# MDA-Unet: A Multi-Scale Dilated Attention U-Net for Medical Image Segmentation
## 3 Proposed Model
### Hybrid Hierarchical Dilated Convolution Module (HHDC)  
The encoder path progressively reduces the resolution of the input feature map, which misses the details of small objects that are even hard to recover with skip connections, reducing the prediction produced by each unit. Since contextual information is critical in disambiguating local cues [34], then the reduction in the receptive field is an undesirable price to pay for the segmentation of the objects. In addition, the segmentation task is challenging when the object is very small or when the background dominates the image and suppresses the object's signal [35]. Therefore, dilated convolution is beneficial in enlarging the receptive field to compensate for the reduction in feature maps induced by the max-pooling operation applied along the encoder path of the U-Net. Dilated convolution [36] is a special form of standard convolution in which the alignment of kernel weights is expanded by a dilation rate which broadens the field of view of the filters. Thereby, using the dilation rate, we can adjust the filter's field of view to capture multi-scale context information. For example, in dilated convolution, the receptive field of a 3 \(\times\) 3 dilated convolution with a dilation rate of 3 resembles the receptive field of a standard 5 \(\times\) 5 convolution. So, dilated convolution increases the receptive field at no additional computation since only n \(\times\) n pixels participate in the convolution operation. Dilated convolution is applied over a two-dimensional feature map \(x\), where for each location \(i\) on the output \(y\) and kernel size \(k\), a filter \(w\) is applied as defined in [36]:  
\[y[i]=\sum_{k}x[i+dk]w[k] \tag{5}\]  
where the dilation rate \(d\) is equivalent to the stride with which the input signal is sampled. This process resembles convolving the input \(x\) with the up-sampled filters produced by inserting _(d-1)_ zeroes between two consecutive filter values along each spatial dimension. Despite the efficiency of dilated convolution in increasing the receptive field, the segmentation mask generated by simply one dilation rate throughout the whole model still does not cover all semantic strengths. In addition, progressively increasing the dilation rate fails to capture small local features [37] and introduces unwanted checkboard or gridding artifacts problems. This gridding artifact problem occurs when a feature map has higher-frequency content than the sampling rate of the dilated convolution. This problem results in the inconsistency of local information and hampers the performance of the model [35]. In this regard, [PERSON] et al. [24] proposed parallelized dilated convolution module with different dilation rates, called the atrous spatial pyramid pooling (ASPP). They added it as a decoder module to effectively recover detailed object boundaries. However, the ASPP module learns many parameters and has high memory requirements. In addition, [PERSON] et al. [35] stacked different dilated convolutions to learn contextual representation from the larger receptive field and keep a high spatial resolution until the final segmentation layer. Their model has provided outstanding performance in comparison to other segmentation models. Still, it also has a high memory requirement since it avoids any feature downsampling all the way through the final output. A similar strategy was suggested in [32; 38]. So, the past few models integrated dilated convolution either in a parallelized or a stacked way. However, [PERSON] et al. [39] introduced the efficient spatial pyramid module (ESP), where all of the dilated convolution branches are calculated in parallel, and the branch with the largest dilation rate determines the receptive field. Thus, all of the neurons in each branch share the same field of view, which is still insufficient for scale variation. However, they have concluded that the hierarchical addition of dilated convolutions overcomes the gridding artifacts problem.