High Quality Content by WIKIPEDIA articles! A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter. For example, (2t) = 4 (t) is a comparametric equation, when we define g(t) = f(2t), so that we have g = 4 no longer contains the parameter, t. The comparametric equation g = 4 has a family of solutions, one of which is = t2. To see that = t2 is a solution, we merely substitute back in: g = (2t) = (2t)2 = 4t2 = 4 , so that g = 4 . Comparametric equations arise naturally in signal processing when we have multiple measurements of the same phenomenon, in which each of the measurements was acquired using a different sensitivity. For example, two or more differently exposed pictures of the same subject matter give rise to a comparametric relationship, the solution of which is the response function of the camera, image sensor, or imaging system.

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