Reconstruction of Outdoor Sculptures from Silhouettes under Approximate Circular Motion of an Uncalibrated Hand-Held Camera

This paper presents a novel technique for reconstructing an outdoor sculpture from an uncalibrated image sequence acquired around it using a hand-held camera. The technique introduced here uses only the silhouettes of the sculpture for both motion estimation and model reconstruction, and no corner detection nor matching is necessary. This is very important as most sculptures are composed of smooth textureless surfaces, and hence their silhouettes are very often the only information available from their images. Besides, as opposed to previous works, the proposed technique does not require the camera motion to be perfectly circular (e.g., turntable sequence). It employs an image rectification step before the motion estimation step to obtain a rough estimate of the camera motion which is only approximately circular. A refinement process is then applied to obtain the true general motion of the camera. This allows the technique to handle large outdoor sculptures which cannot be rotated on a turntable, making it much more practical and flexible.

APPROXIMATE GAUSS-MARKOV REALISATION OF MULTIVARIATE STOCHASTIC PROCESSES.

Given a spectral density matrix or, equivalently, a real autocovariance sequence, the author seeks to determine a finite-dimensional linear time-invariant system which, when driven by white noise, will produce an output whose spectral density is approximately PHI ( omega ), and an approximate spectral factor of PHI ( omega ). The author employs the Anderson-Faurre theory in his analysis.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.