https://www.chenk.top/en/tags/3d-reconstruction/Recent content in 3D Reconstruction on Chen Kai BlogHugoenWed, 23 Apr 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/17-linear-algebra-in-computer-vision/Wed, 23 Apr 2025 09:00:00 +0000https://www.chenk.top/en/linear-algebra/17-linear-algebra-in-computer-vision/<p>Computer vision is the science of teaching machines to see. What is striking is how thoroughly the whole field reduces to linear algebra: an image is a matrix, a geometric transformation is a matrix product, a camera is a <span class="math-inline">$3 \times 4$</span> projection matrix, two-view geometry is the equation <span class="math-inline">$\mathbf{x}_2^\top \mathbf{F}\, \mathbf{x}_1 = 0$</span> , and 3D reconstruction is a sparse linear least-squares problem. Once you see the field through that lens, what once looked like a zoo of algorithms turns out to be a small set of linear-algebraic ideas applied repeatedly.</p>https://www.chenk.top/en/standalone/tennis-cv-system-design/Sat, 31 Aug 2024 09:00:00 +0000https://www.chenk.top/en/standalone/tennis-cv-system-design/<p>A 6.7 cm tennis ball travels at over 200 km/h. Reconstructing its 3D trajectory from eight 4K cameras in real time, while also classifying each player&rsquo;s stroke, involves <strong>small-object detection, multi-view geometry, Kalman filtering, physics modeling, and human-pose estimation</strong> — all at once. This post follows the same steps as in deployment: state the constraints, survey the literature, choose, build, and lay out a millisecond-by-millisecond budget for production.</p> <hr> <h2 id="what-you-will-learn" class="heading-anchor">What You Will Learn<a href="#what-you-will-learn" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><ul> <li>Why traditional detectors collapse on 10–20 px tennis balls and how the TrackNet line fixes it</li> <li>Multi-camera calibration, PTP synchronisation, and DLT triangulation in code and math</li> <li>A 9-state Kalman filter coupled with a drag-plus-Magnus ODE for trajectory prediction</li> <li>Action recognition: rule-based templates vs. end-to-end learning, and when each wins</li> <li>How to fit detection → 3D → tracking → pose → analytics into a 16.7 ms / frame budget</li> </ul> <p><strong>Prerequisites</strong>: pinhole camera model, basic Kalman filtering, and some PyTorch inference experience.</p>