Synthesis of the rotational blur kernel in a digital image using measurements of a triaxial gyroscope

A method for calculating of a blur kernel arising from the rotation of a digital camera is proposed. The rotation is measured with a three-axis gyroscope attached to the camera. Differential equations of a continuous trajectory of the rotational blur starting from a selected pixel are obtained. These equations are presented both in the form of an explicit system of differential equations for the blur curve in the focal plane and in the form of a matrix equation for the increment of the camera attitude. An expression is given for the integral of the energy illumination from a point light source along the continuous blur trajectory. The integral takes into account the point spread function and the aperture functions of individual photosensitive cells of the photodetector array. The calculation of the integral values for all photosensitive cells illuminated with the point source gives a discrete kernel of rotational blur starting at the selected pixel. Algorithms for the numerical integration of the blur equations are described. The analysis of the blur equations are carried out, characteristic features of the kernels are highlighted and their non-homogeneity is shown, with the kernels of rotational blur revealed not to coincide with each other for different pixels. An example of the synthesis of the blur kernels for given rotation parameters of the digital camera is given.