An embodiment of a video-surveillance method comprising: activating a video camera for acquiring, for a surveillance system comprising the aforesaid video camera, a digital video sequence of images of a scene to be surveyed, detecting given events and transmitting to a remote center images of the aforesaid digital video sequence of images acquired according to the result of the aforesaid operation of event detection. An embodiment includes: executing an operation of extraction of key frames on the aforesaid digital video sequence of images for composing a visual storyboard, detecting given events on the basis of data supplied by one or more event sensors for generating an event signal, controlling operating states assumed by the aforesaid key-frame-extraction operation as a function of the values assumed by the aforesaid event signal, and transmitting the aforesaid visual storyboard to the aforesaid remote center.