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Hierarchical Model-Based Motion Estimation

J. BergenP. AnandanK. HannaR. Hingorani

article1992ECCV1,507 citations

Presents a unified multiresolution framework that combines local and global constraints across parametric and non-parametric motion models to achieve accurate and computationally efficient image registration across large displacements.

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Extracting motion information from video sequences is essential across modern technologies such as autonomous vehicle navigation, robotics, video compression, and surveillance. A major operational challenge in visual motion analysis is handling large displacements without failing into false matches or requiring prohibitive computational power, while dealing with scenes containing complex 3D structures or multiple moving objects.

The article demonstrates a unified, hierarchical framework that computes diverse representations of visual motion by treating motion estimation as a model-based image registration problem. Its objective is to show that various motion models can be solved reliably using a single mathematical formulation embedded within a coarse-to-fine multiresolution hierarchy.

The authors develop a four-step pipeline consisting of multiresolution image decomposition, motion estimation via iterative minimization, image warping, and coarse-to-fine parameter refinement. Instead of extracting generic motion first and fitting geometric models later, the framework directly applies specific physical and geometric constraints to guide the alignment process. The authors formulate and evaluate four distinct motion representations: a six-parameter affine model for distant scenes, an eight-parameter planar surface model for flat terrain, a rigid body motion model combining global camera movement with local depth estimation, and a general optical flow model assuming smooth motion within local patches.

The findings confirm that the unified framework operates effectively across all four models on real-world video sequences. First, the hierarchical multiresolution approach successfully overcomes aliasing and false matching for large displacements, establishing that multiresolution processing is fundamentally necessary for stable optimization rather than merely a speed enhancement. Second, the affine flow model reliably compensates for camera-induced motion in aerial sequences, isolating independent moving targets such as helicopters. Third, the planar surface model isolates ground plane motion, cleanly separating flat surfaces from residual background parallax. Fourth, the rigid body model successfully resolves camera rotation and translation across outdoor scenes while simultaneously estimating an inverse depth map. Finally, the general flow formulation accurately registers scenes containing multiple independently moving objects without requiring predefined global models.

These results demonstrate that incorporating physical motion models directly into the estimation process produces significantly more accurate, robust, and computationally efficient results than unconstrained smoothing methods. For technical leaders and system architects, this unified formulation reduces the software and algorithmic complexity needed across diverse applications, including automated target detection, remote sensing, spatial navigation, and video coding standards.

Organizations developing computer vision systems should adopt this hierarchical model-based approach, selecting the simplest motion model that fits their operating environment to balance computational efficiency against scene flexibility. When background geometry is known or distant, parametric affine or planar models should be prioritized to minimize processing overhead. Where general navigation is required, the rigid body model should be deployed to recover 3D depth and ego-motion.

The article notes that the framework's primary limitations occur in regions lacking distinct visual texture, where local depth and flow cannot be uniquely determined, and along motion boundaries where model assumptions break down. Nevertheless, because global motion parameters aggregate information across the entire image, confidence in the overall motion and camera tracking estimates remains high even when individual local estimates encounter untextured areas.

Sarnoff Corporationestimation methodhierarchical modelmotion informationhierarchical model-based motion estimationoptical flow computationcamera motion
Bergen et al (1992).pdf
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Abstract

This paper describes a hierarchical estimation framework for the computation of diverse representations of motion information. The key features of the resulting framework (or family of algorithms) are a global model that constrains the overall structure of the motion estimated, a local model that is used in the estimation process, and a coarse-fine refinement strategy. Four specific motion models: affine flow, planar surface flow, rigid body motion, and general optical flow, are described along with their application to specific examples.

Topics

estimation methodhierarchical modelmotion informationmotion modelshierarchical structuresmotion analysismotion datablock matchingmotion fields

Keywords

hierarchical model-based motion estimationoptical flow computationcamera motionrigid motionlocal image structure

Table of Contents

  • 1 Introduction
  • 1.1 Hierarchical estimation
  • 1.2 Motion Models
  • 1.3 Paper Organization
  • 2 Hierarchical Motion Estimation
  • 3 Motion Models
  • 3.1 Affine Flow
  • 3.2 Planar Surface Flow
  • 3.3 Rigid Body Model
  • 3.4 General Flow Fields
  • 4 Discussion
  • References

Knowls

  1. Knowl 1 — Unified Hierarchical Framework for Model-Based Motion Estimation

    model/method

    The hierarchical motion estimation framework unifies optical flow, parametric transformations, and 3D rigid motion recovery by casting motion estimation as an image registration problem. Given two successive frames I(x,t)I(\mathbf{x}, t) and I(x,t−1)I(\mathbf{x}, t-1), the framework aligns pixels by minimizing a common Sum of Squared Differences (SSD) objective function over different parameterizations of the displacement field u(x)=(u(x,y),v(x,y))T\mathbf{u}(\mathbf{x}) = (u(x, y), v(x, y))^T.

    The framework consists of four interdependent components:

    1. Pyramid Construction: Decomposes input images into multiresolution representations using a Laplacian pyramid. This spatial-frequency decomposition separates coarse structural motion from high-frequency detail.

    2. Motion Estimation: Optimizes model-specific parameters via Gauss-Newton minimization of the intensity constancy error on the current pyramid level, using a first-order Taylor series approximation.

    3. Image Warping: Warps the source frame I(t−1)I(t-1) toward the reference frame I(t)I(t) using the current displacement field estimate ui(x)\mathbf{u}_i(\mathbf{x}) via bilinear interpolation. Subsequent estimation iterations at that level compute incremental updates δu(x)\delta \mathbf{u}(\mathbf{x}) based on the warped frame difference.

    4. Coarse-to-Fine Refinement: Propagates estimated parameters from coarse pyramid levels to finer levels as initializations. Global parametric coefficients are transmitted directly, whereas dense local fields (such as optical flow or depth maps) are expanded using pyramid interpolation operators.

    Hierarchical estimation prevents false matches caused by aliasing when high spatial frequency components undergo large displacements, smoothing non-convex objective surfaces at coarse scales.

  2. Knowl 2 — Incremental Gauss-Newton Formulation for Image Registration

    equation

    Under the intensity constancy assumption applied to Laplacian pyramid images, a point at spatial position x=(x,y)T\mathbf{x} = (x, y)^T in frame I(x,t)I(\mathbf{x}, t) corresponds to position x−u(x)\mathbf{x} - \mathbf{u}(\mathbf{x}) in the preceding frame I(x,t−1)I(\mathbf{x}, t-1), giving the objective over region R\mathcal{R}:

    E({u})=∑x∈R(I(x,t)−I(x−u(x),t−1))2E(\{\mathbf{u}\}) = \sum_{\mathbf{x} \in \mathcal{R}} \left( I(\mathbf{x}, t) - I(\mathbf{x} - \mathbf{u}(\mathbf{x}), t - 1) \right)^2

    Given a current flow estimate ui(x)\mathbf{u}_i(\mathbf{x}), the incremental displacement δu(x)=(δu(x,y),δv(x,y))T\delta \mathbf{u}(\mathbf{x}) = (\delta u(x, y), \delta v(x, y))^T is computed by taking a first-order Taylor series expansion of the warped image before squaring, yielding the quadratic error measure:

    E({δu})=∑x∈R(ΔI(x)+∇I(x)Tδu(x))2E(\{\delta \mathbf{u}\}) = \sum_{\mathbf{x} \in \mathcal{R}} \left( \Delta I(\mathbf{x}) + \nabla I(\mathbf{x})^T \delta \mathbf{u}(\mathbf{x}) \right)^2

    where ∇I(x)=(∂I∂x,∂I∂y)T\nabla I(\mathbf{x}) = \left( \frac{\partial I}{\partial x}, \frac{\partial I}{\partial y} \right)^T is the spatial gradient evaluated on the reference frame I(x,t)I(\mathbf{x}, t), and ΔI(x)\Delta I(\mathbf{x}) is the displaced frame difference between the reference image and the warped previous image:

    ΔI(x)=I(x,t)−I(x−ui(x),t−1)\Delta I(\mathbf{x}) = I(\mathbf{x}, t) - I(\mathbf{x} - \mathbf{u}_i(\mathbf{x}), t - 1)

  3. Knowl 3 — Taxonomy of Global and Local Motion Models in Direct Registration

    definition

    Motion estimation models are categorized along two complementary dimensions describing the global and local structural constraints placed on the displacement field u(x)\mathbf{u}(\mathbf{x}):

    1. Fully Parametric (Purely Global) Models: The motion across a visual region is entirely governed by a low-dimensional parameter vector p\mathbf{p} such that u(x)=u(x;p)\mathbf{u}(\mathbf{x}) = \mathbf{u}(\mathbf{x}; \mathbf{p}) (e.g., 6-parameter affine flow or 8-parameter planar flow). These strongly constrain motion, allowing full flow recovery in textureless regions provided a few points in the region possess sufficient image structure.

    2. Quasi-Parametric (Global and Local) Models: Motion is decomposed into a global parameter vector shared across the visual field and a spatially varying local component per pixel or patch (e.g., 3D rigid body motion combining global egomotion parameters t,ω\mathbf{t}, \boldsymbol{\omega} with a local depth map Z(x)Z(\mathbf{x})). The global parameters constrain local velocity vectors to lie on 1D lines in velocity space, enabling motion estimation from 1D image structure (edges).

    3. Non-Parametric (Purely Local) Models: Motion is constrained only by local smoothness or patch uniformity without an explicit global motion model (e.g., general optical flow with locally constant displacement). These models apply to arbitrary scene geometry and independent object motions but require 2D image structure (corners or textures) and iterative fill-in across uniform areas.

  4. Knowl 4 — Quasi-Parametric Rigid Body Motion Estimation via Alternating Optimization

    algorithm

    This algorithm simultaneously recovers 3D camera egomotion (translation t∈R3\mathbf{t} \in \mathbb{R}^3 and angular velocity ω∈R3\boldsymbol{\omega} \in \mathbb{R}^3) and a dense scene inverse depth map 1/Z(x)1/Z(\mathbf{x}) from an image sequence within a coarse-to-fine Laplacian pyramid.

    Input: Reference image ItI_t, source image It−1I_{t-1}, number of pyramid levels LL, iterations per level KK, focal length ff
    Output: Translation t=(tx,ty,tz)T\mathbf{t} = (t_x, t_y, t_z)^T, rotation ω=(ωx,ωy,ωz)T\boldsymbol{\omega} = (\omega_x, \omega_y, \omega_z)^T, dense inverse depth map 1/Z(x)1/Z(\mathbf{x})
    Build LL-level Laplacian pyramids for ItI_t and It−1I_{t-1}
    Initialize t←(0,0,1)T\mathbf{t} \leftarrow (0, 0, 1)^T, ω←(0,0,0)T\boldsymbol{\omega} \leftarrow (0, 0, 0)^T
    Initialize 1/Z(x)←01/Z(\mathbf{x}) \leftarrow 0 for all pixels at coarsest level L−1L-1
    for level l=L−1l = L-1 down to 0:
        if l<L−1l < L-1:
            Upsample 1/Z(x)1/Z(\mathbf{x}) from level l+1l+1 using pyramid expansion
        for iteration k=1k = 1 to KK:
            Compute flow u(x)=1Z(x)A(x)t+B(x)ω\mathbf{u}(\mathbf{x}) = \frac{1}{Z(\mathbf{x})} \mathbf{A}(\mathbf{x})\mathbf{t} + \mathbf{B}(\mathbf{x})\boldsymbol{\omega}
            Warp It−1(l)I_{t-1}^{(l)} towards It(l)I_t^{(l)} using u(x)\mathbf{u}(\mathbf{x}) via bilinear interpolation
            Compute ΔI(x)=It(l)(x)−It−1(l)(x−u(x))\Delta I(\mathbf{x}) = I_t^{(l)}(\mathbf{x}) - I_{t-1}^{(l)}(\mathbf{x} - \mathbf{u}(\mathbf{x}))
            Compute gradient ∇I(x)\nabla I(\mathbf{x}) on It(l)I_t^{(l)}
            for each pixel x\mathbf{x}:
                Assuming frontal-planar depth over 5×55 \times 5 window, compute closed-form inverse depth update:
                1/Z∗(x)=−∑5×5(∇ITAt)(ΔI−∇ITAti/Zi(x)+∇ITBω−∇ITBωi)∑5×5((∇I)TAt)21/Z^*(\mathbf{x}) = \frac{-\sum_{5 \times 5} (\nabla I^T \mathbf{A}\mathbf{t}) (\Delta I - \nabla I^T \mathbf{A}\mathbf{t}_i / Z_i(\mathbf{x}) + \nabla I^T \mathbf{B}\boldsymbol{\omega} - \nabla I^T \mathbf{B}\boldsymbol{\omega}_i)}{\sum_{5 \times 5} ((\nabla I)^T \mathbf{A}\mathbf{t})^2}
            Substitute symbolic 1/Z∗(x)1/Z^*(\mathbf{x}) into Eglobal=∑xE(t,ω,1/Z∗(x))E_{global} = \sum_{\mathbf{x}} E(\mathbf{t}, \boldsymbol{\omega}, 1/Z^*(\mathbf{x}))
            Update t\mathbf{t} and ω\boldsymbol{\omega} via one Gauss-Newton step on EglobalE_{global}
            Evaluate 1/Z(x)1/Z(\mathbf{x}) numerically using updated t\mathbf{t} and ω\boldsymbol{\omega}
    return t\mathbf{t}, ω\boldsymbol{\omega}, 1/Z(x)1/Z(\mathbf{x})

  5. Knowl 5 — Instantaneous Rigid Body Image Velocity Field

    equation

    For a pinhole camera with focal length ff observing a 3D rigid scene point at spatial coordinates (X,Y,Z)(X, Y, Z) projecting onto image coordinates x=(x,y)T=(fX/Z,fY/Z)T\mathbf{x} = (x, y)^T = (f X / Z, f Y / Z)^T, the instantaneous image flow u(x)=(u(x,y),v(x,y))T\mathbf{u}(\mathbf{x}) = (u(x, y), v(x, y))^T induced by 3D translational velocity t=(tx,ty,tz)T\mathbf{t} = (t_x, t_y, t_z)^T and rotational velocity ω=(ωx,ωy,ωz)T\boldsymbol{\omega} = (\omega_x, \omega_y, \omega_z)^T is:

    u(x)=1Z(x)A(x)t+B(x)ω\mathbf{u}(\mathbf{x}) = \frac{1}{Z(\mathbf{x})} \mathbf{A}(\mathbf{x})\mathbf{t} + \mathbf{B}(\mathbf{x})\boldsymbol{\omega}

    where the coordinate-dependent geometry matrices A(x)\mathbf{A}(\mathbf{x}) and B(x)\mathbf{B}(\mathbf{x}) are defined as:

    A(x)=[−f0x0−fy]\mathbf{A}(\mathbf{x}) = \begin{bmatrix} -f & 0 & x \\ 0 & -f & y \end{bmatrix}

    B(x)=[xyf−f2+x2fyf2+y2f−xyf−x]\mathbf{B}(\mathbf{x}) = \begin{bmatrix} \frac{xy}{f} & -\frac{f^2+x^2}{f} & y \\[6pt] \frac{f^2+y^2}{f} & -\frac{xy}{f} & -x \end{bmatrix}

    The translational flow term depends on the local scene depth Z(x)Z(\mathbf{x}) and points radially with respect to the focus of expansion, whereas the rotational flow term is independent of scene depth.

  6. Knowl 6 — Planar Surface Motion Model and Estimation with Known Egomotion

    model/method

    A 3D planar surface satisfies k1X+k2Y+k3Z=1k_1 X + k_2 Y + k_3 Z = 1, where k=(k1,k2,k3)T\mathbf{k} = (k_1, k_2, k_3)^T specifies the plane slant, tilt, and distance from the camera origin. The inverse depth at image pixel x=(x,y)T\mathbf{x} = (x, y)^T is given by:

    1Z(x)=r(x)Tk\frac{1}{Z(\mathbf{x})} = \mathbf{r}(\mathbf{x})^T \mathbf{k}

    where r(x)=(xf,yf,1)T\mathbf{r}(\mathbf{x}) = \left( \frac{x}{f}, \frac{y}{f}, 1 \right)^T and ff is camera focal length. Substituting this into the instantaneous rigid motion equation yields:

    u(x)=(A(x)t)(r(x)Tk)+B(x)ω\mathbf{u}(\mathbf{x}) = (\mathbf{A}(\mathbf{x})\mathbf{t}) (\mathbf{r}(\mathbf{x})^T \mathbf{k}) + \mathbf{B}(\mathbf{x})\boldsymbol{\omega}

    When camera egomotion (t,ω)(\mathbf{t}, \boldsymbol{\omega}) is known or estimated globally, solving for the plane parameters reduces to estimating the 3-vector k\mathbf{k}. Given a current plane estimate k0\mathbf{k}_0, the incremental displacement is δu(x)=(A(x)t)r(x)Tδk\delta \mathbf{u}(\mathbf{x}) = (\mathbf{A}(\mathbf{x})\mathbf{t}) \mathbf{r}(\mathbf{x})^T \delta \mathbf{k}.

    Minimizing the linearized SSD error yields the 3×33 \times 3 linear system for δk\delta \mathbf{k}:

    [∑xr(x)(tTA(x)T∇I(x))(∇I(x)TA(x)t)r(x)T]δk=−∑xr(x)(tTA(x)T∇I(x))ΔI(x)\left[ \sum_{\mathbf{x}} \mathbf{r}(\mathbf{x}) (\mathbf{t}^T \mathbf{A}(\mathbf{x})^T \nabla I(\mathbf{x})) (\nabla I(\mathbf{x})^T \mathbf{A}(\mathbf{x}) \mathbf{t}) \mathbf{r}(\mathbf{x})^T \right] \delta \mathbf{k} = - \sum_{\mathbf{x}} \mathbf{r}(\mathbf{x}) (\mathbf{t}^T \mathbf{A}(\mathbf{x})^T \nabla I(\mathbf{x})) \Delta I(\mathbf{x})

    where ΔI(x)=I(x,t)−I(x−u0(x),t−1)\Delta I(\mathbf{x}) = I(\mathbf{x}, t) - I(\mathbf{x} - \mathbf{u}_0(\mathbf{x}), t - 1). This formulation provides stable estimates over narrow fields of view where unconstrained 8-parameter quadratic flow estimation is ill-conditioned.

  7. Knowl 7 — Hierarchical Affine Motion Model and Parameter Estimation

    model/method

    When scene surfaces are sufficiently distant from the camera, visual motion is modeled as a 6-parameter affine transformation:

    u(x)=[u(x,y)v(x,y)]=[a1+a2x+a3ya4+a5x+a6y]=X(x)a\mathbf{u}(\mathbf{x}) = \begin{bmatrix} u(x, y) \\ v(x, y) \end{bmatrix} = \begin{bmatrix} a_1 + a_2 x + a_3 y \\ a_4 + a_5 x + a_6 y \end{bmatrix} = \mathbf{X}(\mathbf{x})\mathbf{a}

    where a=(a1,a2,a3,a4,a5,a6)T∈R6\mathbf{a} = (a_1, a_2, a_3, a_4, a_5, a_6)^T \in \mathbb{R}^6 and

    X(x)=[1xy0000001xy]\mathbf{X}(\mathbf{x}) = \begin{bmatrix} 1 & x & y & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & x & y \end{bmatrix}

    Given the current affine estimate ai\mathbf{a}_i, the image is warped using flow field X(x)ai\mathbf{X}(\mathbf{x})\mathbf{a}_i. The incremental parameter update δa\delta \mathbf{a} is obtained by minimizing:

    E(δa)=∑x(ΔI(x)+∇I(x)TX(x)δa)2E(\delta \mathbf{a}) = \sum_{\mathbf{x}} \left( \Delta I(\mathbf{x}) + \nabla I(\mathbf{x})^T \mathbf{X}(\mathbf{x}) \delta \mathbf{a} \right)^2

    Setting ∂E∂δa=0\frac{\partial E}{\partial \delta \mathbf{a}} = 0 yields the 6×66 \times 6 linear system:

    [∑xX(x)T∇I(x)∇I(x)TX(x)]δa=−∑xX(x)T∇I(x)ΔI(x)\left[ \sum_{\mathbf{x}} \mathbf{X}(\mathbf{x})^T \nabla I(\mathbf{x}) \nabla I(\mathbf{x})^T \mathbf{X}(\mathbf{x}) \right] \delta \mathbf{a} = - \sum_{\mathbf{x}} \mathbf{X}(\mathbf{x})^T \nabla I(\mathbf{x}) \Delta I(\mathbf{x})

    where ΔI(x)=I(x,t)−I(x−X(x)ai,t−1)\Delta I(\mathbf{x}) = I(\mathbf{x}, t) - I(\mathbf{x} - \mathbf{X}(\mathbf{x})\mathbf{a}_i, t - 1) and ∇I(x)\nabla I(\mathbf{x}) is the spatial image gradient.

  8. Knowl 8 — Hierarchical Local Optical Flow Estimation

    model/method

    For unconstrained flow fields without a global parametric structure, the displacement field is modeled by assuming constant incremental flow δu=(δu,δv)T\delta \mathbf{u} = (\delta u, \delta v)^T over a local 5×55 \times 5 pixel patch WW centered at each pixel x\mathbf{x}.

    The incremental flow vector δu\delta \mathbf{u} minimizes the local sum of squared errors:

    E(δu)=∑x∈W(ΔI(x)+∇I(x)Tδu)2E(\delta \mathbf{u}) = \sum_{\mathbf{x} \in W} \left( \Delta I(\mathbf{x}) + \nabla I(\mathbf{x})^T \delta \mathbf{u} \right)^2

    which yields the 2×22 \times 2 normal equations at each pixel:

    [∑x∈W∇I(x)∇I(x)T]δu=−∑x∈W∇I(x)ΔI(x)\left[ \sum_{\mathbf{x} \in W} \nabla I(\mathbf{x}) \nabla I(\mathbf{x})^T \right] \delta \mathbf{u} = - \sum_{\mathbf{x} \in W} \nabla I(\mathbf{x}) \Delta I(\mathbf{x})

    While a single pixel produces a rank-1 outer product matrix ∇I∇IT\nabla I \nabla I^T (the aperture problem), summing over 25 pixels in the patch yields a full rank-2 system unless the gradient vectors ∇I(x)\nabla I(\mathbf{x}) are strictly collinear everywhere in WW. Embedding this local estimation within the multiresolution warping hierarchy allows recovery of large non-parametric displacements while maintaining smooth spatial variation.

  9. Knowl 9 — Multi-Resolution Egomotion Estimation Progression on Outdoor Sequence

    data/table

    The rigid body motion algorithm recovers the camera rotational velocity vector Ω=(Ωx,Ωy,Ωz)\boldsymbol{\Omega} = (\Omega_x, \Omega_y, \Omega_z) (in radians/frame) and unit translational velocity vector T=(Tx,Ty,Tz)\mathbf{T} = (T_x, T_y, T_z) across successive resolutions of a Laplacian pyramid for an outdoor sequence. Processing begins at level 3 (subsampled by a factor of 8) with initial values Ω=(0,0,0)\boldsymbol{\Omega} = (0, 0, 0) and T=(0,0,1)\mathbf{T} = (0, 0, 1), executing 10 iterations per resolution level.

    Resolution Ω=(Ωx,Ωy,Ωz)\boldsymbol{\Omega} = (\Omega_x, \Omega_y, \Omega_z) T=(Tx,Ty,Tz)\mathbf{T} = (T_x, T_y, T_z)
    Initial (.0000,.0000,.0000)(.0000, .0000, .0000) (.0000,.0000,1.0000)(.0000, .0000, 1.0000)
    32×3032 \times 30 (.0027,.0039,−.0001)(.0027, .0039, -.0001) (−.3379,−.1352,.9314)(-.3379, -.1352, .9314)
    64×6064 \times 60 (.0038,.0041,.0019)(.0038, .0041, .0019) (−.3319,−.0561,.9416)(-.3319, -.0561, .9416)
    128×120128 \times 120 (.0037,.0012,.0008)(.0037, .0012, .0008) (−.0660,−.0383,.9971)(-.0660, -.0383, .9971)
    256×240256 \times 240 (.0029,.0006,.0013)(.0029, .0006, .0013) (−.0255,−.0899,.9956)(-.0255, -.0899, .9956)

    The progression shows that coarse levels (32×3032 \times 30) rapidly correct large initial translation errors, while finer levels (128×120128 \times 120 to 256×240256 \times 240) refine rotation and translation components to achieve sub-pixel alignment.

Coverage note — Qualitative visual figures showing compensated frame differences, helicopter tracking, and optical flow vector fields were omitted as their algorithmic and quantitative content is fully represented in the motion model knowls and the egomotion progression table.

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Citation

MLA
Bergen, J. R., et al. “Hierarchical Model-based Motion Estimation”. Lecture Notes in Computer Science, Springer Berlin Heidelberg, 1992, pp. 237–52, https://doi.org/10.1007/3-540-55426-2_27.
APA
Bergen, J. R., Anandan, P., Hanna, K. J., & Hingorani, R. (1992). Hierarchical model-based motion estimation. In Lecture Notes in Computer Science (pp. 237–252). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-55426-2_27
Chicago
Bergen, J. R., P. Anandan, K. J. Hanna, and R. Hingorani. 1992. “Hierarchical Model-based Motion Estimation”. In Lecture Notes in Computer Science. Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-55426-2_27.
Harvard
Bergen, J.R. et al. (1992) “Hierarchical model-based motion estimation”, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 237–252. Available at: https://doi.org/10.1007/3-540-55426-2_27.
Vancouver
1. Bergen JR, Anandan P, Hanna KJ, Hingorani R (1992) Hierarchical model-based motion estimation. In: Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp 237–252

BibTeX

@inbook{Bergen_1992, title={Hierarchical model-based motion estimation}, ISBN={9783540470694}, ISSN={1611-3349}, url={http://dx.doi.org/10.1007/3-540-55426-2_27}, DOI={10.1007/3-540-55426-2_27}, booktitle={Computer Vision — ECCV′92}, publisher={Springer Berlin Heidelberg}, author={Bergen, James R. and Anandan, P. and Hanna, Keith J. and Hingorani, Rajesh}, year={1992}, pages={237–252} }
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