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3D Rigid/Nonrigid RegistrationRegistration 1)Known features, correspondences, transformation model – feature basedfeature based 2)Specific motion type, unknown correspondences – feature basedfeature based 3) Known transformation model, unknown correspondences – region basedregion based 4) Specific motion model – feature basedfeature based 5) Unknown motion model, unknown correspondences – region based
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Visual Motion Jim Rehg (G.Tech)
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Motion (Displacement) of Environment Image plane Scene Flow Motion Field Visual motion results from the displacement of the scene with respect to a fixed camera (or vice-versa). Motion field is the 2-D velocity field that results from a projection of the 3-D scene velocities
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Examples of Visual Motion
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Applications of Motion Analysis Visual tracking Structure recovery Robot (vehicle) navigation
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Applications of Motion Analysis Visual tracking Structure recovery Robot (vehicle) navigation
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Motion Segmentation Where are the independently moving objects (and how many are there)?
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Optical Flow 2-D velocity field describing the apparent motion in an image sequence A vector at each pixel indicates its motion (between a pair of frames). Ground truthHorn and Schunk
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Optical Flow and Motion Field In general the optical flow is an approximation to the motion field. When the scene can be segmented into rigidly moving objects (for example) the relationship between the two can be made precise. We can always think of the optical flow as summarizing the temporal change in an image sequence.
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Computing Optical Flow Courtesy of Michael Black
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Cost Function for Optical Flow Courtesy of Michael Black
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Lucas-Kanade Method Brute-force minimization of SSD error can be inefficient and inaccurate Many redundant window evaluations Answer is limited to discrete u, v pairs
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Lucas-Kanade Method Problems with brute-force minimization of SSD error Many redundant window evaluations Answer is limited to discrete u, v pairs Related to Horn-Schunk optical flow equations Several key innovations Early, successful use of patch-based model in low-level vision. Today these models are used everywhere. Formulation of vision problem as non-linear least squares optimization, a trend which continues to this day.
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Optical Flow Estimation
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Optical Flow Constraint
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Optimization
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Quality of Image Patch Eigenvalues of the matrix contain information about local image structure Both eigenvalues (close to) zero: Uniform area One eigenvalue (close to) zero: Edge No eigenvalues (close to) zero: Corner
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Contributions of Lucas-Kanade Basic idea of patch or template is very old (goes back at least to Widrow) But in practice patch models have worked much better than the alternatives: Point-wise differential equations with smoothness Edge-based descriptions Patchs provide a simple compact enforcement of spatial continuity and support (robust) least-squares estimators.
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Lets Talk Applications
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Alain Pitiot, Ph.D. Siemens Molecular Imaging - Advanced Applications Medical Image Registration (a short overview) Summer School 2005
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SOME APPLICATIONS Medical Image Registration
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Motivation Advances in imaging technology novel modalities see beyond: inside (non-invasive), during (dynamic processes), at small scale (increased resolution) Understanding and correlating structure & function - automated/aided diagnosis - image guided surgery/radio-therapy - treatment/surgery planning - medical atlases - longitudinal studies: disease progression, development
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Definitions Def. #1: put two images into spatial correspondence goal: extract more/better information Def. #2: maximize similarity between transformed source image & target image CT (thorax)PET (thorax) source image target image + transformed target image Anatomical Functional
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Taxonomy Nature of application Subject - intrasubject - intersubject - atlas Homer Simpson (MRI, coronal section)
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Nature of application Subject - intrasubject - intersubject - atlas Homer Simpson (rest position) Homer Simpson (monkey position) very similar shapes Taxonomy
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Nature of application Subject - intrasubject - intersubject - atlas Homer Simpson Homo sapiens sapiens brain expect larger differences Taxonomy
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Nature of application Subject - intrasubject - intersubject - atlas Homer Simpson (MRI) Homer Simpson (labelled atlas) Taxonomy
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Nature of application Subject - intrasubject - intersubject - atlas Registration basis - extrinsic - intrinsic Taxonomy
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Nature of application Subject - intrasubject - intersubject - atlas Registration basis - extrinsic - intrinsic stereotactic frame fast, explicit computation prospective, often invasive, often rigid transf. only Taxonomy
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Nature of application Subject - intrasubject - intersubject - atlas Registration basis - extrinsic - intrinsic versatile, minimally invasive no ground truth PET scintillography Taxonomy
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Registration basis extrinsic intrinsic - landmark based - segmentation based - voxel based fast accuracy limited by localization precision CT PET Taxonomy | Nature of Application
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Registration basis extrinsic intrinsic - landmark based - segmentation based - voxel based segmented corpora callosa fast accuracy limited by segmentation combine with voxel based Taxonomy | Nature of Application
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Registration basis extrinsic intrinsic - landmark based - segmentation based - voxel based cryo. section myelin-stained histological section most flexible approach resource intensive combine with previous techniques Taxonomy | Nature of Application
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Nature of input images Modality Combination: - mono-modal: same modality for source and target - multi-modal: different modality Dimensionality - spatial: 2-D/2-D, 2-D/3-D, 3-D/3-D - temporal a few imaging modalities Taxonomy
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Constraints fusion maximize similarity between transformed source & target Transformation space - flexibility rigid, affine, parameterized, free-form - support local, global choose space that fits anatomy and/or application global local rigid affine parameterized fluid/elastic Taxonomy
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Constraints Similarity measure “intensities of matched images verify criterion” - to each hypothesis its measure: conservation affine functional statistical Taxonomy conservation of intensity SSD affine relationship correlation coefficient functional relationship correlation ratio statistical dependence mutual information source target
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Constraints Similarity measure “intensities of matched images verify criterion” - to each hypothesis its measure: conservation affine functional statistical Taxonomy conservation of intensity SSD affine relationship correlation coefficient functional relationship correlation ratio statistical dependence mutual information source target
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Constraints Similarity measure “intensities of matched images verify criterion” - to each hypothesis its measure: conservation affine functional statistical Taxonomy conservation of intensity SSD affine relationship correlation coefficient functional relationship correlation ratio statistical dependence mutual information source target
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Constraints Similarity measure “intensities of matched images verify criterion” - to each hypothesis its measure: conservation affine functional statistical Taxonomy conservation of intensity SSD affine relationship correlation coefficient functional relationship correlation ratio statistical dependence mutual information source target
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Constraints Similarity measure “intensities of matched images verify criterion” - to each hypothesis its measure: conservation affine functional statistical Taxonomy conservation of intensity SSD affine relationship correlation coefficient functional relationship correlation ratio statistical dependence mutual information source target
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Optimization Often iterative - deterministic gradient descent - stochastic simulated annealing Taxonomy
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Optimization Often iterative - deterministic gradient descent - stochastic simulated annealing Taxonomy
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Optimization Often iterative - deterministic gradient descent - stochastic simulated annealing Taxonomy
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Optimization Often iterative - deterministic gradient descent - stochastic simulated annealing Heteroclite bag of tricks - progressive refinement - multi-scale (multi-resolution) Taxonomy
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Optimization Often iterative - deterministic gradient descent - stochastic simulated annealing bag of tricks - progressive refinement - multi-scale (multi-resolution) Taxonomy
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Issues Validation No ground truth in general case (ill-posed problem) Precision, robustness, reliability, etc. Semi-automated registration Is fully-automated desirable ? Which compromise between fully and semi ?
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Specific Application
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Image Guided Surgery
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Conventional Surgery: Seeing surfaces Provided by Nakajima, Atsumi et al.
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Computer Assisted Surgery: seeing through surfaces
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Goal: Assist Surgeons Surgical Planning & Simulation Maximize Tumor Removal Minimize Damage to Critical Structures Intraoperative Visualizations via 3D Slicer
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Pre-Operative Image Processing Construct 3D Models Semi-Automated Segmentation DTMRI Tract Tracing Register all pre-operative data
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Integrated Preoperative Data F. Talos
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Patient-specific models Gering_fmri
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Segmentation of Neural Structures
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Intraoperative Image Processing Acquire one or more volumetric (interventional) MRI (iMRI) images Determine non-rigid registration of Pre- and Intra- operative data
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Construct Intraoperative Visualization transmit image data and 3D models thru volumetric deformation integrate with iMRI images and models display with 3D Slicer LCD screen in front of surgeon in iMRI coordinate visualization with intraoperative instruments
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3D Slicer: tool for Visualization Registration Segmentation Measurements Realtime Integration Provided by D. Gering
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3D Slicer Demo...
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More Examples
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More examples of correspondence: Motion (tracking) beating heart We have to establish correspondence between specific points on the object boundary from frame to frame
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Template matching In matching we estimate “position” of a rigid template in the image “Position” includes global location parameters of a rigid template: - translation, rotation, scale,… Face template image
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Flexible template matching In flexible template matching we estimate “position” of each rigid component of a template
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3D Doctor Multimodal registrationregistration
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Warping example
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