Barrett's esophagus (BE) is a premalignant condition that has an increased risk to turn into esophageal adenocarcinoma. Classification and staging of the different changes (BE in particular) in the esophageal mucosa are challenging since they have a very similar appearance. Confocal laser endomicroscopy (CLE) is one of the newest endoscopy tools that is commonly used to identify the pathology type of the suspected area of the esophageal mucosa. However, it requires a well-trained physician to classify the image obtained from CLE. An automatic stage classification of esophageal mucosa is presented. The proposed model enhances the internal features of CLE images using an image filter that combines fractional integration with differentiation. Various features are then extracted on a multiscale level, to classify the mucosal tissue into one of its four types: normal squamous (NS), gastric metaplasia (GM), intestinal metaplasia (IM or BE), and neoplasia. These sets of features are used to train two conventional classifiers: support vector machine (SVM) and random forest. The proposed method was evaluated on a dataset of 96 patients with 557 images of different histopathology types. The SVM classifier achieved the best performance with 96.05% accuracy based on a leave-one-patient-out cross-validation. Additionally, the dataset was divided into 60% training and 40% testing; the model achieved an accuracy of 93.72% for the testing data using the SVM. The presented model showed superior performance when compared with four state-of-the-art methods. Accurate classification is essential for the intestinal metaplasia grade, which most likely develops into esophageal cancer. Not only does our method come to the aid of physicians for more accurate diagnosis by acting as a second opinion, but it also acts as a training method for junior physicians who need practice in using CLE. Consequently, this work contributes to an automatic classification that facilitates early intervention and decreases samples of required biopsy.