Notes.md

为了构建一个 flow + confidence 的统一模型

为什么这样统一了就好：因为都有需求

definition

a given image pair $X = (I^q, I^r)$ of spatial size $H \times W$, the aim of dense matching is to estimate a flow field $Y \in \mathbb{R}^{H \times W \times 2}$.

Most learing-based methods address this problem by training a network $F$ with parameters $\theta$ that directly predicts the flow as $Y=F(X;\theta)$.

This work additionally learn the conditional probability density $p(Y|X;\theta)$

in Flow cases, there is a commonly performed method

不确定性预测：uncertainty prediction

Global correlation layer $$ C_G(f^r, f^q){ijkl} = (f{ij}^r)^\mathsf{T}f_{ij}^q, (i,j),(k,l) \in {1, \dots, H} \times {1, \dots, W} $$ 这是一个4D的张量

Local correlation layer，就仅仅对（i,j）的邻域去scalar product $$ C_L(f^r, f^q){ijkl} = (f{ij}^r)^\mathsf{T}f_{ij}^q, (i,j)\in {1, \dots, H} \times {1, \dots, W}, (k,l) \in {-R,\dots, R} $$

$$ w^* = \arg\min_w $$