This paper proposes a heteroscedastic uncertainty estimation framework for
unsupervised medical image registration. Existing methods rely on objectives
(e.g. mean-squared error) that assume a uniform noise level across the image,
disregarding the heteroscedastic and input-dependent characteristics of noise
distribution in real-world medical images. This further introduces noisy
gradients due to undesired penalization on outliers, causing unnatural
deformation and performance degradation. To mitigate this, we propose an
adaptive weighting scheme with a relative $\gamma$-exponentiated
signal-to-noise ratio (SNR) for the displacement estimator after modeling the
heteroscedastic noise using a separate variance estimator to prevent the model
from being driven away by spurious gradients from error residuals, leading to
more accurate displacement estimation. To illustrate the versatility and
effectiveness of the proposed method, we tested our framework on two
representative registration architectures across three medical image datasets.
Our proposed framework consistently outperforms other baselines both
quantitatively and qualitatively while also providing accurate and sensible
uncertainty measures. Paired t-tests show that our improvements in registration
accuracy are statistically significant. The code will be publicly available at
https://voldemort108x.github.io/hetero_uncertainty/.

该研究论文提出了一种用于无监督医学图像配准的异方差不确定性估计框架，通过建模异方差噪声并采用自适应加权方案与相对 γ 指数化信噪比 (SNR) 结合的位移估计器，提高了位移估计的准确性，并在定量和定性上优于其他基准方法。

噪声医学图像的概率无监督登记的异方差不确定性估计

Heteroscedastic Uncertainty Estimation for Probabilistic Unsupervised  Registration of Noisy Medical Images

Displacement estimation is a critical step of virtually all Ultrasound
Elastography (USE) techniques. Two main features make this task unique compared
to the general optical flow problem: the high-frequency nature of ultrasound
radio-frequency (RF) data and the governing laws of physics on the displacement
field. Recently, the architecture of the optical flow networks has been
modified to be able to use RF data. Also, semi-supervised and unsupervised
techniques have been employed for USE by considering prior knowledge of
displacement continuity in the form of the first- and second-derivative
regularizers. Despite these attempts, no work has considered the tissue
compression pattern, and displacements in axial and lateral directions have
been assumed to be independent. However, tissue motion pattern is governed by
laws of physics in USE, rendering the axial and the lateral displacements
highly correlated. In this paper, we propose Physically Inspired ConsTraint for
Unsupervised Regularized Elastography (PICTURE), where we impose constraints on
the Poisson's ratio to improve lateral displacement estimates. Experiments on
phantom and in vivo data show that PICTURE substantially improves the quality
of the lateral displacement estimation.

本研究提出了一种基于物理启发的无监督正则化弹性成像方法，通过对材料泊松比的约束，改善了横向位移估计的质量。实验结果表明，该方法可以显著提高弹性成像中横向位移的估计质量。

基于物理模型的无监督正则化超声弹性成像约束

Physically Inspired Constraint for Unsupervised Regularized Ultrasound Elastography

As camera-based documents are increasingly used, the rectification of
distorted document images becomes a need to improve the recognition
performance. In this paper, we propose a novel framework for both rectifying
distorted document image and removing background finely, by estimating
pixel-wise displacements using a fully convolutional network (FCN). The
document image is rectified by transformation according to the displacements of
pixels. The FCN is trained by regressing displacements of synthesized distorted
documents, and to control the smoothness of displacements, we propose a Local
Smooth Constraint (LSC) in regularization. Our approach is easy to implement
and consumes moderate computing resource. Experiments proved that our approach
can dewarp document images effectively under various geometric distortions, and
has achieved the state-of-the-art performance in terms of local details and
overall effect.

通过全卷积神经网络 (FCN) 估算像素位移来实现文档图像矫正与背景消除，我们提出了一种新的框架来估算像素位移，训练 FCN 通过回归失真文档的位移，我们提出了局部平滑约束（LSC）作为正则化以控制平滑度。实验表明，我们的方法在各种几何失真下可有效去除文档图像畸变，并在局部细节和总体效果上取得了最先进的性能。