Given an object of interest that evolves in time, one often wants to detect possible changes in its properties. The first changes may be small and occur in different scales and it may be crucial to detect them as early as possible. Examples include identification of potentially malignant changes in skin moles or the gradual onset of food quality deterioration. Statistical scale-space methodologies can be very useful in such situations since exploring the measurements in multiple resolutions can help identify even subtle changes. We extend a recently proposed scale-space methodology to a technique that successfully detects such small changes and at the same time keeps false alarms at a very low level. The potential of the novel methodology is first demonstrated with hyperspectral skin mole data artificially distorted to include a very small change. Our real data application considers hyperspectral images used for food quality detection. In these experiments the performance of the proposed method is either superior or on par with a standard approach such as principal component analysis.