On multidimensional velocity filter banks for video-based motion analysis of world-coordinate objects

Multidimensional digital filters for point-target detection in cluttered infrared scenes

“…Clearly there are a large number of possible design permutations here, especially when it is appreciated that the process of frequency estimation in each dimensions is separable and that a different approach may be adopted in each dimension 31 ; however, this paper deals with only one approach, which is arguably the simplest from a conceptual perspective. A direct-digital-design approach is adopted to avoid the need for s-plane analysis and unforeseen artifacts associated with the discretization of an analog prototype 9,10,11 . Like the approach taken in Ref.…”

“…Three-dimensional (3-D) filters provide a convenient mechanism for the integration of the spatial and temporal axes into a coherent framework and offer a wide range of design alternatives 9 finite impulse response (FIR) or infinite impulse response (IIR), recursive or non recursive, with nominal pass-bands of arbitrary shape (e.g. plane, beam, wedge/fan 9,10,11 , pyramid 12 , cone 13 , donut 14 , etc.). While these filters have proven to be very effective in novel imaging, audio/acoustic and radio-frequency applications 9 , they offer rapidly diminishing returns when they are applied to the problem of foreground enhancement and background cancellation in infrared sensors, because typical scenes of interest are highly non-stationary, due to object edges/boundaries for instance.…”

Digital Filter Designs for Recursive Frequency Analysis

“…and 𝐻 ana,𝑘 (𝑧) = 1 1+𝑎 𝑘 𝑧 −1 (11) where 𝑎 𝑘 = −𝑒 𝑗𝜔 𝑘 and 𝑟 = 𝑒 𝜎𝑀 (12) with 𝜎 being a forgetting-factor (𝜎 < 0), which is multiplied here by a factor of 𝑀 to ensure that the pole radius is the same as the filters described in the next section. This technique does not use the outer feedback loop (𝑐 fbk = 0) thus the use of the synthesis factors (𝑐 syn ) is optional.…”