updates

content/CSE5519/CSE5519_E4.md

@@ -1,2 +1,19 @@
 # CSE5519 Advances in Computer Vision (Topic E: 2024: Deep Learning for Geometric Computer Vision)
 
+## DUSt3R: Geometric 3D Vision Made Easy.Links to an external site.
+
+[link to paper](https://arxiv.org/pdf/2312.14132)
+
+### Novelty in DUSt3R
+
+Use point map to represent the 3D scene, combining with the camera intrinsics to estimate the 3D scene.
+
+Direct-RGB to 3D scene.
+
+Use ViT to encode the image, and then use two Transformer decoder (with information sharing between them) to decode the two representation of the same scene $F_1$ and $F_2$. Direct regression from RGB to point map and confidence map.
+
+>[!TIP]
+>
+> Compared with previous works, this paper directly regresses the point map and confidence map from RGB, producing a more accurate and efficient 3D scene representation.
+> 
+> However, I'm not sure how the information across the two representations is shared in the Transformer decoder. If for a multiview image, there are two pairs of images that don't have any overlapping region, how can the model correctly reconstruct the 3D scene?

content/Math401/Extending_thesis/Math401_R1.md

@@ -234,7 +234,7 @@ Then the measurable space $(\Omega, \mathscr{B}(\mathbb{C}), \lambda)$ is a meas
 
 If $\Omega=\mathbb{R}$, then we denote such measurable space as $L^2(\mathbb{R}, \lambda)$.
 
-<details>
+</details>
 
 #### Probability space
 
@@ -426,7 +426,7 @@ is a pure state.
 
 </details>
 
-## Drawing the connection between the space $S^{2n+1}$, $CP^n$, and $\mathbb{R}$
+## Drawing the connection between the space $S^{2n+1}$, $\mathbb{C}P^n$, and $\mathbb{R}$
 
 A pure quantum state of size $N$ can be identified with a **Hopf circle** on the sphere $S^{2N-1}$.
 

content/Math401/Extending_thesis/Math401_S4.md

@@ -1,4 +1,4 @@
-# Math 401, Fall 2025: Thesis notes, S4, Bargmann space
+# Math 401, Fall 2025: Thesis notes, S4, Complex function spaces and complex manifold
 
 ## Bargmann space (original)