In this work, we present an image segmentation algorithm based on the convolutional neural network framework where the scale space theory is incorporated in the course of training procedure. The construction of data augmentation is designed to apply the scale space to the training data in order to effectively deal with the variability of regions of interest in geometry and appearance such as shape and contrast. The proposed data augmentation algorithm via scale space is aimed to improve invariant features with respect to both geometry and appearance by taking into consideration of their diffusion process. We develop a segmentation algorithm based on the convolutional neural network framework where the network architecture consists of encoding and decoding substructures in combination with the data augmentation scheme via the scale space induced by the heat equation. The quantitative analysis using the cardiac MRI dataset indicates that the proposed algorithm achieves better accuracy in the delineation of the left ventricles, which demonstrates the potential of the algorithm in the application of the whole heart segmentation as a compute-aided diagnosis system for the cardiac diseases.