## 2 Biomedical Image Segmentation
### The Limitation of Probabilistic Models in Biomedical Image Segmentation  
Probabilistic models, despite their strengths in capturing uncertainty and variability, are not without criticisms, especially when applied to biomedical image segmentation. Two key challenges are their sensitivity to noise and limitations in handling complex anatomical structures.  
Probabilistic models, including GMMs and HMMs, can be sensitive to noise in biomedical images. Noise, arising from various sources such as acquisition processes, instrumentation, or biological variability, introduces variations in pixel intensities that may not be adequately modeled by the assumed probability distributions. This sensitivity can lead to inaccuracies in segmentation results, impacting the reliability of identified structures [31].  
Various strategies have been proposed to mitigate sensitivity to noise. These include pre-processing techniques such as image smoothing or denoising to enhance the signal-to-noise ratio before applying probabilistic models. Additionally, advanced probabilistic models that explicitly consider noise characteristics, such as robust variants of GMMs, have been explored to enhance the robustness of segmentation in noisy environments.  
Probabilistic models may face limitations in accurately segmenting complex anatomical structures with irregular shapes and intricate boundaries. Traditional models, such as GMMs, assume a certain level of simplicity in the underlying probability distributions, which may not adequately capture the nuanced variations in intensity profiles present in intricate anatomical regions [41].  
Addressing the challenge of handling complex anatomy involves adopting more sophisticated probabilistic models or combining probabilistic approaches with other segmentation techniques. Advanced models, such as non-parametric Bayesian models, provide a more flexible representation of underlying probability distributions, accommodating the intricacies of complex anatomies. Hybrid approaches, incorporating machine learning or deep learning components alongside probabilistic models, have demonstrated improved segmentation accuracy for complex structures.  
While probabilistic models face criticisms, there is an opportunity for improvement through integration with advanced computational techniques. Combining probabilistic models with deep learning architectures allows for a more data-driven and adaptive approach to biomedical image segmentation. Deep learning methods can learn complex hierarchical features directly from the data, potentially mitigating some of the limitations associated with probabilistic models [35].  
Challenges in integrating advanced computational techniques include the need for large annotated datasets, potential overfitting, and increased computational complexity. Striking a balance between the interpretability of probabilistic models and the representational power of deep learning is an ongoing research endeavor.  
In conclusion, while probabilistic models like GMMs and HMMs offer valuable tools for biomedical image segmentation, they are not immune to criticisms. Sensitivity to noise and challenges in handling complex anatomy highlight the need for continued research to enhance the robustness and adaptability of these models. Strategies such as noise reduction, utilization of advanced probabilistic models, and integration with deep learning hold promise for addressing these criticisms and advancing the state of the art in biomedical image segmentation. As the field continues to evolve, a synergistic approach that combines the strengths of probabilistic models with emerging computational techniques is likely to pave the way for more accurate and reliable segmentation outcomes in complex biomedical imaging scenarios.