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Moments

Moments. Ku-Yaw Chang canseco@mail.dyu.edu.tw Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University. Moments of Random Variables. If x is a discrete random variable the expected value of x, denoted by E(x), is defined by

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Moments

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  1. Moments Ku-Yaw Chang canseco@mail.dyu.edu.tw Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University

  2. Moments of Random Variables • If x is a discrete random variable • the expected value of x, denoted by E(x),is defined by Where x1, …, xn are all the possible outcomes of x and p(xi) is the probability that x=xi Moments

  3. Moments of Random Variables • The expected value E(x) • Denoted by  or x • Also called the mean of x • Also called the first moment of the distribution • k th moment is defined as Moments

  4. Variance • Second central moment • Also called the variance • Describe the spread of the values about its mean • A convenient measure of the spread of a distribution • x : standard deviation Moments

  5. Moments of Random Variables • kth central moment • Also called the kth moment about the mean Moments

  6. XY plane • Moment of order (p+q) • Central Moment of order (p+q) and Moments

  7. Moments • Moments not invariant under translation of the patter. • Central moments are invariant to translation of the pattern. • Ideally, moments should be invariant to • Translation • Rotation • Scale Moments

  8. Brightness • Average gray level of an image • M*N image Moments

  9. Contrast • Amount of variation of its gray levels • Also known as the standard deviation Moments

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