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Measurement and modeling of depth cue combination: in defense of weak fusion
 Vision Research
, 1995
"... Various visual cues provide information about depth and shape in a scene. When several of these cues are simultaneously available in a single location in the scene, the visual system attempts to combine them. In this paper, we discuss three key issues relevant to the experimental analysis of depth c ..."
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Cited by 133 (21 self)
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Various visual cues provide information about depth and shape in a scene. When several of these cues are simultaneously available in a single location in the scene, the visual system attempts to combine them. In this paper, we discuss three key issues relevant to the experimental analysis of depth cue combination in human vision: cue promotion, dynamic weighting of cues, and robustness of cue combination. We review recent psychophysical studies of human depth cue combination in light of these issues. We organize the discussion and review as the development of a model of the depth cue combination process termed modified weak fusion (MWF). We relate the MWF framework to Bayesian theories of cue combination. We argue that the MWF model is consistent with previous experimental results and is a parsimonious summary of these results. While the MWF model is motivated by normative considerations, it is primarily intended to guide experimental analysis of depth cue combination in human vision. We describe experimental methods, analogous to perturbation analysis, that permit us to analyze depth cue combination in novel ways. In particular these methods allow us to investigate the key issues we have raised. We summarize recent experimental tests of the MWF framework that use these methods. Depth Multiple cues Sensor fusion
On stable numerical differentiation
 Mathem. of Computation
, 1968
"... Abstract. A new approach to the construction of finitedifference methods is presented. It is shown how the multipoint differentiators can generate regularizing algorithms with a stepsize h being a regularization parameter. The explicitly computable estimation constants are given. Also an iterative ..."
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Cited by 39 (22 self)
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Abstract. A new approach to the construction of finitedifference methods is presented. It is shown how the multipoint differentiators can generate regularizing algorithms with a stepsize h being a regularization parameter. The explicitly computable estimation constants are given. Also an iteratively regularized scheme for solving the numerical differentiation problem in the form of Volterra integral equation is developed. 1.
On the Design of Optimal Filters for GradientBased Motion Estimation
 In: Proc. Intern. Conf. on Computer Vision
, 2002
"... Gradient based approaches for motion estimation (OpticalFlow) refer to those techniques that estimate the motion of an image sequence based on local changes in the image intensities. ..."
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Cited by 25 (0 self)
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Gradient based approaches for motion estimation (OpticalFlow) refer to those techniques that estimate the motion of an image sequence based on local changes in the image intensities.
Optimal Differentiation Based On Stochastic Signal Models
 IEEE Transactions on Signal Processing
, 1991
"... The problem of estimating the time derivative of a signal from sampled measurements is addressed. The measurements may be corrupted by coloured noise. A key idea is to use stochastic models of the signal to be differentiated and of the measurement noise. Two approaches are suggested. The first is ba ..."
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Cited by 13 (3 self)
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The problem of estimating the time derivative of a signal from sampled measurements is addressed. The measurements may be corrupted by coloured noise. A key idea is to use stochastic models of the signal to be differentiated and of the measurement noise. Two approaches are suggested. The first is based on a continuoustime stochastic process as model of the signal. The second approach uses a discretetime ARMA model of the signal and a discretetime approximation of the derivative operator. The introduction of this approximation normally causes a small performance degradation, compared to the first approach. There exists an optimal (signal dependent) derivative approximation, for which the performance degradation vanishes. Digital differentiators are presented in a shift operator polynomial form. They minimize the mean square estimation error. In both approaches, they are calculated from a linear polynomial equation and a polynomial spectral factorization. (The first approach also requ...
Stable numerical differentiation: when is it possible
 Jour. Korean SIAM
"... Abstract. Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative f ′ given noisy data fδ. Computational aspects of the problem are discussed and illustrate ..."
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Cited by 11 (8 self)
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Abstract. Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative f ′ given noisy data fδ. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation. 1.
A Variational Method for Numerical Differentiation
, 1995
"... this paper, we suggest a method for numerical differentiation that we believe avoids some of the limitations mentioned above. Given a real valued, smooth function u defined on the closed interval [a; b], we construct an associated functional, ..."
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Cited by 4 (0 self)
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this paper, we suggest a method for numerical differentiation that we believe avoids some of the limitations mentioned above. Given a real valued, smooth function u defined on the closed interval [a; b], we construct an associated functional,
A Stable Finite Difference Ansatz for Higher Order Differentiation of NonExact Data
 Bull. Austral. Math. Soc
, 1996
"... If standard central difference formulas are used to compute second or third order derivatives from measured data even quite precise data can lead to totally unusable results due to the basic instability of the differentiation process. Here an averaging procedure is presented and analysed which allow ..."
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Cited by 4 (1 self)
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If standard central difference formulas are used to compute second or third order derivatives from measured data even quite precise data can lead to totally unusable results due to the basic instability of the differentiation process. Here an averaging procedure is presented and analysed which allows the stable computation of low order derivatives from measured data. The new method first averages the data, then samples the averages and finally applies standard difference formulas. The size of the averaging set acts like a regularization parameter and has to be chosen as a function of the grid size h. 1991 Mathematics Subject Classification. 65D25. 1. Introduction Let the given (observational or nonexact) data be defined by d := fd j = f(t j ) + ffl j ; t j = jh; h = 1=n; j = 0; 1; 2; \Delta \Delta \Delta ; ng; (1) where f(t) denotes the underlying, but unknown, signal process and the ffl j denote the (observational or nonexact) errors which are assumed to be identical and independe...
A scheme for stable numerical differentiation
 J. COMP. APPL. MATH.
, 2006
"... A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are ..."
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Cited by 2 (1 self)
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A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is numerically more efficient than some other methods, in particular, than variational regularization.
2. SOLUTION DEPLETION EXPERIMENTS
"... 3. NONPARAMETRIC RESGRESSION ESTIMATES 3.1 Defining the basic model ..."
Acquisition, Processing, and Analysis of Pedal Motion Data in Bicycling
"... I would like to thank the staff at the Radlabor Freiburg (Radlabor GmbH, Freiburg, Germany) for the use of the laboratory facilities and for providing assistance with the measurement devices. In cycling, force applied to the pedal is conventionally measured using strain gauges or piezoelectric force ..."
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I would like to thank the staff at the Radlabor Freiburg (Radlabor GmbH, Freiburg, Germany) for the use of the laboratory facilities and for providing assistance with the measurement devices. In cycling, force applied to the pedal is conventionally measured using strain gauges or piezoelectric force transducers within the pedal body or at the crank. This thesis takes a different approach to determine pedal force based on motion capturing. Pedal force is calculated as the sum of forces needed to overcome the resistance of the ergometer brake and the moment of inertia of the ergometer’s flywheel. The former is obtained from cadence and power measurements of the ergometer, the latter by means of flywheel inertia and angular acceleration of the crank. The crank angle was determined by tracking the pedal movement using motion capturing. Then the second derivative of the crank angle gave its angular acceleration. As noise inherent in measurement data causes serious problems when computing derivatives, the data was smoothed beforehand. Three smoothing techniques were applied: a Butterworth filter, a Kalman smoother, and singular spectrum analysis. The angular acceleration obtained by the three methods was similar. The analysis of the pedal motion data revealed that systematic errors and strong measurement noise prevent sufficiently accurate estimates of the angular acceleration of the crank. Therefore, the resulting pedal force estimates differ considerably from the force obtained by a pedal force measurement device (Powertec System). ii Kurzfassung