From rigid geometry and camera imaging to SLAM, robot calibration, and grasping. Follow a structured learning map or use it as a quick reference for engineering problems.
Xcam = R Xobj + t
s [u, v, 1]T = K Xcam
Quick Start
Networks may predict keypoints, dense correspondences, depth, or pose directly. Each must ultimately answer the same question: where should a 3D point in the object frame appear in the current image?
6D Pose
R describes the orientation of the object frame relative to the camera frame; t gives the object origin's 3D position in the camera frame. Together, they define a rigid transform.
Establish transform directions, coordinate axes, and units before choosing an algorithm. Many apparent model failures are caused by inconsistent conventions.
Identify the target region using a 2D box, instance segmentation, or a candidate crop.
Predict keypoints, object coordinates, dense correspondences, depth, or surface normals.
Use PnP, RANSAC, 3D–3D alignment, direct regression, or optimization.
Check reprojection, silhouette, or depth residuals, then refine with ICP or rendering-based alignment.
Learning Paths
The same geometric concepts appear in 3D vision, SLAM, and robotics. Each learning path reuses the knowledge modules in an order suited to its application.
Path 01
Start with coordinates and projection, then learn correspondences, pose solvers, registration, and evaluation.
Path 02
Understand the connections between camera motion, multiview geometry, and object-level maps.
Path 03
Connect visual estimates to calibration, error propagation, and closed-loop control.
Path 04
Progress from object pose to gripper orientation, reachability, and closed-loop execution.
Path 05
Connect model preparation, real-world annotation, synthetic generation, quality control, and evaluation.
Knowledge Map
Six sections organize topics by their prerequisites, with domain tags connecting related applications. Each module can grow independently with derivations, examples, and interactive demonstrations.
Geometry Foundations
Build the mathematical language, coordinate conventions, and intuition for rotations used throughout the knowledge system.
Start with position, orientation, and degrees of freedom to understand the overall object pose estimation problem.
Planned interaction:Interactive 6D pose overview
Describe 3D rigid motion using matrices, homogeneous coordinates, SO(3), and SE(3).
Establish consistent directions and notation across world, object, camera, pixel, robot, and gripper frames.
Planned interaction:Coordinate frame and transform chain lab
Compare the meanings and pitfalls of Euler angles, rotation matrices, axis–angle, quaternions, and continuous rotation representations.
Planned interaction:Rotation representation converter
Imaging & Solvers
Understand how 3D points become pixels and how correspondences recover pose.
Understand perspective projection through the full chain from object points to camera coordinates and pixels.
Planned interaction:Pinhole camera projection lab
Recover rotation and translation between camera and object frames from 2D–3D point correspondences.
Planned interaction:PnP and RANSAC demonstration
Distinguish closed-form rigid alignment, global registration, and local iterative refinement that depends on initialization.
Planned interaction:Umeyama and ICP registration demonstration
Perception Systems
Extend single-frame geometry to perception systems with multiple modalities, multiple views, and continuous motion.
Connect camera motion, epipolar geometry, triangulation, bundle adjustment, and object-level maps.
Planned interaction:Two-view geometry and SLAM graph lab
Connect detection, geometric cues, hypothesis generation, pose refinement, and confidence into a complete system.
Compare what color, depth, point clouds, and multiple views can and cannot resolve in pose estimation.
Planned interaction:Modality information and reliable fusion lab
Data & Evaluation
Understand the protocols behind the numbers, from real-world annotation and synthetic data to symmetry-aware evaluation.
Cover the full process from model preparation and calibrated capture to pose ground-truth generation and quality validation.
Planned interaction:Annotation transform chain and data audit lab
Explore assets, physical scene layouts, camera sampling, multi-channel annotations, sensor noise, and sim-to-real transfer.
Planned interaction:Sampling, sensor, and sim-to-real audit lab
Understand why one observation may support multiple equally plausible poses and how to represent these alternatives.
Planned interaction:Equivalent poses and multimodal confidence lab
Evaluate rotation, translation, surface distance, visibility, and task success under the appropriate protocols.
Planned interaction:Metrics, matching, and error breakdown lab
Robotics & Manipulation
Connect visual pose estimates to robot coordinate chains and turn them into executable actions.
Build the complete coordinate chain connecting the camera, robot base, end effector, tool, and target object.
Planned interaction:Coordinate chains, hand–eye observability, and spatial–temporal error budget lab
Turn object poses into reachable, collision-free grasping or assembly actions that can be executed under feedback control.
Planned interaction:Grasp transforms, feasibility filtering, and closed-loop risk lab
Practice & Frontier
Learn practical debugging patterns and explore open-world perception, CAD-free methods, and emerging 3D representations.
Resolve common issues involving units, transform directions, matrix order, intrinsic updates, and sensor alignment.
Planned interaction:Pose conventions, imaging pipelines, and solver readiness lab
Use explicit task boundaries to navigate category-level and open-world pose estimation, CAD-free methods, neural 3D representations, nonrigid objects, and embodied perception.
Planned interaction:Problem boundaries, monocular scale ambiguity, and evidence audit lab
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Build Roadmap
Build a stable structure, then expand from core geometry into data, systems, and emerging research. Page status will be updated as the content and interactions develop.
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