# Review — Shape-Aware Organ Segmentation by Predicting Signed Distance Maps

**Better Segmentation by Predicting Signed Distance Maps (SDM)**

Shape-Aware Organ Segmentation by Predicting Signed Distance Maps,SDM, by Pennsylvania State University, Tencent Hippocrates Research Lab, and Shandong Cancer Hospital and Institute, Over 60 Citations (Sik-Ho Tsang @ Medium)

2020 AAAI

Medical Imaging, Medical Image Analysis, Image Segmentation, Multi-Task Learning

**Existing approaches**often produce results that**do not capture the overall shape**of the target organ and often**lack smoothness**.- By converting the segmentation task into
**predicting an Signed Distance Map (**SDM),**better smoothness and continuity in shape**are obtained. Specifically, an**approximated Heaviside function**to train the model by**predicting SDMs and segmentation maps simultaneously**.

# Outline

**SDM Learning****Results**

**1. SDM Learning**

## 1.1. Model Architecture

**3D U-Net****variant**with**6 downsampling operations**, with the**largest receptive field has size 64³**.- The model contains
**6 skip connections between different scales of feature maps**. **Leaky ReLU**is used instead of ReLU.- The deconvolution is replaced by
**trilinear upsampling followed by convolution.** - More importantly,
**Group Normalization**

## 1.2. Standard Loss Function

**Dice loss**is used as, to measure the overlapping between ground-truth and predicted segmentation maps and is defined as:*Lseg*

- where
*N*is the number of classes,*t*denotes the*t*-th organ class.*yt*and*pt*represent the ground-truth annotation and model prediction, respectively.

## 1.3. SDM Learning

- Given a target organ and
**a point**, the*x*in the 3D medical image**Signed Distance Map (SDM) which maps**is defined as:*R*³ to*R*

- where
represents the*S***surface**of the target organ,, respectively. In other words, the absolute value of SDM indicates the distance from the point to the closest point on organ surface, while the sign indicates either inside or outside the organ. Note that the zero distance or zero level set means that the point is on the surface of the organ.*Ωin*and*Ωout*denote the region inside and outside the target organ

- The
**ground-truth SDM**is**approximated using Danielsson’s algorithm (Danielsson 1980)**based on the ground-truth segmentation map. - (Please read details of Danielsson’s algorithm form lecture notes by Stanford University.)
is*Φ*(*x*)**further normalized**to be in the**range [-1, 1]**for each input image and use the**tanh**activation in the**output**layer. The normalization is done**by dividing the SDM by the maximum positive value for points outside the organ**, or**by the minimum negative value for points inside the organ.**- The Heaviside function is used for generating segmentation map, but it is not differentiable.
- A
**smooth approximation**to the**Heaviside****function**is proposed, which is defined as:

- where
controls the*k***steepness of the curve and closeness to the original Heaviside function**, larger*k*means closer approximation. due to the fact that such value guarantees around 99.9% overlapping between converted segmentation map and the original segmentation map.*k*=1500

- Sole L1 loss will have unstable training. Thus,
**L1 loss**is**combined**with the**proposed regression loss**based on a product that is defined as:

- where
represents the*yt***ground-truth SDM**anddenotes the*pt***predicted SDM**. The**intuition**behind taking the product of prediction and ground-truth is that we want to**penalize the output SDM for having the wrong sign**. - The
**total loss**is:

- where
*λ*=10.

# 2. Results

## 2.1. Authors’ Collected Hippocampus Segmentation Dataset

The proposed

jointing training with SDM and segmentation mapachievesbest performancesin all evaluation metrics.

**The learned SDM with only SDM training**obtains**smoothest contours**, while the**joint training**of SDM and segmentation map**predicts more accurate organ boundary**. Overall, they both preserve the shape of hippocampus and align well with the ground-truth SDM.

Segmentation by

jointly training with SDM and binary map supervisiongetbest performances.

## 2.2. MICCAI Head and Neck Auto Segmentation Challenge 2015 Dataset

- For
**both Dice and HD95**, the proposed methods**improve upon previous state-of-the-arts significantly**, especially in small organs such as Chiasm, left and right Optic Nerve. - Compared with the proposed backbone network trained with Dice loss only, the
**joint training**model has a**slightly lower Dice score**, while**still outperforms other state-of-the-art methods by a large margin**.

## 2.3. Ablation Study

- The proposed backbone network
**trained with only segmentation prediction**generally performs well, however, it**produces some isolated false positives far away from the actual organ**. - The backbone network
**trained with only SDM prediction**has smooth outputs, but**does not converge on the small organs**. - The
**joint****training**with the proposed SDM loss**converges well**on all organs and**preserves continuous shape**.

- The backbone network trained with the
**proposed loss**achieves**best scores in all evaluation metrics.**

While the network needs to predict the segmentation and SDM, it is a kind of **multi-task learning**.

## Reference

[2020 AAAI] [SDM]

Shape-Aware Organ Segmentation by Predicting Signed Distance Maps

## 4.2. Biomedical Image Segmentation

**2015** … **2020** [MultiResUNet] [UNet 3+] [Dense-Gated U-Net (DGNet)] [Non-local U-Net] [SAUNet] [SDM] **2021 **[Expanded U-Net]