  The task of image segmentation is to classify each pixel in the image based
on the appropriate label. Various deep learning approaches have been proposed
for image segmentation that offers high accuracy and deep architecture.
However, the deep learning technique uses a pixel-wise loss function for the
training process. Using pixel-wise loss neglected the pixel neighbor
relationships in the network learning process. The neighboring relationship of
the pixels is essential information in the image. Utilizing neighboring pixel
information provides an advantage over using only pixel-to-pixel information.
This study presents regularizers to give the pixel neighbor relationship
information to the learning process. The regularizers are constructed by the
graph theory approach and topology approach: By graph theory approach, graph
Laplacian is used to utilize the smoothness of segmented images based on output
images and ground-truth images. By topology approach, Euler characteristic is
used to identify and minimize the number of isolated objects on segmented
images. Experiments show that our scheme successfully captures pixel neighbor
relations and improves the performance of the convolutional neural network
better than the baseline without a regularization term.
