] between probability measures, and | are the marginal and conditional probability ...
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
The underlying color matching functions can be thought of as the spectral sensitivity curves of three linear light detectors yielding the CIE tristimulus values X, Y and Z. Collectively, these three functions describe the CIE standard observer. [ 9 ]
In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations.
The relative contrast is given by the absolute value of the optical transfer function, a function commonly referred to as the modulation transfer function (MTF). Its values indicate how much of the object's contrast is captured in the image as a function of spatial frequency.
The Mandelbrot set, one of the most famous examples of mathematical visualization. Mathematical phenomena can be understood and explored via visualization. Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).