This paper presents a novel human home activity recognition (HAR) system designed for smart homes that utilize depth silhouettes and ℜ transformation to continuously recognize the daily activities of the elderly and disabled in an indoor environment for better lifecare and e-healthcare services. Previously, ℜ transformation has been applied only on binary silhouettes that provide only the shape information of human activities. In this work, ℜ transformation was utilized on depth silhouettes such that the depth information of human body parts could be used in HAR in addition to the shape information. In ℜ transformation, 2D directional projection maps are computed via Radon transform, and then 1D feature profiles, which are translation and scaling invariants. Then, by applying the principle component analysis and linear discriminant analysis, the prominent activity features would be extracted. Finally, Hidden Markov Models would be used to train and recognize daily home activities. The results showed a mean recognition rate of 96.55% over ten typical home activities, whereas the same system utilizing binary silhouettes could achieve only 85.75%. The proposed methodology should be useful in designing and developing a compact HAR system that can be practically used in a smart environment including smart home for the care of the elderly, infirmed or disabled people.