Appearance Models Shape models represent shape variation Eigen-models can represent texture variation Combined appearance models represent both

Appearance Models Statistical model of shape and texture Generative model –general –specific –compact

Building Appearance Models For each example extract shape vector Build statistical shape model, Shape, x = (x 1,y 1, …, x n, y n ) T

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

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

Interpolation using Triangles Region of interest enclosed by triangles. Moving nodes changes each triangle Just need to map regions between two triangles

Barycentric Co-ordinates

Three linear equations in 3 unknowns

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

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

Thin-Plate Spline Interpolation Function has form

Building Texture Models For each example, extract texture vector Normalise vectors (as for eigenfaces) Build eigen-model Texture, g Warp to mean shape

Face Texture Model

Textured Shape Modes Shape variation (texture fixed) Generate position of control points Warp mean texture image (Mean points go to new points, X)

Textured Shape Model

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

Learning Correlations Model assuming shape and texture independent Model accounting for correlations between shape and texture

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.)

Combined Appearance Models Varying c changes both shape and texture

Combined Appearance Model Generate shape, X, and texture, g Warp texture so mean control points lie on new X

Face Appearance Model

Sub-cortical structures 72 examples 123 points 5000 pixel model Ventricles Lentiform Nucleus Caudate Nucleus

Shape and Texture Modes Shape variation (texture fixed) Texture variation (shape fixed)

Combined Appearance Model Shape and texture correlated

Full brain slice Shape: Texture:

Full brain slice Combined Mode 1 Combined Mode 2

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

View-Based Models Build 3 distinct models –Exploit symmetry Profile Profile (Reflected) Frontal Half-ProfileHalf-Profile (Reflected)

Face Profile Model Mode 1: Mode 2:

Half-Profile Model Mode 1: Mode 2:

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

3D Models = + Mesh Texture

Interpreting Images (1) Place model in image Measure Difference Update Model Iterate