From 9b98f1e4b182bc8d182909a5c811856d2cdd2f97 Mon Sep 17 00:00:00 2001 From: Trance-0 <60459821+Trance-0@users.noreply.github.com> Date: Wed, 3 Sep 2025 20:33:56 -0500 Subject: [PATCH] update --- content/CSE5519/CSE5519_E1.md | 201 +++++++++++++++++++++++++++- public/CSE5519/DispNet.png | Bin 0 -> 84877 bytes public/CSE5519/GeoNet_result.png | Bin 0 -> 276787 bytes public/CSE5519/PoseNet_DepthNet.png | Bin 0 -> 99904 bytes public/CSE5519/SceneFlowNet.png | Bin 0 -> 37471 bytes 5 files changed, 199 insertions(+), 2 deletions(-) create mode 100644 public/CSE5519/DispNet.png create mode 100644 public/CSE5519/GeoNet_result.png create mode 100644 public/CSE5519/PoseNet_DepthNet.png create mode 100644 public/CSE5519/SceneFlowNet.png diff --git a/content/CSE5519/CSE5519_E1.md b/content/CSE5519/CSE5519_E1.md index 2f67137..554e574 100644 --- a/content/CSE5519/CSE5519_E1.md +++ b/content/CSE5519/CSE5519_E1.md @@ -4,6 +4,10 @@ > > This topic is presented by Me. and will be the most detailed one for this course, perhaps. +## Data set of the scene: KITTI + +[link to the website](http://www.cvlibs.net/datasets/kitti/) + ## PoseNet A Convolutional Network for Real-Time 6-DOF Camera Relocalization (ICCV 2015) @@ -274,11 +278,55 @@ This is a method that estimates both depth and camera pose motion from a single Jointly training a single-view depth CNN and a camera pose estimation CNN form unlabelled monocular video sequences. +### Assumptions for PoseNet & DepthNet + +1. The scene is static and the only motion is the camera motion. +2. There is no occlusion/disocclusion between the target view and the source view. +3. The surface is Lambertian. + ![View synthesis as supervision](https://notenextra.trance-0.com/CSE5519/Unsupervised_Learning_DepthNet_PoseNet.png) -### View synthesis as supervision +Let $I_{t-1}, I_{t}, I_{t+1}$ be three consecutive frames in the video. -Notice that in mo +First, we use the DepthNet to estimate the depth of $I_t$ to obtain $\hat{D}_t$. We use the PoseNet to estimate the camera pose motion between $I_{t-1}$ and $I_{t+1}$ to obtain two transition vector $\hat{T}_{t\to t-1}$ and $\hat{T}_{t\to t+1}$. + +Then use the information we have from $\hat{D}_t$ and $\hat{T}_{t\to t-1}, \hat{T}_{t\to t+1}$ with frame $I_{t-1}$ and $I_{t+1}$ to synthesize the image $\hat{I}_s$ from $I_{t-1}$ and $I_{t+1}$. + +Note that $\hat{I}_s$ is the synthesized prediction for $I_t$. + +### Loss function for PoseNet & DepthNet + +Notice that in the training process, we can generate the supervision for PoseNet & DepthNet by using **view synthesis as supervision**. + +#### View synthesis as supervision + +Let $\mathcal{I}=\{I_1,I_2,I_3,\cdots,I_n\}$ be the video sequence. Note that $I_t(p)$ is the pixel value of $I_t$ at point $p$. + +The loss function generated by view synthesis is: + +$$ +\mathcal{L}_{vs}=\sum_{I_s\in\mathcal{I}}\sum_{p\in I_s}\left|I_t(p)-\hat{I}_s(p)\right| +$$ + +#### Differentiable depth image-based rendering + +Assume that the transition and rotation between the frames are smooth and differentiable. + +Let $p_t$ denote the pixel coordinates of $I_t$ at time $t$. Let $K$ denote the camera intrinsic matrix. We can always obtain $p_t$'s projected coordinates to our source view $p_s$ by the formula: + +$$ +p_s\sim K\hat{T}_{t\to s}\hat{D}_t(p_t)K^{-1}p_t +$$ + +The we use spacial transformer network to sample continuous pixel coordinates. + +### Compensation for PoseNet & DepthNet + +Since it's inevitable that there are some moving objects or occlusions between the target view and the source view, in pose net we also train a few additional layers to estimate our confidence (explainability mask) of the camera motion. + +### Architecture for PoseNet & DepthNet + +![Architecture for PoseNet & DepthNet](https://notenextra.trance-0.com/CSE5519/PoseNet_DepthNet.png) ## Unsupervised Monocular Depth Estimation with Left-Right Consistency @@ -288,6 +336,91 @@ Notice that in mo This is a method that use pair of images as Left and Right eye to estimate depth. Increased consistency by flipping the right-left relation. +**Intuition:** Given a calibarated pair of binocular cameras, if we cna learn a function that is able to reconstruct one image from the other, then we have learned something about the depth of the scene. + +### DispNet and Scene flow + +![DispNet and Scene flow](https://notenextra.trance-0.com/CSE5519/DispNet.png) + +[link to the paper](https://arxiv.org/pdf/1512.02134) + +#### Scene flow + +Scene flow is the underlying 3D motion field that can be computed from stereo videos or RGBD videos. + +Note, these 3D quantities can be computed only in the case of known camera intrinsics (i.e., $K$ matrix) and extrinsics (i.e., camera pose, translation, etc.). + +Scene flow can be reconstructed only for surface points that are visible in both the left and the right frame. + +Especially in the context of convolutional networks, it is particularly interesting to estimate also depth and motion in partially occluded areas + +#### Disparity + +Disparity is the difference in the x-coordinates of the same point in the left and right images. + +![SceneFlowNet](https://notenextra.trance-0.com/CSE5519/SceneFlowNet.png) + +If there is time difference between the "left" and "right" images, by the difference between the disparity, we can estimate the scene flow, that is, non-rigid motion of the scene. + +Object that have the same disparity in both images is "moving along with the camera". + +Object that is moving away, or moving toward the camera, will have higher disparity. + +### Assumptions for Left-right consistency Network + +1. Lambertian surface. +2. No occlusion/disocclusion between the left and right image (for computing scene flow). + +### Loss functions for Left-right consistency Network + +$$ +\mathcal{L}=\alpha_{ap}(\mathcal{L}_{ap}^l+\mathcal{L}_{ap}^r)+\alpha_{ds}(\mathcal{L}_{ds}^l+\mathcal{L}_{ds}^r)+\alpha_{lr}(\mathcal{L}_{lr}^l+\mathcal{L}_{lr}^r) +$$ + +The loss function consists of three parts: + +Let $N$ denote the number of pixels in the image. + +#### Appearance matching loss + +Let $I^l$ denote the left image, $I^r$ denote the right image, $\hat{L}^l$ denote the left image reconstructed from the right image. + +$\hat{I}^l$ denote the left image reconstructed from the right image with the predicted disparity map $d^l$. + +The appearance matching loss for left image is: + +$$ +\mathcal{L}_{ap}^l=\frac{1}{N}\sum_{p\in I^l}\alpha \frac{1-\operatorname{SSIM}(I^l(p),\hat{I}^l(p))}{2}+(1-\alpha)\left\|I^l(p)-\hat{I}^l(p)\right\| +$$ + +Here $\operatorname{SSIM}$ is the structural similarity index. + +[link to the paper: structure similarity index](https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1284395) + +$\alpha$ is a hyperparameter that balances the importance of the structural similarity and the pixel-wise difference. In this paper, $\alpha=0.85$. + +#### Disparity Smoothness Loss + +Let $\partial d$ denote the disparity gradient. $\partial_x d^l_p$ and $\partial_y d^l_p$ are the disparity gradient in the x and y directions respectively on the left image of pixel $p$. + +The disparity smoothness loss is: + +$$ +\mathcal{L}_{ds}^l=\frac{1}{N}\sum_{p\in I^l}\left|\partial_x d^l_p\right|e^{-\left|\partial_x d^l_p\right|}+\left|\partial_y d^l_p\right|e^{-\left|\partial_y d^l_p\right|} +$$ + +#### Left-right disparity consistency loss + +Our network produces two disparity maps, $d^l$ and $d^r$. We can use the left-right consistency loss to enforce the consistency between the two disparity maps. + +$$ +\mathcal{L}_{lr}^l=\frac{1}{N}\sum_{p\in I^l}\left|d^l_p-d^r_{p+d^l_p}\right| +$$ + +### Architecture of Left-right consistency Network + +![Architecture of Left-right consistency Network](https://notenextra.trance-0.com/CSE5519/Left-right_consistency_Network.png) + ## GeoNet Unsupervised Learning of Dense Depth, Optical Flow and Camera Pose (CVPR 2018) @@ -300,16 +433,80 @@ Depth Estimation from single monocular image. [link to the repository](https://github.com/yzcjtr/GeoNet) +### Architecture for GeoNet + ![GeoNet](https://notenextra.trance-0.com/CSE5519/GeoNet.jpg) ### Rigid structure constructor Combines the DepthNet and PoseNet to estimate the depth and camera pose motion from [Unsupervised Learning of Depth and Ego-Motion From Video](#unsupervised-learning-of-depth-and-ego-motion-from-video). +We denote the output of the Rigid structure constructor from frame $t$ to $s$ as $f^{rig}_{t\to s}$. The function output is a 2D vector showing the shift of the pixel coordinates. + +Recall from previous paper, + +$$ +\begin{aligned} +p_t+f^{rig}_{t\to s}(p_t)&=KT_{t\to s}D_t(p_t)K^{-1}p_t\\ +f^{rig}_{t\to s}(p_t)&=K(T_{t\to s}D_t(p_t)+I)K^{-1}p_t-p_t +\end{aligned} +$$ + ### Non-rigid motion localizer Use [Left-right consistency](#unsupervised-monocular-depth-estimation-with-left-right-consistency) to estimate the non-rigid motion by training the ResFlowNet. +We denote the output of the Non-rigid motion localizer from frame $t$ to $s$ as $f^{res}_{t\to s}$. SO the final full flow prediction is $f^{full}_{t\to s}=f^{res}_{t\to s}+f^{rig}_{t\to s}$. + +Let $\hat{I}^{rig}_s$ denote the inverse wrapped image from frame $s$ to $t$. Note that $\hat{I}^{rig}_s$ is the prediction of $I_t$ from $I_s$, using the rigid structure constructor. + +Recall from previous paper, we rename the $\mathcal{L}_{ap}^l$ to $\mathcal{L}_{rw}$. + +$$ +\mathcal{L}_{rw}=\frac{1}{N}\sum_{p\in I^l}\alpha \frac{1-\operatorname{SSIM}(I^l(p),\hat{I}^{rig}_s(p))}{2}+(1-\alpha)\left\|I^l(p)-\hat{I}^{rig}_s(p)\right\|_1\tag{1} +$$ + +Then we use $\mathcal{L}_{ds}$ to enforce the smoothness of the disparity map. + +$$ +\mathcal{L}_{ds}=\sum_{p\in I^l}\left|\partial_x d^l_p\right|e^{-\left|\partial_x d^l_p\right|}+\left|\partial_y d^l_p\right|e^{-\left|\partial_y d^l_p\right|}=\sum_{p_t}|\nabla D(p_t)|\cdot \left(e^{-|\nabla I(p_t)|}\right)^T\tag{2} +$$ + +Replacing $\hat{I}^{rig}_s$ with $\hat{I}^{full}_s$, in (1) and (2), we get the $\mathcal{L}_{fw}$ and $\mathcal{L}_{fs}$ for the non-rigid motion localizer. + ### Geometric consistency enforcement Finally, we use an additional geometric consistency enforcement to handle non-Lambertian surfaces (e.g., metal, plastic, etc.). + +This is done by additional term in the loss function. + +Let $\Delta f^{full}_{t\to s}(p_t)=f^{full}_{t\to s}(p_t)-f^{full}_{s\to t}(p_t)$. + +Let $\delta(p_t)$ denote the function belows for arbitrary $\alpha,\beta>0$: + +$$ +\delta(p_t)=\begin{cases} +1 & \text{if }\|\Delta f^{full}_{t\to s}(p_t)\|_2<\max\{\alpha,\beta\|f^{full}_{t\to s}(p_t)\|_1\} \\ +0 & \text{otherwise} +\end{cases} +$$ + +The geometric consistency enforcement loss is: + +$$ +\mathcal{L}_{gc}=\sum_{p_t}\delta(p_t)\|\Delta f^{full}_{t\to s}(p_t)\|_2 +$$ + +### Loss function for GeoNet + +Let $l$ be the set of pyramid image scales. $\langle t,s\rangle$ denote the set of all pairs of frames in the video and their inverse pairs, $t\neq s$. + +$$ +\mathcal{L}=\sum_{l}\sum_{\langle t,s\rangle}\mathcal{L}_{rw}+\lambda_{ds}\mathcal{L}_{ds}+\lambda_{fw}\mathcal{L}_{fw}+\lambda_{fs}\mathcal{L}_{fs}+\lambda_{gc}\mathcal{L}_{gc} +$$ + +$\lambda_{ds},\lambda_{fw},\lambda_{fs},\lambda_{gc}$ are hyperparameters that balance the importance of the different losses. + +### Results for monocular depth estimation + +![GeoNet](https://notenextra.trance-0.com/CSE5519/GeoNet_results.png) \ No newline at end of file diff --git a/public/CSE5519/DispNet.png b/public/CSE5519/DispNet.png new file mode 100644 index 0000000000000000000000000000000000000000..d7ad185be65b5273838d94c192eb685ce05a03a8 GIT binary patch literal 84877 zcma&NV~{RS@Gkg{ZQHia*tTu!jBVSt&lqQH8)t0Wwr6&J_kZuk?ta>g=;*GBs*cX? ztgg%_pNvqD6NiJwh6VrtaFP-tN&o=R`_It?3I5abwW>Sya{_Ww5*Gs0OyQpXG(gP- zWd#9%x;U5*L$IGVl)Z$e699nh{NDkzWk%o*0DKoqiU_K>>s{oysi0`$g!z#^5EDkO z3~f#9t)VH_MRnDLZ#I#f*SK8LSPLUoxJmBn^<*NHeREOJFJmscM}ZZ5fMnAWlK!HAMXG1_zCt$ z;xInL0|fUVL4ijnCWHwQ!+i%8U@W)0d295##y5U1C{5+^!VnM;Wb=BdJ&@Fuxz}Tm z?k~D{wQhU^4|PY?`dWEW0{auf_oYqkO9`;9(1q=`w2{oJ$v#XhM$IL5?Yy(J=JWvf zlsS){JNMq4_88WVJ7sgb!7=O~%+|h3$Ye1gPNIqSPyw|jw7Pxa(r+9YUYuTHR#UeN zY3>rwO~AWeF)1v}3I&y%#n0#Zt0rlO*H9||3Dz6o#31ODG7#2Q2CIP65}=Vr+6*h( 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