Notes
Notes
Every note on Deep Insight, newest first.
- October 12, 2026Imaging Model: Camera Geometry and CalibrationPlaceholder, to be written.
- October 12, 2026Inner products, covariance and correlationStarting from the inner product, centering gives covariance and normalizing gives correlation; the correlation coefficient is the cosine of the angle between the centered vectors. This chapter derives the chain in full and shows where these quantities appear in state estimation and point-cloud processing.
- October 12, 2026The Jacobian and the gradient: the derivative as a local linear mapExtend the one-variable derivative to several variables and it turns from a number into a matrix, the Jacobian; the transpose of a scalar field's Jacobian is the gradient. This chapter derives why the gradient points uphill fastest and is normal to level sets, and works out the Jacobians of camera projection and pose optimization.
- October 12, 2026Cross-correlation and convolution: the sliding inner productAdding a shift to the inner product gives cross-correlation; flipping the kernel gives convolution. This chapter derives how the two relate, why linear time-invariant systems are exactly convolutions, and why normalized cross-correlation is the correlation coefficient over a window, with uses in template matching and stereo.
- October 12, 2026Divergence and curl: what they extract from the JacobianThe Jacobian fully describes what a vector field does near a point, and divergence and curl extract two parts of it. Divergence is the trace and reads off the local change of volume; curl comes from the antisymmetric part and equals twice the local angular velocity. This chapter derives both, their integral forms and the two zero identities, and uses optical-flow divergence to estimate time to contact.
- October 12, 2026Foundations of 3D Reconstruction and Epipolar GeometryPlaceholder, to be written.
- October 12, 2026From convolution to attentionA convolutional layer takes inner products between shared learned templates and local patches; attention takes pairwise inner products between queries and keys generated from the input, then aggregates with softmax weights. This chapter derives both, the origin of the √d scaling and permutation equivariance, and asks how much "measuring relationships" really explains about why the two architectures succeed.
- October 12, 2026Hessian, Laplacian and Poisson reconstructionTaking the Jacobian of the gradient gives the Hessian, and its trace gives the Laplacian. This chapter derives the second-order Taylor expansion, the link between the Laplacian and neighbourhood averages, and the second-order identities, then derives the Poisson surface reconstruction equation from a least-squares energy and shows where the Gauss–Newton approximation of the Hessian comes from.
- October 12, 2026Image FeaturesPlaceholder, to be written.
- October 12, 2026Mutual information: dependence beyond linearityZero correlation does not mean independence. Mutual information measures any form of statistical dependence through probability distributions. This chapter derives its three equivalent definitions and its non-negativity, shows that for Gaussians it is fully determined by the correlation coefficient, reads a confusion matrix as a joint distribution, and shows how it drives camera–LiDAR calibration.
- October 12, 2026Stereo VisionPlaceholder, to be written.
- October 12, 2026Structure from MotionPlaceholder, to be written.
- October 12, 2026Dense Point Cloud ReconstructionPlaceholder, to be written.
- October 12, 2026Surface ReconstructionPlaceholder, to be written.
- October 12, 2026Texture Map GenerationPlaceholder, to be written.
- October 11, 2026Gradient, divergence, curl: what does a field tell us locally?Treat ∇ as a local probe and see what it measures on scalar and vector fields.
- October 10, 2026Where do quaternions come from, and why are they good at rotations?Starting from the formula Hamilton carved on Brougham Bridge, connect unit quaternions to 3D rotation.
- October 9, 2026From geometric maps to predictive world representationsA map tells a robot where the world is; a world model must also say what happens next.