PySR

对于定量神经病理学数据，假设数据分布为泊松分布，对于基因表达数据，假设数据分布为零膨胀负二项分布，对于染色质可及性数据，假设数据分布为伯努利分布，对于空间转录组数据，假设数据分布为负二项分布

ANDI

# Kan

其本质是多层的Kolmogorov网络
一般而言，Kan隐藏层节点数量为$2n+1$，但是原始的两层结构并没有限制其激活函数是否光滑。有时，这些激活函数可能需要用到非常非光滑甚至有分形行为的“病态”函数来表达。这就失去了现实意义。这在实际应用中意义不大。因此，加深网络的直观理由是希望那些原本无法被光滑表示的函数能够被光滑地表示。


$\exp(\sin(x_1^2+x_2^2)+\sin(x_3^2+x_4^2))$,对于这种函数，一般需要构建三层神经网络，第一层学习平方运算，第二层学习sin函数运算，第三层学习指数运算。

**对于函数空间问题**
- 当前的理论假设所有函数都是光滑的
- 乘法运算：可以通过公式$xy = (x+y)^2-(x^2+y^2)$实现
- 除法运算：$\frac{x}{y}=e^{\ln(x)-\ln(y)}$
- 特殊函数：贝塞尔函数.....
- 阶段转换函数：绝对值函数？双曲正切函数？
- 越复杂的函数需要过多层的KAN网络，每一层表示一类运算

## B样条(B-spline)插值

B样条（B-spline）基函数是一组分段多项式函数，用于构造平滑的曲线或函数逼近。

- 节点向量（Knots）：一系列非递减的实数$t_0,t_1,\cdots,t_{n+k}$，其中$n$是基函数的数量，$k$是样条的阶次。
- 阶次$k$：决定了样条的平滑程度的多项式的次数

### 递归定义

- B样条基函数$B_{i,k}(x)$通过Cox-de Boor递归公式定义

- 初始条件(零阶基函数)

$$B_{i,1}(x)=\begin{cases}1& t_i\leq x < t_{i+1}\\0& \text{other}\end{cases}$$

- 递归公式(高阶基函数)

$$B_{i,k}(x)=\frac{x-t_i}{t_{i+k-1}-t_i}B_{i,{k-1}}(x)+\frac{t_{i+k}-x}{t_{i+k}-t_{i+1}}B_{i+1,k-1}(x)$$

### 导数

$$\frac{\partial\phi(x)}{\partial x}=\underset{i=1}{\overset{n}{\sum}} c_i\frac{\partial B_{i,k}(x)}{\partial x}$$

**导数的递归公式**

$$\frac{\partial B_{i,k}(x)}{\partial x}=(k-1)\left(\frac{B_{i,k-1}(x)}{t_{i+k-1}-t_i} - \frac{B_{i+1,k-1}(x)}{t_{i+k}-t_{i+1}} \right)$$

**节点向量获取方法**

- 均匀节点向量：简单易行，适用于数据分布均匀的情况。
- 数据驱动节点向量：根据数据分布设置节点，更好地适应数据特性。
- 自适应节点向量：将节点位置作为可训练参数，提高模型灵活性。

- 平衡模型复杂度和性能：节点数量和可训练参数的增加可能导致过拟合，需要适当正则化。
- 确保数值稳定性：在优化节点位置时，要防止数值不稳定和训练过程的震荡。
- 合理初始化和预处理：良好的初始节点位置和数据预处理有助于模型的训练和性能提升。

































# Medical Image Segmentation

1. [nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation](https://pubmed.ncbi.nlm.nih.gov/33288961/)
2. [Segment Anything](https://arxiv.org/pdf/2304.02643.pdf)
3. [Segment Anything Model for Medical Image Segmentation: Current Applications and Future Directions](https://arxiv.org/pdf/2401.03495.pdf)
4. [SAM2-UNet: Segment Anything 2 Makes Strong Encoder for Natural and Medical Image Segmentation](https://arxiv.org/pdf/2408.08870)
5. [Surgical SAM 2: Real-time Segment Anything in Surgical Video by Efficient Frame Pruning](https://arxiv.org/pdf/2408.07931)
6. [SAM 2 in Robotic Surgery: An Empirical Evaluation for Robustness and Generalization in Surgical Video Segmentation](https://arxiv.org/pdf/2408.04593)
7. [A Foundation Model for Brain Lesion Segmentation with Mixture of Modality Experts](https://arxiv.org/pdf/2405.10246)




# nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation

## Summary of the nnU-Net Method:
- **nnU-Net** is an automated deep learning-based segmentation method designed specifically for biomedical imaging.
- **Semantic Segmentation**: The paper discusses how semantic segmentation is crucial for both scientific discovery and clinical applications.
- **Challenges in Current Methods**: Existing segmentation methods require significant expertise for task-specific design and configuration, which can be prone to errors, especially in three-dimensional biomedical imaging.
- **Automated Configuration**: nnU-Net addresses this by automating the configuration of the segmentation pipeline, including preprocessing, network architecture, training, and post-processing, making it adaptable to any new dataset without manual intervention.
- **Three Parameter Groups**:
  1. **Fixed Parameters**: Design decisions that do not change between datasets.
  2. **Rule-Based Parameters**: Parameters that depend on the dataset properties.
  3. **Empirical Parameters**: These are learned from the data during the training process.
- **Performance**: The nnU-Net method has been validated across numerous datasets, outperforming many specialized solutions in international biomedical segmentation competitions.

## Methodology:
- **Pipeline Configuration**: nnU-Net collects design decisions into a “pipeline fingerprint” that reflects all the essential information for segmentation. It reduces the design choices to only the necessary ones and infers these using a set of heuristic rules.
- **Training Process**: Networks are trained with deep supervision, meaning additional auxiliary losses are added to the decoder at all but the two lowest resolutions, which helps inject gradients deeper into the network.

## Application:
- nnU-Net is shown to outperform existing methods on a wide range of tasks, indicating that the detailed method configuration has a more significant impact on performance than architectural variations.

## Discussion:
- The paper emphasizes that the success of nnU-Net comes from the careful and systematic method configuration rather than novel architecture or loss functions. This suggests a shift from purely empirical approaches towards more structured and rule-based configurations in deep learning for biomedical imaging.

# Segment Anything

## Introduction:
- **Objective**: Introduces the "Segment Anything Model" (SAM) for generalizable segmentation using prompt-based inputs, enabling zero-shot transfer across data distributions.
- **Key Contributions**:
  1. **Segment Anything Task**: A task aimed at creating a model that can segment any object in any image without task-specific training.
  2. **Segment Anything Model (SAM)**: A model capable of zero-shot segmentation on diverse datasets.
  3. **Segment Anything Dataset (SA-1B)**: The largest dataset with over 1 billion masks from 11 million images.

## Methodology:
- **Data Engine**: A semi-automated pipeline for generating the SA-1B dataset, combining manual annotation with model-assisted labeling.
- **SAM Architecture**: Accepts various prompts (e.g., points, boxes, text) and outputs segmentation masks. Trained on diverse images for wide generalization.

## Results:
- **Performance**: SAM excels in zero-shot performance on tasks like edge *detection and instance segmentation*, often *surpassing* fully supervised models.
- **Scalability**: SA-1B dataset enables SAM to tackle complex and *ambiguous* segmentation tasks.

## Discussion:
- **Generalization**: SAM's strength lies in its ability to generalize across different images and tasks without additional training.
- **Impact**: The release of SAM and SA-1B is expected to advance computer vision by providing robust tools for segmentation and a vast dataset for future research.

## Conclusion:
- **Contribution**: The "Segment Anything" initiative advances the development of generalizable models, reducing the need for task-specific models and annotations.
- **Open Source**: Both SAM and SA-1B are publicly available to promote further research.

# Segment Anything Model for Medical Image Segmentation: Current Applications and Future Directions

## Introduction:
- **Objective**: Explores the application of SAM2 for biomedical images and videos, addressing its potential and challenges in this domain.
- **Key Contributions**:
  1. **Adaptation of SAM2**: Discusses the applicability of SAM2 to biomedical imaging.
  2. **Survey of Efforts**: Reviews recent uses of SAM2 in biomedical segmentation tasks.

## Methodology:
- **Data Challenges**: Highlights differences between natural and medical images that affect segmentation.
- **Model Adaptation**: Emphasizes the need for domain-specific fine-tuning of SAM2.

## Results:
- **Performance Variability**: SAM2’s effectiveness varies across biomedical datasets.
- **Annotation Efficiency**: Shows promise in reducing the annotation workload in biomedical imaging.

## Discussion:
- **Impact**: SAM2 has significant potential in clinical applications, but requires addressing the domain gap.
- **Future Directions**: Advocates for more research in adapting SAM2 to biomedical datasets.

## Conclusion:
- **Contribution**: Highlights opportunities and challenges of using SAM2 in biomedical imaging.
- **Ongoing Research**: Encourages continued research and adaptation efforts for SAM2 in the biomedical field.

# SAM2-UNet: Segment Anything 2 Makes Strong Encoder for Natural and Medical Image Segmentation

## Introduction:
- **Objective**: Introduces SAM2-UNet, utilizing the SAM2 model as a strong encoder for U-shaped segmentation models in natural and medical images.
- **Key Contributions**:
  1. **SAM2-UNet Framework**: Combines SAM2's Hiera backbone with a U-shaped decoder.
  2. **Adapter Integration**: Enables parameter-efficient fine-tuning.

## Methodology:
- **Architecture**: Consists of SAM2’s Hiera encoder, receptive field blocks (RFBs), adapters, and a U-shaped decoder.
- **Loss Function**: Utilizes weighted IoU and binary cross-entropy losses.

## Results:
- **Performance**: Achieves state-of-the-art results across various tasks like camouflaged object detection, salient object detection, marine animal segmentation, mirror detection, and polyp segmentation.

## Discussion:
- **Effectiveness**: Demonstrates strong performance and suggests SAM2-UNet as a new baseline for future research.

## Conclusion:
- **Contribution**: Sets a new standard for segmentation tasks in both natural and medical domains.

# Surgical SAM 2: Real-time Segment Anything in Surgical Video by Efficient Frame Pruning

## Introduction:
- **Objective**: Introduces Surgical SAM 2 (SurgSAM-2), a model for real-time segmentation in surgical videos using Efficient Frame Pruning (EFP).
- **Key Contributions**:
  1. **Efficient Frame Pruning (EFP)**: Manages memory by retaining only the most informative frames.
  2. **Real-time Performance**: Enhances efficiency and segmentation accuracy in surgical video analysis.

## Methodology:
- **Architecture**: Combines EFP with SAM2 for improved real-time processing.
- **Application**: Tailored for surgical video segmentation.

## Results:
- **Performance**: Achieves a 3x increase in FPS and state-of-the-art segmentation performance.

## Discussion:
- **Impact**: Makes real-time surgical video segmentation feasible.
- **Future Directions**: Potential for further optimization and broader applications.

## Conclusion:
- **Contribution**: Sets a new standard for surgical video segmentation, enhancing both efficiency and accuracy.

# Summary of the "Prompt-Enhanced SAM for Medical Image Segmentation: A Detailed Analysis" Paper

## Introduction:
- **Objective**: The paper explores the use of a prompt-enhanced Segment Anything Model (SAM) for medical image segmentation, improving upon the base SAM architecture.
- **Key Contributions**:
  1. **Prompt-Enhanced Approach**: Integrates specific prompts to enhance SAM’s performance in medical imaging.
  2. **Medical Domain Focus**: Tailors the SAM architecture for various medical imaging tasks, addressing domain-specific challenges.

## Methodology:
- **Architecture**: Combines SAM with domain-specific prompts to improve segmentation accuracy.
- **Application**: Focused on critical medical imaging tasks, like tumor and organ segmentation.

## Results:
- **Performance**: Demonstrates superior accuracy and efficiency in segmenting medical images compared to standard models.

## Discussion:
- **Impact**: The proposed model significantly improves segmentation in medical imaging, which could enhance clinical decision-making.
- **Future Directions**: Calls for further refinement of prompt strategies and exploration in other medical imaging domains.

## Conclusion:
- **Contribution**: Establishes a robust foundation for using prompt-enhanced SAM in medical image segmentation, paving the way for advanced clinical applications.