Shape From Silhouettes I

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Shape from Silhouettes IGuido GerigCS 6320, Spring 2015Credits: Marc Pollefeys, UNC Chapel Hill, some of the figuresand slides are also adapted from J.S. Franco, J. Matusik’spresentations, and referenced papers)

Shape from silhouettesSlides fromLazebnik,MatusikYerexand othersAutomatic 3D Model Construction for Turn-Table Sequences,A.W. Fitzgibbon, G. Cross, and A. Zisserman, SMILE 1998

Big Picture Multi-cameraenvironments Dynamic sceneOutdoor data capturing with 9 video cameras behind the Ackland Museum,UNC-Chapel Hill, 2006/8/24. Pictured by Jae Hak Kim. N cameras observe the scene and produce Nvideo streams What can we do with this data?

Motivation: MoviesSinha Sudipta, UNC PhD 2008

Motivation: 3D from MoviesSinha Sudipta, UNC PhD 2008

Motivation: 3D from Movies:Replay from arbitrary viewpointsSinha Sudipta, UNC PhD 2008

What can we do with this data? Reconstruct scene objects:–shape from silhouettes–photo-consistencyCalibrate cameras– recover epipolar geometryFit specific models (articulated models)

Outline Silhouettes––––––basic conceptsextract silhouettesfundamentals about using silhouettesreconstruct shapes from silhouettesuse uncertain silhouettescalibrate from silhouettes Perspectives and interesting ideas

Silhouettes of objects of interest Silhouettes are the regions where objects ofinterest project in images Silhouettes can generally be obtained usinglow level information (fast) They give information about the global shapeof scene objects

How to extract silhouettes? Sometimes done manually (for offlineapplications, ground truth and verifications) Region based-extraction (automatic)– silhouette extraction is a 2-region imagesegmentation problem, w/ specificsolutions: chroma keying (blue, green background) background subtraction (pre-observed static ordynamic background)(refer to segmentation course)

How to extract silhouettes? Contour-based extraction focus on silhouette outline instead of regionitself–snakes, active contours: fitting of a curve to highgradients in image, local optimizationYilmaz&Shah ACCV04

How to extract silhouettes? (cont.) Background subtractionSimple thresholdingTrain an appearance model foreach pixel, from a set ofbackground images RGB 3D-Gaussian modelHSV modelGMM modelNon-parametric model(histogram/kernel densityfunction) Apply the pixel color to the model,then classify it to beforeground/background We will talk about this in moredetail later

Why use a Visual Hull? Good shape representationCan be computed efficientlyNo photo-consistency requiredAs bootstrap of many fancyrefinement background foregroundbackground-foreground

Outline Silhouettes––––––basic conceptsextract silhouettesfundamentals about using silhouettesreconstruct shapes from silhouettesuse uncertain silhouettescalibrate from silhouettes Perspectives and cool ideas

What is shape fromsilhouette? The silhouette, or occluding contourof an object in an image containssome information about the 3Dshape of the object. Given a single silhouette image ofan object, we know that the 3Dobject lies inside the volumegenerated by back-projecting thesilhouette area using the cameraparameters.

What is shape fromsilhouette? With multiple views of thesame object, we canintersect the generalizedcones generated by eachimage, to build a volumewhich is guaranteed tocontain the object. The limiting smallestvolume obtainable in thisway is known as the visualhull of the object.

Literature Theory– Laurentini ’94, Petitjean ’98, Laurentini ’99 Solid cone intersection:– Baumgart ’74 (polyhedra), Szeliski ’93 (octrees) Image-based visual hulls– Matusik et al. ’00, Matusik et al. ’01 Advanced modeling– Sullivan & Ponce ’98, Cross & Zisserman ’00,Matusik et al. ’02 Applications– Leibe et al. ’00, Lok ’01, Shlyakhter et al. ’01

One-view silhouette geometry

Multi-view silhouette geometry:the Visual HullVisual hull Maximal volume consistentwith silhouettes[Laurentini94] [Baumgart74] Viewing cone Can be seen as theintersection of viewing conesProperties: Containment property: contains real scene objectsConverges towards the shape of scene objects minusconcavities as N increasesProjective structure: simple management of visibilityproblems

Visual Hull: A 3D Example

Convex Hull: ComputationalGeometry ProblemIn mathematics, the convex hull orconvex envelope for a set of points Xin a real vector space V is theminimal convex set containing X.Convex hull: Elasticband analogy:Concave parts ofobject not part ofhull.In computational geometry, it iscommon to use the term "convexhull" for the boundary of the minimalconvex set containing a given nonempty finite set of points in the plane.Unless the points are collinear, theconvex hull in this sense is a simpleclosed polygonal chain.

Convex Hull: ComputationalGeometry ProblemHint: Calculate the convex hull based on the Delauneytriangulation and its dual, the Voronoi diagram.

Outline Silhouettes––––––basic conceptsextract silhouettesfundamentals about using silhouettesreconstruct shapes from silhouettesuse uncertain silhouettescalibrate from silhouettes Perspectives and cool ideas

What representation for scene objects?Voxel gridSurfaceVolumetric approachesSurface approachesImage-basedapproachesPolyhedron meshA priori knowledgeex: articulated model

General idea and assumptions 2 main families of approaches for VH:– focus on visual hull as volume: locate portions ofspace that don't project in silhouettes (carving) use 2D silhouette regions in images– focus on visual hull as surface: locate theboundary surface of the visual hull use 2D silhouette contours in images General assumptions:– very good silhouettes are extracted– views are calibrated parameters and positions are known

Computational complexity Intersection of many volumes can be slow Simple polyhedron-polyhedron intersectionalgorithms are inefficient To improve performance, most methods:– Quantize volumesand/or– Perform Intersection computations in 2D not 3D

Algorithms Standard voxel basedmethodMarching Intersections Exact polyhedral methods Image-based visual hulls

Voxel based– First the object space is split up into a 3Dgrid of voxels.– Each voxel is intersected with eachsilhouette volume.– Only voxels that lie inside all silhouettevolumes remain part of the final shape.

Visual hull as voxel grid Identify 3D region using voxel carving– does a given voxel project inside all silhouettes? pros: simplicity cons: bad precision/computation timetradeoff

Classical voxel grid improvement:octrees Same principle, but refinement throughspace subdivision[Szeliski TR 90’]

Marching intersectionsTarini et al., 2002– The object space is again split up into a 3D grid.– The grid used is made of 3 sets of rays, rather thanvoxels.– Rays are aligned with the 3 axes, and store points ofentry/exit into the volume– Each silhouette cone can be converted to themarching intersections data structure.– Then merging them is reduced to 1D intersectionsalong each ray.M. Tarini et al, Marching intersections, Anefficient Approach to Shape from Silhouette

Marching intersections example

Marching intersections example

Marching intersections -ConceptM. Tarini et al,Marchingintersections, Anefficient Approachto Shape fromSilhouette Given a curve Select reference grid Intersections between curve and horizontal andvertical lines: MI Create look-up-table for each non-empty box

Marching intersections Silhouettes Convert conoid structures to MI datastructure Intersection tested in 2D image: purely 2Doperation Intersection of conoids: AND operations on MIdatastructures

Marching intersections SilhouettesFinal step: Convert MI datastructure representingall intersections to triangular mesh

Marching intersections Silhouettes

Example: Student Project Compute visual hull with silhouette images from multiplecalibrated camerasCompute Silhouette ImageVolumetric visual hull computationDisplay the result

Algorithms Standard voxel basedmethod Exact polyhedral methods Image-based visual hulls

Exact Polyhedral MethodsWojciech Matusik et al.– First, silhouette images are converted topolygons. (convex or non-convex, withholes allowed)– Each edge is back projected to form a 3dpolygon.– Then each polygon is projected onto eachimage, and intersected with each silhouettein 2D.– The resulting polygons are assembled toform the polyhedral visual hullWojciech Matusik, An Efficient Visual Hull Computation Algorithm

Exact Polyhedral MethodsWojciech Matusik, An Efficient Visual Hull Computation Algorithm

Exact Polyhedral - example

Wojciech Matusik et al.

Wojciech Matusik et al.

Metric Cameras and Visual-HullReconstruction from 4 viewsFinal calibration quality comparable to explicit calibration procedure

IBVH Results Approximately constant computation perpixel per camera Parallelizes Consistent with input silhouettes Lw9aFaHobao

IBVH Results

Image Based Visual Hulls Lw9aFaHobaoSee also: UdmBW4kDcok

Video ShadingMovie uRpSG9iYW8%26image-based-visualhulls%3D&ei Zc8ES8wggaKyA73OrcIK&sa X&oi video result&resnum 5&ct thumbnail&ved 0CCQQuAIwBA&usg AFQjCNETWA Eqgy8 10mJUmc540zpx8T6A

Non-parametric model (histogram/kernel density function) Apply the pixel color to the model, . - use uncertain silhouettes - calibrate from silhouettes Perspectives and cool ideas. What is shape from . Advanced modeling - Sullivan & Ponce '98, Cross & Zisserman '00, Matusik et al. '02

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