## 1 Introduction  
Artificial intelligence seeks to resemble the capabilities of human beings represented in machines, and it is involved in human fields such as learning, reasoning, adaptation, and self-correction [1]. Within this field, neural networks and image processing are working together in order to generate an accurate classification model, improving learning from the extraction of characteristics and patterns. In addition, the combination of these two fields can be seen applied in regenerative medicine, microbiology, hematology, precision agriculture, and tumor identification, among others. In Reference [2], the authors obtained an improvement in the classification and learning speed of a model that adapts to the characteristics of the input data. The implementation of a convolutional neural network with image processing was performed, in which the results were produced similarly for different types of files and sizes, making use of semantic segmentation by the means of an FCN (fully convolutional network), in which the delimitation and separation of objects was carried out. In Reference [2], the authors had difficulty in improving the resolution of high-quality images and videos from making use of convolutional neural networks; by analyzing each of the contained pixels, it was demonstrated that the implementation of a convolutional layer at the pixel level improved the quality of the images and videos without the need for a great expense of computational resources. This is why the combination of a convolutional neural network (CNN) with image segmentation methods offers the opportunity to optimize the results. The use of an AR-Sandbox [3; 4] is a technique that allows us to close the gap between two-dimensional (2D) and three-dimensional (3D) visualization when projecting a digital topographic map on a landscape of isolated space, improving spatial thinking and modeling skills of people, with the purpose of placing it within the use of early childhood education and rehabilitation through motor therapy, which will be expanded upon in the Image Acquisition Section. For these reasons, this study's motivation is to create contributions towards image recognition based in other fields, such as immersive techniques, through deep learning by the means of convolutional neural networks, making use of hyperparameter optimization and image processing. This article presents the preliminary results of a prediction model implementation that is based on convolutional neural networks for the classification of geometrical figures, contemplating previous steps such as the acquisition of images using the AR-Sandbox augmented reality device, and the processing of these images through segmentation by color-space. The purpose of applying this type of segmentation to the images acquired with the AR-Sandbox is to improve the model performance of the selected convolutional neural network, improving the extraction and identification of characteristics of the geometric figures in the prediction phase, and preserving a high percentage of similarity between the original image and the segmented image. To ensure this aspect, the efficiency of the segmentation method is evaluated by using the similarity coefficients of Jaccard and Sorensen-Dice [5], which will be discussed later, in order to integrate the model with the AR-Sandbox for future applications in rehabilitation and education. The prediction model is made using the Keras neural network library under the TensorFlow framework and the Talos library in order to carry out the configuration, performance, and evaluation of hyperparameter optimization by implementing a Random Search algorithm, through an implementation made in Python. Additionally, the Talos library works with any Keras model [5]. The rest of the article is organized as follows. Section 2 consists of the background, where works related to the topics to be developed are discussed.