why and how have defined a function in the form, and how connect p_j smoothly?

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MatLab

image-processing

Dear All

In the following section, why and how have defined a function in the form, and how connect p_j smoothly?
this is how Matlab programing?
In this section, we will provide a direct and practical way to do image compression by using two-dimensional nonseparable scaling function interpolation.
We shall denote the value of the pixel in row j_1 and the column j_2 of the image by p_j; j := (j_1; j_2). Whereas transform coding is most often described solely in terms of the discrete pixel values p_j, our analysis is based on interpreting the image as a smooth, compact support function f(x,y) defined on R^2 with the values p_j at (j_1/2^m, j_2/2^m)[connect p_j smoothly, (x, y)∈[ − 1/2^m , 1] × [ − 1/2^m , 1] − ( j_1/2^m ; j_2/2^m )],
and 0 at (p , q), ((p , q)∈R^2 − [ − 1/2^m, 1] × [ − 1/2^m, 1]).

Thank you for your help.