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Related Concept Videos

Uncertainty: Overview00:59

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.
Curvilinear Motion: Rectangular Components01:23

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...
Propagation of Uncertainty from Random Error00:59

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 Error01:10

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...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...

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Related Experiment Video

Updated: Jun 26, 2026

Photorealistic Learned Landscapes for Augmented Reality
06:54

Photorealistic Learned Landscapes for Augmented Reality

Published on: June 27, 2025

RIGI: Rectifying Image-to-3D Generation Inconsistency via Uncertainty-Aware Learning.

Jiacheng Wang, Zhedong Zheng, Wei Xu

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |June 24, 2026
    PubMed
    Summary

    This study introduces an uncertainty-aware framework for image-to-3D generation, improving 3D model quality. It addresses data imperfections by modeling and mitigating epistemic uncertainty for more robust results.

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    Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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    Generating Strictly Controlled Stimuli for Figure Recognition Experiments
    05:39

    Generating Strictly Controlled Stimuli for Figure Recognition Experiments

    Published on: March 18, 2019

    Area of Science:

    • Computer Vision
    • 3D Reconstruction
    • Machine Learning

    Background:

    • Image-to-3D generation seeks to create 3D models from single 2D images.
    • Conventional methods often fail due to epistemic uncertainty from imperfect multi-view data.
    • Deterministic optimization in existing pipelines neglects crucial uncertainty information.

    Purpose of the Study:

    • To develop an uncertainty-aware optimization framework for more robust and reliable 3D generation.
    • To explicitly model and mitigate epistemic uncertainty in the image-to-3D pipeline.
    • To enhance the geometric and perceptual plausibility of generated 3D models.

    Main Methods:

    • Implemented a progressive sampling strategy with varying camera elevations to enhance viewpoint coverage.
    • Estimated epistemic uncertainty using discrepancies between two independently optimized Gaussian models.
    • Incorporated an uncertainty map into regularization for adaptive loss weighting, suppressing unreliable supervision.

    Main Results:

    • Significantly reduced artifacts and inconsistencies in generated 3D models.
    • Demonstrated higher-quality 3D generation compared to conventional approaches.
    • Provided theoretical analysis with a probabilistic upper bound on expected generation error.

    Conclusions:

    • The proposed uncertainty-aware optimization framework enhances image-to-3D generation robustness.
    • Explicitly modeling epistemic uncertainty leads to superior 3D model quality.
    • The method offers a promising direction for reliable 3D reconstruction from single images.