# Adaptive Voxel-Weighted Loss Using L1 Norms in Deep Neural Networks for Detection and Segmentation of Prostate Cancer Lesions in PET/CT Images

arXiv: https://arxiv.org/abs/2502.02756 · HTML: https://mlsanity.com/paper/2502.02756/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Generalised Dice overlap as a deep learning loss function for highly unbalanced segmentations](https://mlsanity.com/paper/1707.03237/) (2017)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [3D MRI brain tumor segmentation using autoencoder regularization](https://mlsanity.com/paper/1810.11654/) (2018)
- [The Importance of Skip Connections in Biomedical Image Segmentation](https://mlsanity.com/paper/1608.04117/) (2016)
- [Gradient Harmonized Single-stage Detector](https://mlsanity.com/paper/1811.05181/) (2018)
- [SAM-Med3D: Towards General-purpose Segmentation Models for Volumetric Medical Images](https://mlsanity.com/paper/2310.15161/) (2023)
- [Unified Focal loss: Generalising Dice and cross entropy-based losses to handle class imbalanced medical image segmentation](https://mlsanity.com/paper/2102.04525/) (2021)
- [Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation](https://mlsanity.com/paper/1805.02798/) (2018)
- [AnatomyNet: Deep Learning for Fast and Fully Automated Whole-volume Segmentation of Head and Neck Anatomy](https://mlsanity.com/paper/1808.05238/) (2018)
- [Bridging the Gap Between Vision Transformers and Convolutional Neural Networks on Small Datasets](https://mlsanity.com/paper/2210.05958/) (2022)
- [Bridging Category-level and Instance-level Semantic Image Segmentation](https://mlsanity.com/paper/1605.06885/) (2016)
- [blob loss: instance imbalance aware loss functions for semantic segmentation](https://mlsanity.com/paper/2205.08209/) (2022)
- [Do We Really Need Dice? The Hidden Region-Size Biases of Segmentation Losses](https://mlsanity.com/paper/2104.08717/) (2021)
- [Towards Flexible Inductive Bias via Progressive Reparameterization Scheduling](https://mlsanity.com/paper/2210.01370/) (2022)
- [Comprehensive framework for evaluation of deep neural networks in detection and quantification of lymphoma from PET/CT images: clinical insights, pitfalls, and observer agreement analyses](https://mlsanity.com/paper/2311.09614/) (2023)
- [Segmentation of Prostate Tumour Volumes from PET Images is a Different Ball Game](https://mlsanity.com/paper/2407.10537/) (2024)
- [How to Segment in 3D Using 2D Models: Automated 3D Segmentation of Prostate Cancer Metastatic Lesions on PET Volumes Using Multi-angle Maximum Intensity Projections and Diffusion Models](https://mlsanity.com/paper/2407.18555/) (2024)

## Built on by (most cited first, 1 of 1)

- [Comprehensive Evaluation of Quantitative Measurements from Automated Deep Segmentations of PSMA PET/CT Images](https://mlsanity.com/paper/2504.16237/) (2025)

## Abstract (arXiv)

Accurate automated detection of recurrent prostate cancer in PSMA PET/CT scans is challenging due to heterogeneous lesion size, activity, anatomical location, and intra- and inter-class imbalances. Conventional deep learning loss functions often produce suboptimal optimization, as gradients are dominated by easy background voxels or extreme outliers. To address this, we propose L1-weighted Dice Focal Loss (L1DFL), which harmonizes gradient magnitudes across voxels using L1 norms to adaptively weight samples based on classification difficulty, resulting in well-calibrated predictions with a bimodal separation between correct and incorrect predictions. We trained three 3D convolutional networks (Attention U-Net, SegResNet, U-Net) and a transformer-based UNETR model on 380 PSMA PET/CT scans. PET and CT volumes were concatenated as input to the models. We also fine-tuned SAM-Med3D foundation model with the different loss functions and evaluated their performance. Across architectures, L1DFL consistently outperformed Dice Loss (DL) and Dice Focal Loss (DFL), achieving at least a 4% improvement in Dice Similarity Coefficient. F1 scores were higher by 6% and 26% compared to DL and DFL, respectively. While DFL produced more false positives and DL struggled with larger lesions, L1DFL achieved balanced detection, minimizing false detections while maintaining high true positive rates. The gradient harmonization mechanism ensured robustness across varying lesion sizes, volumes, and spread. The code is publicly available at: https://github.com/ObedDzik/pca_segment.git.