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Motion estimation techniques are widely used in today's video processing systems. The frequently used techniques are frequency-domain motion estimation methods, most notably phase correlation (PC). If the image frames are corrupted by Gaussian noises, then cross-correlation and related techniques do not work well. In this paper, however, we have studied this topic from a viewpoint different from the above. Our scheme is based on the bispectrum method for sub-pixel motion estimation of noisy image sequences. Experimental results show that our proposed method performs significantly better than PC technique.

Image frames are generated by scanning a scene several times a second where each frame, generally, consists of two regions. One region, referred to as stationary
background, is virtually the same as the previous frame. The other region,
referred to as moving data, has moved with respect to the previous frame.
Estimating the motion between image frames has long been a problem of interest
in areas such as video compression, robot vision, and biomedical engineering
[

Many motion estimation schemes have been developed.
They can be classified into spatial-domain and frequency-domain approaches. The
spatial-domain algorithms consist of matching
algorithms and gradient-based algorithms. The frequency domain algorithms
consist of phase correlation algorithms, wavelet transform-based algorithms,
and DCT-based algorithms [

HOS-based methods have already been proposed to
estimate motion between image frames [

The problem of motion estimation can be stated as follows: “given an image sequence, compute a representation of the motion field that best aligns pixels in one frame of the sequence with those in the next” [

The third-order autocumulants and cross-cumulants of a
zero-mean from 2D random field

The discrete bispectrum of the frame

Due to the shift-invariance of the
bispectrum

As we can see from (

Although we have now taken only a small portion of the
whole spectrum [

Thus, the third-order hologram,

As a result, by finding the location of the pulse in
(

The co-ordinates

Subpixel performance is a critical element of the proposed algorithm. With reference to our previously published work [

Subpixel accuracy of motion measurements is obtained
dy variable-separable fitting performed in the neighborhood of the maximum
using one-dimensional quadratic function. Using the notation in (

The location of the maximum of the fitted function
provides the required subpixel motion estimate

The fractional part

Finally, the horizontal and vertical components of the subpixel accurate motion estimate are obtained by computing the location of the maxima of each of the above fitted quadratics.

In [

To prove the feasibility of the proposed method, we compared it to a PC technique implemented in a similar manner as our approach. In this section, we examine a few examples and compare the performance, efficiency, and complexity of the two methods. In our experiments, we used the well-known test sequences: foreman (176 pixels by 144 lines), mother-daughter and Stefan (352 pixels by 288 lines), table tennis (352 pixels by 240 lines). Although the original sequences are in color, only the luminance (brightness) component is used to estimate the motion vectors.

To assess the performances of the different motion
estimation techniques, the following comparisons were made. First, the
subjective quality of the estimated motion field was evaluated, showing the
capability of the algorithm to estimate the true motion in the scene. Second,
the PSNR of motion compensated was measured, giving insight about the quality
of the prediction. Results obtained using the foreman, mother-daughter and
Stefan sequences are shown in Figure

PSNR obtained for noisy sequences (SNR = 10 dB).

The ability of the bispectrum method to accurately
estimate the displacement vector field from a degraded sequence is demonstrated in Figure

Motion field for the mother-daughter sequence in the presence of noise.

PC

Bispectrum

In terms of motion compensated images, from mother-daughter sequence, we observe better compensated images by the proposed
method. We also observe that the motion compensated images for the “our
method” are much closer to the original images. Thus, the “our scheme” is able to measure the motion vector more accurately and is more robust in general. Overall, the bispectrum typically offers better visual quality images than the PC method. Figure

Prediction for frame 3 of the mother-daughter.

Original image

PC

Bispectrum

Comparisons of the PC and bispectrum methods indicate
that the bispectrum is a robust technique for motion vector. Results of these comparisons are shown for different noise levels and video sequences. Additive
Gaussian noise (AGN) was added to image sequences with an input SNR varying from 15 dB to 28 dB. Figure

The comparison between two methods for the computation time.

Sequences | Methods | Motion estimation |
---|---|---|

computation time (sec) | ||

Foreman | Bispectrum | 0.72 |

PC | 0.61 | |

Mother-daughter | Bispectrum | 0.61 |

PC | 0.57 | |

Stefan | Bispectrum | 0.67 |

PC | 0.59 | |

Table tennis | Bispectrum | 0.57 |

PC | 0.48 |

PSNR versus frame number for motion compensated prediction of the table tennis sequence.

In this paper, the bispectrum method for subpixel motion estimation of noisy image sequences in frequency-domain was presented. The “our” proposed method provides an advantage over the PC algorithm in the presence of AGN. With “our method,” the displacement vector field is smoother, providing a more accurate measure of object motion. At relatively low noise levels, the bispectrum performance is comparable to its performance in the noise-free environment. At high noise levels SNR around 10 dB, the PC fails, yet even under these extreme conditions, the bispectrum provides improvement in performance over the PC algorithm. In addition to its PSNR performance, the bispectrum also yields smooth motion fields.