|
In signal processing of multidimensional signals, for example in computer vision, the intrinsic dimension of the signal describes how many variables are needed to represent the signal. For a signal of ''N'' variables, its intrinsic dimension ''M'' satisfies ''0 ≤ M ≤ N''. Usually the intrinsic dimension of a signal relates to variables defined in a Cartesian coordinate system. In general, however, it is also possible to describe the concept for non-Cartesian coordinates, for example, using polar coordinates. == Example == Let ''f(x1, x2)'' be a two-variable function (or signal) which is of the form :''f(x1,x2)'' = ''g(x1)'' for some one-variable function ''g'' which is not constant. This means that ''f'' varies, in accordance to ''g'', with the first variable or along the first coordinate. On the other hand, ''f'' is constant with respect to the second variable or along the second coordinate. It is only necessary to know the value of one, namely the first, variable in order to determine the value of ''f''. Hence, it is a two-variable function but its intrinsic dimension is one. A slightly more complicated example is :''f(x1,x2)'' = ''g(x1 + x2)'' ''f'' is still intrinsic one-dimensional, which can be seen by making a variable transformation :x1 + x2 = y1 :x1 - x2 = y2 which gives :''f(y1,y2)'' = ''g(y1)'' Since the variation in ''f'' can be described by the single variable ''y1'' its intrinsic dimension is one. For the case that ''f'' is constant, its intrinsic dimension is zero since no variable is needed to describe variation. For the general case, when the intrinsic dimension of the two-variable function ''f'' is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero, one, or two are sometimes referred to as ''i0D'', ''i1D'' or ''i2D'', respectively. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「intrinsic dimension」の詳細全文を読む スポンサード リンク
|