This research aims to improve the quality of life for visually impaired individuals by identifying obstacles in an indoor environment using a solution approach. The approach uses a Convolutional Neural Network (CNN) to extract features and detect objects from real-time video. A head-mounted image acquisition device detects objects and provides audio information to the visually impaired. The system processes live video streams frame-by-frame, processing each frame as separate images. The authors incorporate additional variables into a novel two-step iterative approach to solve complex computer vision problems. The proposed method improves computational efficiency and accuracy, opening up promising avenues for future research. The paper also presents a new mathematical formulation of curve and surface reconstitute algorithms by introducing auxiliary variables. Moving object detection is crucial for intelligent video monitoring systems, as it allows for accurate extraction of foreground objects. This paper aims to detect real moving objects from un-stationary backgrounds, limiting false negatives and achieving maximum application independence. The model and motion of the target objects are assumed to be unknown. Introduce a new mathematical formulation for curve and surface reconstruction algorithms, introducing auxiliary variables and minimizing energy. This approach transforms an implicit data constraint into an explicit convex reconstruction problem, simplifying it. The formulation also allows for more precise parameter settings, ensuring convergence to a minimum. And demonstrate the properties and results of this new auxiliary problem, mainly when the potential is a function of the distance to the closest feature point.