2016
DOI: 10.1177/0278364916684019
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A new perspective and extension of the Gaussian Filter

Abstract: The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. The GF represents the belief of the current state by a Gaussian distribution, whose mean is an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependences in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate… Show more

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Cited by 13 publications
(8 citation statements)
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“…The Gaussian smoothing operator is a 2-D convolution operator employed to blur images and remove detail and noise. In this sense, it is similar to the median filter, but it uses a discrete kernel representing the shape of the Gaussian hump (Wüthrich, Trimpe, Cifuentes, Kappler, & Schaal, 2017). The gaussian filter was generally used to suppress the speckle noise in OCT images (Devi, Ramkumar, Kumar, & Sasi, 2021).…”
Section: Image Preprocessingmentioning
confidence: 99%
“…The Gaussian smoothing operator is a 2-D convolution operator employed to blur images and remove detail and noise. In this sense, it is similar to the median filter, but it uses a discrete kernel representing the shape of the Gaussian hump (Wüthrich, Trimpe, Cifuentes, Kappler, & Schaal, 2017). The gaussian filter was generally used to suppress the speckle noise in OCT images (Devi, Ramkumar, Kumar, & Sasi, 2021).…”
Section: Image Preprocessingmentioning
confidence: 99%
“…In general, Gaussian noise with zero mean and unit variance during the process of measurement is typically assumed [20] in analytical developments, whereas it has been observed that in some cases this is not accurate [6]. A Gaussian noise with non-zero mean and non-unit variance errors, w ∼ N ( w , σ 2 w ), introduces a systematic error and a random uncertainty respectively in field measurements.…”
Section: Simulationsmentioning
confidence: 99%
“…In general, the existing filtering methodologies compute either the predictions with respect to the conditional probability distribution p(x k |z :k ), such as PF, or with respect to the probability joint distribution p(x k , z k |z :k−1 ), such as EKF, see [20] and the references therein. One of the differences between these methods is the computational cost.…”
Section: Introductionmentioning
confidence: 99%
“…10 Then, the images are filtered to eliminate noise with a Gaussian filter whose window size is 16 3 16. 11 Consequently, the images are segmented by illumination to extract the laser strip in the image. The extracted laser strips from the two cameras are shown in Figure 9.…”
Section: The Tire Profile Laser Strip Image Processingmentioning
confidence: 99%
“…There is a difference between the measured depth and the real depth when the laser plane does not pass through the tire's axis as mentioned in section ''Mathematical model of the measuring system and analysis.'' The real depth can be obtained with the measured depth by following steps: (1) calculate l with the measured h and the known r by expression (8); (2) calculate the angle u by expression (9) or (10); and (3) calculate the real depth with the measured depth by expression (11). The abovementioned steps are implemented in a LabVIEW program developed in this research.…”
Section: The Measure Of the Tread Depthmentioning
confidence: 99%