## 1 Introduction
To resolve the issues of image compression, state-of-the-art techniques based on the frameworks of wavelet transform [33; 34; 35; 36; 37] and neural networks [38; 39; 40; 41; 42; 43; 44] in probabilistic perspectives have brought about their fruitful achievements. The wavelet-transform-based techniques usually use a specific wavelet technique based on the Mallat filter [37] to decompose images of interest into a dyadic decomposition structure. Then, those generated sub-band samples become easy to be quantized and coded. Technically, the main features of the downsize images can be easily further extracted for image compression by partitioning the employed images into hierarchical trees. Among the relevant techniques, the method of embedded block coding with optimized truncation [33] and the algorithm of spatial partitioning of images into hierarchical trees [34] are two typical and popular techniques of image compression in practical applications. Neural-network-based methods provide another avenue for image compression. The technique of recurrent neural networks (RNN) and the long-short-term memory (LSTM) method can be applied to the problems of compression ratios on images of arbitrary size [38; 39]. The meshes over an image of interest only need to be trained once, and re-training is unnecessary while changing the size of the image or the compression ratio. The reconstruction accuracy only relates to the connectivity of intra-mesh and the representation code. Then, the well-trained encoder model can have good efficiency. Experimentally, the Google research team provided their study result using the RNN with LSTM [38; 39]. Improvements of 8.8% area under the rate-distortion curve and about 33 dB of peak signal to noise ratio guarantee the quality of their proposed method. The technique of convolutional neural network (CNN) is also a powerful method in the field of machine vision. Since the AlexNet won the champion of ILSVRC 2012 [45], the CNN technique has replaced conventional hand-crafted feature extraction and classifiers. The CNN technique provides an end-to-end approach [42; 43] and elegantly reinforces the accuracy of pattern recognition and the efficiency of image compression [44; 45]. Despite the outstanding performance, the mentioned techniques of image compression also have some intrinsic problems embedded in their mathematical frameworks. First, most mentioned techniques were developed to focus on the compression of large-scale imagery. Therefore, these techniques would fail to reconstruct small-scale or low-resolution images mathematically. Secondly, most of the assumptions of those proposed techniques could not match the real image data structures. For instance, these techniques assume that the high-resolution image will have more high-frequency information. Last, the worst problem is that the mentioned technique would cost more CPU estimation time in training processes due to their high computational complexity [46; 47]. To the purpose of medical image segmentation, the edge-based active contour models [5; 9; 10; 48] and the machine learning methods [5; 9; 32; 48; 50; 51; 52; 53] are two main solutions regarding the medical image segmentation. The edge-based active contour models were developed based on the concept of energy minimization, starting with the well-known snake model [54; 55]. Among the energy minimization approaches, the level set methods have received much attention [56; 57; 58; 59; 60]. A planar closed curve is defined to execute the active model on medical images of interest, using a zero-level set of a level set function. Then, a level set equation is used to estimate the evolution of the level set function. The level set equation often includes an edge stop function with a Gaussian kernel, a potential function, and several energy parameters regarding the distance regularization energy, the length terms, and the area term [48]. Additionally, the energy parameters always need to be estimated by experiments or simulations.