The course content grouped into seven blocks, with the learning goals of each block and where to find them. The priorities come from the first exam and the hints for the resit.
Scope (from the organization slide, this is binding): Lecture 1 Intro, 2 Camera Models and Coordinate Systems, 3 Classical 3D Reconstruction, 4 Stereo Vision and Depth Estimation, 5 Surface Reconstruction and Procrustes, 6 Neural Fields and Point-Based Representations, 7 NeRF, 8 Gaussian Splatting and Point Clouds, 9 Advanced Learning-Based 3D Reconstruction, 10 and 11 Generative Models, 12 Recap.
Legend
π΄ was in the exam Β· π hint for the resit or high probability Β· π‘ covers the gap of forgotten tasks Β· β high value
Skill: Calculate, Explain, Compare, Transfer (apply to a new scenario), Symbols (name every symbol of a given formula), MC (enough for multiple choice).
Recommended Order
flowchart LR E["1 Β· Block E<br/>NeRF / 3DGS π΄"] --> CD["2 Β· Blocks C + D<br/>surfaces, fields π΄"] CD --> A["3 Β· Block A<br/>calculations π΄"] A --> G["4 Β· Block G<br/>generative π΄"] G --> F["5 Β· Block F<br/>DUSt3R π΄"] F --> B["6 Β· Block B<br/>epipolar, SfM π "] B --> R["7 Β· Recap<br/>gap scan"]
- Block E (NeRF / 3DGS): confirmed in the exam, many points.
- Blocks C + D (surfaces + fields): the transfer task point cloud β mesh.
- Block A (calculations): quick, safe points.
- Block G (generative models, TRELLIS): confirmed in the exam, plus the diffusion hints.
- Block F (DUSt3R, point maps).
- Block B (epipolar geometry, 8-point, bundle adjustment): named in the hints, not confirmed in the first exam.
- At the end: go through all Self-Test sections as a gap scan.
Block A: Camera Model and Calculations π΄
| Learning goal | Skill |
|---|---|
| Rearrange the pinhole model in both directions (link) | Calculate β |
| Intrinsics: focal length , principal point , skew, pixel size (link) | Calculate + MC |
| The chain world β camera β film β pixel (link) | Explain |
| Extrinsics , ; homogeneous coordinates (link, link) | Explain |
| Rotation representations: Euler, axis-angle, rotation matrix, quaternions (no singularities, 4 numbers, good for interpolation) π‘ (link) | MC |
Practice
3 to 5 tasks of the type βmove the camera back until two objects appear equally tallβ and βcompute from , , β: Worked Examples.
Block B: Classical Reconstruction and Stereo π π‘
| Learning goal | Skill |
|---|---|
| Epipolar geometry: derive the essential matrix (calibrated) and the fundamental matrix with (link, link) | Explain β |
| 8-point algorithm: why SVD (overdetermined homogeneous system β smallest singular vector), why a second SVD (enforce rank 2) (link, link) | Explain β |
| Image rectification: after rectification the image planes differ only by a translation (link) | Explain |
| Stereo matching: disparity, , similarity metrics SAD / SSD / NCC (link) | MC |
| Multi-view stereo, monocular depth (data / architecture / training objective) (link) | Explain |
| SfM pipeline + bundle adjustment: joint refinement of cameras and 3D points via the reprojection error (link, link) | Explain β |
Block C: Surface Reconstruction and Alignment π΄π
| Learning goal | Skill |
|---|---|
| Implicit vs. explicit representations, pros and cons (link) | MC + Explain |
| Level sets: storage , narrow band as the fix | Explain |
| Point clouds: unordered, no connectivity, uneven density, incomplete (link) | MC |
| Marching cubes / squares: how a scalar field becomes a mesh (link) | Transfer β |
| Poisson surface reconstruction: oriented points β vector field β β octree + multigrid; screened PSR adds a data term (link) | Explain β |
| Procrustes: translation = centroid difference, rotation = SVD of the cross-covariance, scale = quotient of sums; know the notation (link) | Explain β |
| ICP: alternate correspondences and Procrustes; needs a good initialization (link) | Explain |
| Subdivision surfaces (Catmull-Clark, Loop) π‘ (link) | MC |
Block D: Neural Fields and Point-Based Learning π΄π
| Learning goal | Skill |
|---|---|
| Occupancy, UDF, SDF: differences and when to use which (link) | Explain β |
| Implicit surface with a network: training vs. inference (link) | Transfer β |
| Why an SDF needs inside/outside β watertight GT; workarounds (normals + PSR, UDF / NDF) | Transfer β |
| PointNet / PointNet++: permutation invariance, hierarchical set abstraction (link, link) | Explain |
| Point Transformer: vector attention over kNN neighborhoods, relative positional encoding via an MLP (link) | MC |
Block E: Neural Rendering π΄ (highest priority)
| Learning goal | Skill |
|---|---|
| Volume rendering equation (NeRF): name every symbol, , , , , (link) | Symbols ββ |
| Explain transmittance and density intuitively (link) | Explain ββ |
| NeRF input/output ; positional encoding; view dependence (link) | Explain |
| 3DGS rendering equation: every symbol, , / opacity, , SH color (link) | Symbols ββ |
| Covariance and why (stays positive semi-definite, ellipsoid) (link) | Explain β |
| Relation to the Gaussian distribution (link) | Explain β |
| NeRF vs. 3DGS: implicit vs. explicit, ray marching vs. rasterization, speed, memory, editing, training time, quality (link) | Compare ββ |
| Splatting pipeline: project to 2D Gaussians, tile-based rasterization, sorting, adaptive density control (link, link) | Explain |
This was exam task 4, described as βquite doableβ. Safe points here.
Block F: Learning-Based Reconstruction π΄π‘
| Learning goal | Skill |
|---|---|
| Point map: dense, pixel-aligned, one 3D point per pixel, convertible to depth (link) | Explain β |
| Point cloud vs. point map in one sentence | MC + Explain β |
| DUSt3R: two unposed, uncalibrated images β two point maps in camera 1βs frame; Siamese encoder + cross-attention decoder; normalized regression loss (link, link) | Explain β |
| MASt3R: metric point maps, extra matching head, reciprocal NN matching; pairwise β global alignment (link) | MC |
| Why DUSt3R lags on DTU: regression vs. subpixel triangulation, no GT poses, zero-shot (link) | Explain |
| Classical vs. learned: epipolar geometry / triangulation / BA vs. matching / mono depth / cross-view attention (link) | Compare |
| Focal length from point maps (Weiszfeld) π‘ (link) | MC |
Block G: Generative Models π΄
| Learning goal | Skill |
|---|---|
| DDPM: reconstruct algorithms 1 and 2 line by line, reason about (slides 33, 35) π (link) | Explain ββ |
| DDPM β DDIM (far fewer sampling steps, not Markovian) (link) | MC |
| Flow matching vs. diffusion π (link) | Compare β |
| Structured vs. unstructured latents: spatially aligned / interpolation / locality vs. VecSet / structure in the features / transformer friendly (link) | Compare ββ |
| Why many latents instead of one global latent (fine details) | Explain β |
| Structure types: voxel and triplane | MC |
| TRELLIS / SLAT: features on active voxels (those that intersect the surface); grid = coarse geometry, features = detail; one latent β 3DGS, NeRF, mesh (link) | Explain ββ |
| Design axes: input condition / output representation / explicit vs. latent diffusion / generative backbone (link) | Transfer β |
| Zero-1-to-3: diffusion for novel views, conditioned on the image and the relative extrinsics (link) | Explain |
| Hunyuan3D 2.0: VecSet based, importance sampling at edges, farthest point sampling, SDF via cross-attention π‘ (link) | MC |
| Image-conditioned point cloud diffusion (PCΒ²): enrich points with projected image features π‘ (link) | MC |
| Combine pieces: depth + diffusion for the back of a scene π (link) | Transfer β |
Two Things to Train Separately
1. The transfer schema
Task 3 showed that knowing marching cubes is not enough: you have to draw a pipeline and separate training from inference. Practice this on 3 or 4 made-up scenarios, for example:
- a robot sees a mug from one side and needs its full mesh
- a phone video of a room should become a real-time viewable 3D scene
- two holiday photos without camera information should give a 3D point cloud
2. Parsing the task text
The biggest loss of points in the first exam was tactical. Bring a highlighter, read every task twice, number the hidden sub-questions in the text and tick them off. See Exam tactics.