Image Morphing. The user is responsible for defining correspondences between features Very popular technique. since Michael Jackson s clips

Transcription

1 Image Morphing

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3 Image Morphing

4 Image Morphing

5 Image Morphing The user is responsible for defining correspondences between features Very popular technique since Michael Jackson s clips

6 Morphing Coordinate Grid Approach Feature-Based Approach

7 Coordinate Grid Source and destination images Overlay upon both a 2-D lattice of points Points along edges must remain on edges Internal points can be in different positions Same number of points in both Points define movement of pixels

8 Coordinate grid approach A curved mesh is then generated using the grid intersection points as control points for an interpolation scheme such as Catmull-Rom splines.

9 Coordinate Grid Approach Interpolate vertices to get intermediate grid Create two images by stretching pixels Cross dissolve the two

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11 Image morphing details Two pass scheme, applied to both source and destination image First pass: Auxiliary grid is created by taking x s from first, y s from intermediate

12 Aux grid Auxiliary image Original 1 (take x s) Intermediate Image (take y s)

13 Aux grid Auxiliary image Fit a spline (Catmull-Rom) Original 1 Intermediate Image

14 Morphing Images to Intermediate

15 Image morphing details For each scanline: Get curve intersections These define separate stretches Get pixel range for each stretch Result is passed to the second pass (over columns)

16 For given pixel in the auxiliary image, determine the range of pixel coordinates in the source image For example, pixel 6 of auxiliary grid maps to pixel coordinates 3.1 to 5.5 of image

17 Pixel splatting (for each scanline) Grid coords original pixels Pixel coords intersections Fit a spline

18 Establishing the auxiliary pixel range for a pixel of the intermediate image. For example, pixel 6 of the intermediate grid maps to pixel coordinates 3.1 to 5.5 of the auxiliary image.

19 Cross-Dissolving

20 Blending factor usually depends linearly on the distance of the intermediate frame from the source & destination image Nonlinear blending might be preferable. Local control of the cross-dissolve rates is also useful

21 Image Morphing Morphing for animated sequences: Define grids on key frames Grids for intermediate frames are created Simple x,y interpolation of intersection points Image morphing performed frame-by-frame

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23 Feature-based morphing Want to use just a set of features Rather than complete grid Feature = line drawn on the image Form intermediate feature image Simple interpolation of features Center/orientation or endpoints Map each pixel to each interpolated feature Compute associated weight

24 Beier & Neeley Example

25 Beier & Neeley Example

26 Feature-Based Morphing Simplest case: user draws one ray on source and destination images to define morph

27 Local Coordinate Systems Let the root of the ray in source image be the coordinate system origin Let the ray in source image correspond to the v axis (unit length) Construct perpendicular to this ray for u axis Every pixel (x, y) of image now mapped to (u, v) using projection to u/v axes

28 Local Coordinate Systems

29 Local Coordinate Systems Perform similar local coordinate system computation for destination image Build s/t axes

30 Mapping Destination to Source (x, y) dest --- (s, t) (s, t) --- (u, v) (u, v) --- (x, y) source Color (x, y) dest with (x, y) source Each line pair defines for each destination pixel a displacement vector to a source image pixel.

31 Warping with One Line Pair

32 Warping with One Line Pair

33 Warping with One Line Pair

34 Warping with One Line Pair

35 Necessary Details More than one line Perform mapping for all line segments Weight each line segment s contribution (displacement vector) with a weight depending on the pixel distance from the line Q 2 Q 1 = length of line segment dist is distance from pixel to line a and b are user specified w = Q a 2 Q + 1 dist p b

36 Necessary Details Pixels close to a line segment are affected more by this segment a close to 0: pixels on the line are rigidly transformed with the line Increasing p: increase effect of longer lines Increasing b: the effect of a line falls off more rapidly.

37 Warping with Multiple Line Pairs

38 Warping Pseudocode

39 Warping Pseudocode

40 Necessary Details Mapping from destination to pixel to source pixel will not land on pixel centers Aliasing results Use quadrilateral centered at source (u, v) location to sample multiple pixels and average

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43 3D shape interpolation Two approaches: Surface based Problems with topologically different objects Volume based Better handling of topologically different objects More computationally intensive

44 Topology Connectivity of an object s surface Teacup- doughnut, ball-blanket: topologically equivalent. Genus: number of holes Ball: 0, Teacup: 1 Difficult to interpolate shape of topologically non-equivalent objects or even genus<> 0 objects using surface based techniques Other definition: vertex/edge connectivity

45 3D shape interpolation Two steps in surface-based 3D shape interpolation (morphing) Establishing correspondences between vertices/edges of source-destination objects Alter vertex-edge topologies of one or both of them so that topologies match. Shape interpolation based on the correspondences. Create intermediate shapes

46 Matching Topology same meshes with same vertex-edge topology Interpolation of 3d vertex positions on a vertex by vertex basis

47 Matching Topology different meshes with same vertex-edge topology N = 5k vertices N = 5k vertices N = 5k vertices N = 5k vertices

48 Matching Topology Project Assignment #1 N = 5k vertices 5 N = 5k vertices

49 Matching Topology Project Assignment #1 Vertex Normal Material (diffuse, specular) Texture (u,v)

50 Techniques for topologies that do not match Star shaped polyhedra Shoot rays from the kernel Interpolate along the rays Star shaped with respect to an axis Split into slices Interpolate each slice as a star-shaped polygon

51 Star-Shaped Polygons (2D) Definition A star-shaped polygon, P, is a simple polygon which contains a non-empty set, K of points, such that every point in K is visible from any other point in the polygon. The set K is called the kernel of P. A convex polygon is a star-shaped polygon whose kernel is equal to the interior of P.

52 Star-Shaped Polygons (2D)

53 Star-Shaped Polygons The kernel can easily be determined by clipping the polygon to the half-planes defined by each edge.

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55 Same technique for star-shaped polyhedra (3D)

56 Axial Slices User defines axis through both objects Slices of objects corresponding to the same value of axis parameter are created 2-D star shaped polygon interpolation techniques are used to interpolate shape of corresponding slices

57 Axial Slices Works in more types of objects than 3D interpolation of star-shaped polyhedra By selecting appropriate axes the slices might define star-shaped polygons out of non-star-shaped polyhedra.

58 Axial Slices

59 Interpolating Slices

60 Contour-Lofting

61 Lofting skinning or surface reconstruction

62 Multiple 2D Slices

63 Map to sphere Used to handle complex polyhedra that cannot be handled by previous method. Source and destination objects are mapped on a unit sphere Entire object surface should map to entire sphere surface with no overlap Simple approach (works only for star shaped polyhedra): project each vertex & edge away from the object center

64 Merging Topologies Projected edges of both objects (now circular arcs) are intersected. The union of vertex-edge topologies is constructed and this is projected back to objects surface. The new objects have the same shape with the old ones but share the same topology.

65 Recursive Subdivision Too many new faces/vertices with topology merging Divide each object in two (or more) meshes Simple approach: divide to front and back mesh by finding paths between topmost bottommost rightmost leftmost vertices and appending them Initial division affects the correspondence between objects.

66 Recursive Subdivision Associate mesh boundaries between objects Create new vertices & edges if needed to achieve same number of edges & vertices. Find a cut through one mesh Create corresponding cut through the second mesh Start from the corresponding vertices Repeat recursively Final result: same topology in both objects