MOTION Model

Road Map Motion Model Non Parametric Motion Field : Algorithms 1.Optical flow field estimation. 2.Block based motion estimation. 3.Pel –recursive based motion. 4.Bayesian concept of motion estimation. BLOCK MOTION MODEL Translational block motion Phase Correlation Based Estimation Optical Flow Based Method (Motion Estimation)

Motion Model Parametric motion model Nonparametric motion model

Parametric motion model It is model used to describe the prospective and orthographic projection from 3-D scene to 2-D projection into image plane. It takes projection from 3-D( displacement,Velocity) rigid body surface to 2-D (displacement,Velocity) into image plane. In case of 2-D motion from 3-D rigid body motion of a planner under orthographic projection can be described by a 6 parameter affine model. For prospective projection : 8 parameter is required. “Source: Digital video processing by Author Tekalp”

Nonparametric motion model Why Non parametric model? The main reason to consider non parametric is that parametric motion models have focused only on 3-D rigid surface(it means non deformable motion of body). No concept about smoothness constrains of rigid body motion. Non parametric model take care about the smoothness (uniformity) constrains. It can be imposed on 2-D motion field without employing 3-D rigid body motion model.

Non Parametric Motion Field : Algorithms There are following non parametric motion model 1.Optical flow field estimation. 2.Block based motion estimation. 3.Pel –recursive based motion. 4.Bayesian concept of motion estimation.

Optical Flow Estimation Method Phase correlation method. Block based optical flow estimation method. Differential methods of estimating optical flow, based on partial derivatives of the image signal as follows: 1.Lucas-Kanade method – regarding image patches and an affine model for the flow field.

Cont… Buxton–Buxton method It is based on a model of the motion of edges in image sequences. Black–Jepson method It finds the coarse optical flow via correlation.

Horn–Schunck method The Horn–Schunck method of estimating optical flow.optical flow It is a global method which introduce a global constraint of smoothness. It solves the aperture problem with the help of global constrained of smoothness.aperture problem chunck_method

Horn and Schunck Method The minimization of the sum of the errors in the equation for the rate of changes of image brightness. It measures the smoothness in the velocity flow.

Horn and Schunck Method Let the total error to be minimized be The minimization is to be accomplished by finding suitable values for optical flow velocity (u,v). The solution can be found iteratively.

Horn and Schunck Method: Directional- Smoothness constraint The directional smoothness constraint: W is a weight matrix depending on the spatial changes in gray level content of the video. The directional-smoothness method minimizes the criterion function:

BLOCK MOTION MODEL Block motion model is an approach to overcome the aperture problem due to independent motion vector (v) of object in given image plane. Block motion model emphasizes on block which consists of moving images. How block motion model will work to overcome the aperture problem? In block motion model, motion vectors of moving object will be unchanged during motion from pixel to pixel within block.

Cont… In block based motion model, motion vector (v) is calculated in following mode: Non overlapping block motion( different motion vectors) Overlapping block motion (taking average motion model of all motion vectors). There are following block motion model 2-D Translation motion model 2-D Generalization /Deformable motion model

Translational block motion XtXt nknk

Phase Correlation Based Estimation Phase correlation is a method based on the translation model of block. It is generalization process of block matching algorithm to track 2-D deformable motion based on spatial transformation like affine transformation or prospective projection.

Phase Correlation Based Estimation There are following steps for phase correlation based estimation: Phase Correlation used to estimate motion. 1. Motion vector (V) for every pixel. 1.Results in a few possible motions for each block. 2.For each pixel in the center of the block, test with each of the possible motions and choose the motion with the smallest MSE. 3.Shift block by small amount and compute new phase correlation and repeat.

Phase Correlation Based Estimation 1.Given block B 1,B 2 from each image 2.Compute 2D FFT(Fast Fourier transformation) of each block 3.Compute cross-power spectrum 1.Normalized value of: F{B 1 } F{B 2 } * 4.Take IFFT to get Phase Correlation Function. 5.This is very similar to the correlation function between the two blocks

Cont…

Optical Flow Based Method (Motion Estimation) OPTICAL FLOW The optical flow is pixel level representation model for motion pattern. In each point in the image is assigned a motion vector. There are following method for estimation of optical flow. 1.Bayesian method 2.Gibbs random field Motion estimation 3.Optical flow equation 4.Second order derivatives of optical flow field

PEL-RECURSIVE METHOD It is predicator –corrector type displacement estimator. The predicator can be taken as the value of the motion estimate the previous pixel location. Linear combination of motion estimation in neighborhood of current pixel.