A low-complexity 3D spatio-temporal FIR filter for enhancing linear trajectory signals

Improving the Attenuation of Moving Interfering Objects in Videos Using Shifted-Velocity Filtering

“…3. Here, H(z x , z y , z t ), (z x , z y , z t ) ∈ C 3 , is a 3-D filter having a planar-shaped or wedge-shaped [10], [18] passband, which encompasses the ω t = 0 plane inside N , and S b (z x , z y ) and S f (z x , z y ), (z x , z y ) ∈ C 2 , are 2-D SVS filters. In order to describe the operation of a shifted VF, let us consider a video signal i in (n x , n y , n t ) consisting of an OOI and an MIO having intensities i ooi (n x , n y , n t ) and i mio (n x , n y , n t ), respectively, and moving with velocities [v x , v y ] T and [v x + ∆v x , v y + ∆v y ] T , respectively.…”

“…It is worthwhile to note that the 2-D SVS filters S b (z x , z y ) and S f (z x , z y ) can be implemented with 2-D shifts with no arithmetic operations [10], [18] if ∆x ooi (n t ) and ∆y ooi (n t ) are integer-valued, i.e., the motion is quantized to pixel level, discarding fractions. Because wedge-shaped passbands are robust to motion estimations errors, the effect of this quantization is negligible on the performance of the shifted VFs as verified in [10].…”

“…Motivated by the architecture of the well-known delay-andsum beamformers [15]- [17, ch. 6], a novel architecture for VFs has been proposed in [18] in order to reduce the computational complexity of VFs. In this architecture, the input video signal is first shifted along the two spatial dimensions using a two-dimensional (2-D) spatial variable-shift (SVS) filter prior to subsequent filtering with a 3-D FIR VF having a wedge-shaped passband.…”

“…We refer to the VFs based on this architecture as shifted VFs. The shifted VF proposed in [18] provides approximately 60% reduction of the computational complexity compared to the state-of-the-art conventional VF having the lowest computational complexity [13]. In [10], the computational complexity of shifted VFs has been further reduced by approximately 50% (compared to the shifted VF proposed in [18]) using a 3-D IIR VF.…”

“…This happens as a result of the narrow angular separation between the spectral regions of support (ROSs) of the OOI and the MIO, which occurs when the velocities are close. Note that, in [10] and [18], only the low-complexity filter architectures for shifted VFs have been analyzed whereas, in this paper, we analyze the significantly improved attenuation of MIOs by shifted VFs using the spectral properties of moving objects in videos and verify using numerical simulations. A representative case, where the velocities of the OOI and the MIOs differ only by 1 pixels/frame indicates that the shifted VFs provide approximately 20 dB improvement in signal-to-interference ratio (SIR) compared to conventional VFs without increasing the computational complexity.…”