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We propose a correspondence approximation approach between temporally adjacent frames for motion analysis. First, energy map is established to represent image spatial features on multiple scales using Gaussian convolution. On this basis, energy flow at each layer is estimated using Gauss-Seidel iteration according to the energy invariance constraint. More specifically, at the core of energy invariance constraint is "energy conservation law" assuming that the spatial energy distribution of an image does not change significantly with time. Finally, energy flow field at different layers is reconstructed by considering different smoothness degrees. Due to the multiresolution origin and energy-based implementation, our algorithm is able to quickly address correspondence searching issues in spite of background noise or illumination variation. We apply our correspondence approximation method to motion analysis, and experimental results demonstrate its applicability. [ABSTRACT FROM AUTHOR]

Freeform surfaces enable imaginative optics by providing abundant degrees of freedom for an optical designer as compared to spherical surfaces. An off-axis two-mirror-based telescope design is presented, in which the primary mirror is a concave prolate spheroid and the secondary mirror is freeform surface-based. The off-axis configuration is employed here for removing the central obscuration problem which otherwise limits the central maxima in the point spread function. In this proposed design, an extended X - Y polynomial is used as a surface descriptor for the off-axis segment of the secondary mirror. The coefficients of this extended polynomial are directly related to the Seidel aberrations, and are thus optimized here for a better control of asymmetric optical aberrations at various field points. For this design, the aperture stop is located 500 mm before the primary mirror and the entrance pupil diameter is kept as 80 mm. The effective focal length is 439 mm and covers a full field of view of 2 deg. The image quality obtained here is near diffraction limited which can be inferred from metrics such as the spot diagram and modulation transfer function. [ABSTRACT FROM AUTHOR]

Optical blur due to lens aberrations and defocus has been demonstrated in some cases to be spatially varying across the image plane. However, existing models in the literature for the point-spread function (PSF) corresponding to this blur are either parameterized and spatially invariant or spatially varying but ad-hoc and discretely defined. A parameterized model is developed and presented for a spatially varying PSF due to lens aberrations and defocus in an imaging system. The model is motivated from an established theoretical framework in physics and is demonstrated to be able to unify a set of hundreds of PSF observations across the image plane into a single 10-parameter model. The accuracy of the model is demonstrated with simulations and measurement data collected by two separate research groups. [ABSTRACT FROM AUTHOR]