Abstract: Security methods and apparatus. In one example, a method includes detecting a motion event in a scene using a motion detector, based on detecting the motion event, acquiring a plurality of images of the scene using an image capture device, applying a motion detection process to the plurality of images to detect motion in the scene, applying an object detection process to at least one of the images to detect an object in the scene, pairing the motion with the object to locate a moving object, identifying the moving object as an unrecognized object, and based at least in part on identifying the moving object as an unrecognized object, triggering a video recording of the scene using the image capture device.

Abstract: A method is provided. The method includes identifying pixels indicative of motion based on a frame of pixels; selecting a region of interest within the frame based on the pixels indicative of motion, the region being a subset of the frame of pixels and including the pixels indicative of the motion; identifying an object based on pixels within the region; and issuing an alarm in response to the region including both the object and the pixels indicative of motion.

Abstract: Motion detection is performed using layouts of different resolutions. A plurality of layouts at different resolutions are generated using an image. Sets of bounding boxes for the different layouts are generated based on areas indicative of motion for the respective layout. The different sets of bounding boxes are combined and motion of one or more objects represented in the image is detected based on combined set of bounding boxes.

Abstract: A method of fast matrix multiplication and a method and apparatus for fast solving of a matrix equation are disclosed. They are useful in many applications including image blurring, deblurring, and 3D image reconstruction, in 3D microscopy and computer vision. The methods and apparatus are based on a new theoretical result—the Generalized Convolution Theorem (GCT). Based on GCT, matrix equations that represent certain linear integral equations are first transformed to equivalent convolution integral equations through change of variables. Then the resulting convolution integral equations are evaluated or solved using the Fast Fourier Transform (FFT). Evaluating a convolution integral corresponds to matrix multiplication and solving a convolution integral equation corresponds to solving the related matrix equation through deconvolution. Carrying-out these convolution and deconvolution operations in the Fourier domain using FFT speeds up computations significantly.