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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

Curvature and Its Interpretation

Curvature and Its Interpretation

Curvature describes how rapidly a curve changes direction at a particular point. A curve with a small curvature bends gently, while a curve with a large curvature turns sharply. For a space curve, the position of a moving object can be described by a vector-valued function r(t), where t often represents time. The direction of motion is determined by the tangent vector, and the unit tangent vector is obtained by normalizing the derivative of the position vector.The unit tangent vector gives the...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

Curvilinear Motion: Rectangular Components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

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Uncertainty reveals surround modulation of shape.

Katinka van der Kooij¹, Susan F te Pas

¹Department of Experimental Psychology, Helmholtz Institute, Universiteit Utrecht, Utrecht, The Netherlands. k.vanderkooij@uu.nl

Journal of Vision

|September 18, 2009

Summary

Contextual visual information influences shape perception. Degraded shape signals lead to assimilation, while clear signals cause contrast, revealing how visual processing integrates context based on reliability.

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Area of Science:

Visual perception
Cognitive neuroscience
Computational vision

Background:

Shape perception is influenced by contextual information, as seen in contrast and assimilation illusions.
Understanding how the brain integrates contextual cues based on signal reliability is crucial for explaining shape perception.

Purpose of the Study:

To investigate how the reliability of shape signals affects surround-induced biases in shape perception.
To elucidate the underlying processes of contextual information integration in shape estimation.

Main Methods:

Visual noise was selectively added to central and surround stimuli to manipulate signal reliability.
Shape perception bias was measured and compared across different noise conditions and a control.
Illusory effects of shape contrast and assimilation were analyzed in relation to stimulus degradation.

Main Results:

A shape-contrast bias was observed when both shape and surround stimuli were clear.
This contrast bias diminished when surround stimuli were degraded.
An assimilation bias emerged when the central shape was degraded, increasing with overall stimulus degradation.

Conclusions:

Shape contrast arises from inference processes in early visual areas using local representations.
Assimilation is linked to inference processes in higher visual areas utilizing global representations.
The reliability of visual signals critically modulates the integration of contextual information in shape perception.