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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.
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Related Experiment Video

Updated: May 10, 2026

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
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Metric3D v2: A Versatile Monocular Geometric Foundation Model for Zero-Shot Metric Depth and Surface Normal

Mu Hu, Wei Yin, Chi Zhang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |August 16, 2024
    PubMed
    Summary

    Metric3D v2, a geometric foundation model, achieves zero-shot metric depth and surface normal estimation from single images. This advances 3D recovery and single-image metrology by resolving scale ambiguity and improving normal prediction accuracy.

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    Area of Science:

    • Computer Vision
    • Geometric Deep Learning
    • 3D Reconstruction

    Background:

    • Monocular depth estimation methods often generalize poorly to real-world metric scales.
    • Surface normal estimation faces challenges in zero-shot performance due to limited labeled data.
    • Accurate 3D recovery from single images requires precise metric depth and surface normal information.

    Purpose of the Study:

    • To introduce Metric3D v2, a geometric foundation model for zero-shot metric depth and surface normal estimation.
    • To address the limitations of existing methods in recovering metric scale and achieving robust zero-shot generalization.
    • To enable accurate single-image metrology and improve monocular Simultaneous Localization and Mapping (SLAM).

    Main Methods:

    • Developed a canonical camera space transformation module to resolve metric ambiguity in depth estimation.
    • Introduced a joint depth-normal optimization module leveraging metric depth data to enhance normal estimation.
    • Trained the model on over 16 million images from diverse camera models with varied annotations.

    Main Results:

    • Metric3D v2 achieves state-of-the-art zero-shot generalization to new camera settings.
    • The model ranks first in multiple zero-shot and standard benchmarks for metric depth and surface normal prediction.
    • Demonstrated accurate metric 3D structure recovery from internet images and reduced scale drift in monocular SLAM.

    Conclusions:

    • Metric3D v2 serves as a versatile geometric foundation model for single-image 3D recovery.
    • The proposed methods significantly improve metric depth and surface normal estimation accuracy in a zero-shot setting.
    • The model paves the way for advanced applications in single-image metrology and dense 3D mapping.