review_of_probability - Digital Image Processing, 3rd ed.

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Unformatted text preview: Digital Image Processing, 3rd ed. www.ImageProcessingPlace.com 19922008 R. C. Gonzalez & R. E. Woods Gonzalez & Woods Review of Probability Objective To provide background material in support of topics in Digital Image Processing that are based on probability and random variables. Review Probability & Random Variables Digital Image Processing, 3rd ed. www.ImageProcessingPlace.com 19922008 R. C. Gonzalez & R. E. Woods Gonzalez & Woods Review of Probability Sets and Set Operations Probability events are modeled as sets, so it is customary to begin a study of probability by defining sets and some simple operations among sets. A set is a collection of objects, with each object in a set often referred to as an element or member of the set. Familiar examples include the set of all image processing books in the world, the set of prime numbers, and the set of planets circling the sun. Typically, sets are represented by uppercase letters, such as A , B , and C , and members of sets by lowercase letters, such as a , b , and c . Digital Image Processing, 3rd ed. www.ImageProcessingPlace.com 19922008 R. C. Gonzalez & R. E. Woods Gonzalez & Woods Review of Probability Sets and Set Operations (Cont) We denote the fact that an element a belongs to set A by If a is not an element of A , then we write A set can be specified by listing all of its elements, or by listing properties common to all elements. For example, suppose that I is the set of all integers. A set B consisting the first five nonzero integers is specified using the notation Digital Image Processing, 3rd ed. www.ImageProcessingPlace.com 19922008 R. C. Gonzalez & R. E. Woods Gonzalez & Woods Review of Probability Sets and Set Operations (Cont) The set of all integers less than 10 is specified using the notation which we read as " C is the set of integers such that each members of the set is less than 10." The "such that" condition is denoted by the symbol | . As shown in the previous two equations, the elements of the set are enclosed by curly brackets. The set with no elements is called the empty or null set , denoted in this review by the symbol . Digital Image Processing, 3rd ed. www.ImageProcessingPlace.com 19922008 R. C. Gonzalez & R. E. Woods Gonzalez & Woods Review of Probability Sets and Set Operations (Cont) Two sets A and B are said to be equal if and only if they contain the same elements. Set equality is denoted by If every element of B is also an element of A , we say that B is a subset of A : If the elements of two sets are not the same, we say that the sets are not equal , and denote this by Digital Image Processing, 3rd ed....
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This note was uploaded on 01/27/2010 for the course ECE Data Netwo taught by Professor Dr.fathi during the Spring '10 term at Shahid Beheshti University.

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review_of_probability - Digital Image Processing, 3rd ed.

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