If for an image function f(x, y), the magnitude of gradient vector is given by: mag(∇f)=[G^2x+G^2y] ^(1/2), then which of the following fact is correct?(a) The component of Gradient vector are linear operator and also the magnitude of the vector(b) The component of Gradient vector are linear operator, but the magnitude are not(c) The component of Gradient vector are nonlinear operator and also the magnitude of the vector(d) The component of Gradient vector are nonlinear operator, but the magnitude are notI got this question during a job interview.My doubt stems from Use of First Order Derivative for Enhancement topic in portion Image Enhancement of Digital Image Processing

If for an image function f(x, y), the magnitude of gradient vector is

1.	If for an image function f(x, y), the magnitude of gradient vector is given by: mag(∇f)=[G^2x+G^2y] ^(1/2), then which of the following fact is correct?(a) The component of Gradient vector are linear operator and also the magnitude of the vector(b) The component of Gradient vector are linear operator, but the magnitude are not(c) The component of Gradient vector are nonlinear operator and also the magnitude of the vector(d) The component of Gradient vector are nonlinear operator, but the magnitude are notI got this question during a job interview.My doubt stems from Use of First Order Derivative for Enhancement topic in portion Image Enhancement of Digital Image Processing
Answer» CORRECT CHOICE is (b) The COMPONENT of GRADIENT VECTOR are linear operator, but the magnitude are not To explain: The component of Gradient vector are linear operator because these are derivatives but the magnitude of the vector are not because of the squaring and square root operations.

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