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Appearance Models Shape models represent shape variation Eigen-models can represent texture variation Combined appearance models represent both
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Appearance Models Statistical model of shape and texture Generative model –general –specific –compact
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Building Appearance Models For each example extract shape vector Build statistical shape model, Shape, x = (x 1,y 1, …, x n, y n ) T
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Building Appearance Models For each example, extract texture vector Shape, x = (x 1,y 1, …, x n, y n ) T Texture, g Warp to mean shape
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Warping texture Problem: –Given corresponding points in two images, how do we warp one into the other? Two common solutions 1.Piece-wise linear using triangle mesh 2.Thin-plate spline interpolation
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Interpolation using Triangles Region of interest enclosed by triangles. Moving nodes changes each triangle Just need to map regions between two triangles
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Barycentric Co-ordinates
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Three linear equations in 3 unknowns
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Interpolation using Triangles To find out where each pixel in new image comes from in old image Determine which triangle it is in Compute its barycentric co-ordinates Find equivalent point in equivalent triangle in original image Only well defined in region of `convex hull’ of control points
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Thin-Plate Spline Interpolation Define a smooth mapping function (x’,y’)=f(x,y) such that –It maps each point (x,y) onto (x’,y’) and does something smooth in between. –Defined everywhere, even outside convex hull of control points
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Thin-Plate Spline Interpolation Function has form
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Building Texture Models For each example, extract texture vector Normalise vectors (as for eigenfaces) Build eigen-model Texture, g Warp to mean shape
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Face Texture Model
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Textured Shape Modes Shape variation (texture fixed) Generate position of control points Warp mean texture image (Mean points go to new points, X)
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Textured Shape Model
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Combined Models Shape and texture often correllated –When smile, shadows change (texture) and shape changes Learning this correlation leads to more compact (and specific) model
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Learning Correlations Model assuming shape and texture independent Model accounting for correlations between shape and texture
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Learning Correlations For each image in training set we have best fitting shape and texture param.s Construct new vector, Apply PCA (mean + eigenvec.s of covar.)
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Combined Appearance Models Varying c changes both shape and texture
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Combined Appearance Model Generate shape, X, and texture, g Warp texture so mean control points lie on new X
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Face Appearance Model
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Sub-cortical structures 72 examples 123 points 5000 pixel model Ventricles Lentiform Nucleus Caudate Nucleus
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Shape and Texture Modes Shape variation (texture fixed) Texture variation (shape fixed)
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Combined Appearance Model Shape and texture correlated
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Full brain slice Shape: Texture:
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Full brain slice Combined Mode 1 Combined Mode 2
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Problems with viewpoint Models require all points visible –Sometimes a problem for 2D images of 3D objects Small rotations (+/-30 o ) of face modelled well Large rotations cause occlusions –Eg eye hidden behind nose etc Solutions 1.Use multiple `view based’ 2D models 2.Use a full 3D model
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View-Based Models Build 3 distinct models –Exploit symmetry Profile Profile (Reflected) Frontal Half-ProfileHalf-Profile (Reflected)
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Face Profile Model Mode 1: Mode 2:
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Half-Profile Model Mode 1: Mode 2:
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3D Models Use 3D shape model (3n-D vectors) Points control a polyhedral mesh Texture mapped onto mesh and modelled Reconstruct by generating new texture and mapping onto 3D mesh described by shape model
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3D Models = + Mesh Texture
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Interpreting Images (1) Place model in image Measure Difference Update Model Iterate
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