A Technique for Image Data Hiding and Reconstruction without by Chae Manjunath

By Chae Manjunath

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CK are the coefficients of the expansion. 1) uses c to stand for the vector of K coefficients and φ to denote a vector of length K containing the basis functions. We often want to consider a sample of N functions, xi (t) = ∑Kk=1 cik φk (t), i = 1, . . 2) where x(t) is a vector of length N containing the functions xi (t), and the coefficient matrix C has N rows K columns. Two brief asides on notation are in order here. We often need to distinguish between referring to a function in a general sense and referring to its value at a specific argument value t.

We refer to these three labels as the generic labels for the functional data object. In R, we supply labels in a list object of length three. 1 Adding Coefficients to Bases to Define Functions 47 In addition to generic labels for each dimension of the data, we may also want, for the range and/or for the replication dimension, to supply sets of labels, each label applying to a specific dimension or replicate. For example, for the gait data, we may want a label such as “Angle” to be common or generic to the two observed angles, but in addition require two labels such as “Knee” and “Hip” to distinguish which angle is being plotted.

C. Specify the number of basis functions. The more you specify, the more variability you can achieve in the function. 10, . . 95 and 1 over [0,1]. d. Plot the basis to see how it looks using the plot command. e. Now evaluate and plot a few derivatives of the basis functions to see how their smoothness diminishes with each successive order of derivative. Chapter 4 How to Build Functional Data Objects We saw in the last chapter that functions are built up from basis systems φ1 (t), . . , φK (t) by defining the linear combination K x(t) = ∑ ck φk (t) = c φ (t).

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