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Convolution: Math, Graphics, and Discrete Signals

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...

Assumptions of Survival Analysis

Assumptions of Survival Analysis

Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Convolution Properties II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Convolution Properties I

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

Introduction To Survival Analysis

Introduction To Survival Analysis

Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
The primary goal of survival analysis is to estimate survival time—the time...

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相关实验视频

Updated: Jul 13, 2025

A Swin Transformer-Based Model for Thyroid Nodule Detection in Ultrasound Images

A Swin Transformer-Based Model for Thyroid Nodule Detection in Ultrasound Images

Published on: April 21, 2023

使用卷积相关视力转换器的不确定性可解释的生存分析.

Zhihao Tang¹, Li Liu², Yifan Shen¹

¹Key Laboratory of Trustworthy Distributed Computing and Service (MoE), Beijing University of Posts and Telecommunications, Beijing, China.

Computerized medical imaging and graphics : the official journal of the Computerized Medical Imaging Society

|October 15, 2023

概括

此摘要是机器生成的。

本研究介绍了一种可解释的视觉转换器模型,用于使用整个幻灯片图像 (WSI) 预测癌症存活率. 该模型处理完整的WSIs以提高准确性,并提供可解释性,帮助临床决策.

关键词:

可以解释的可解释性.组织病理图像组织病理图像对生存分析的分析.变压器变压器变压器不确定性不确定性

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A Swin Transformer-Based Model for Thyroid Nodule Detection in Ultrasound Images

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科学领域:

数字病理学数字病理学
计算瘤学是一种计算瘤学.
精准医学是一门精准的医学.

背景情况:

整体幻灯片图像 (WSIs) 对于癌症诊断至关重要,但由于它们的大小,会带来计算挑战.
现有的模型经常使用WSIs的子集,可能会丢失重要的形态信息.
提高模型可解释性对于临床采用和对人工智能驱动预测的信任至关重要.

研究的目的:

使用完整的WSIs开发一种可解释的癌症诊断生存预测模型.
解决与大规模WSI处理相关的计算挑战.
提高基于人工智能的生存预测的准确性和可解释性.

主要方法:

一个基于视觉变压器架构的新可解释的生存预测模型.
使用双通道卷积层来处理整个WSIs.
纳入 aleatoric 不确定性来量化模型的限制.
开发一种后期的方法来识别突出的图像特征和补丁.

主要成果:

拟议的模型有效地处理完整的WSIs,克服计算限制.
与现有方法相比,该模型在癌症存活率预测方面表现出更高的准确性.
可解释性功能成功地识别了关键的图像区域和支持预测的形态特征.
对两大癌症数据集的评估证实了该模型的有效性和增强的可解释性.

结论:

开发的视觉变压器模型为基于WSI的癌症存活率预测提供了一个计算上可行的和可解释的方法.
该模型能够利用完整的WSIs并提供可解释的结果,从而提高其在精密医学中的临床应用潜力.
纳入不确定性估计有助于在癌症诊断和治疗规划方面的可靠决策.