# 3D Models and Matching

·representations for 3D object models

·particular matching techniques

·alignment-based systems

·appearance-based systems

3D Models

Many different representations have been used to model 3D objects.

Some are very coarse, just picking up the important features.

Others are very fine, describing the entire surface of the object.

Usually, the recognition procedure depends very much on the type of model.

Mesh Models

Mesh models were originally for computer graphics.

With the current availability of range data, they are now used for 3D object recognition.

In addition to matching,They can be used for verification.

Surface-Edge-Vertex Models

SEV models are at the opposite extreme from mesh models.

They specify the (usually linear) features that would be extracted from 2D or 3D data.

They are suitable for objects with sharp edges and corners that are easily detectable and characterize the object.

Generalized-Cylinders

A generalized cylinder is a volumetric primitive defined by:

a space curve axis

a cross section function

Generalized-Cylinder Models

Generalized cylinder models include:

1. a set of generalized cylinders
2. the spatial relationships among them
3. the global properties of the object

Finding GCs in Intensity Data

Generalized cylinder models have been used for several

different classes of objects:

- airplanes (Brooks)

- animals (Marr and Nishihara)

- humans (Medioni)

- human anatomy (Zhenrong Qian)

The 2D projections of standard GCs are

- ribbons

- ellipses

Octrees

- Octrees are 8-ary tree structures that compress a voxel representation of a 3D object.

- Kari Puli used them to represent the 3D objects during the space carving process.

- They are sometimes used for medical object representation.

• Superquadrics are parameterized equations that describe solid shapes algebraically.

• They have been used for graphics and for representing some organs of the human body, ie. the heart.

2D Deformable Models

A 2D deformable model or snake is a function that is fit to some real data, along its contours.

The fitting mimizes:

- internal energy of the contour (smoothness)

- image energy (fit to data)

- external energy (user- defined constraints)

3D Deformable Models

In 3D, the snake concept becomes a balloon that expands to fill a point cloud of 3D data.

Matching Geometric Models via Alignment

Alignment is the most common paradigm for matching 3D models to either 2D or 3D data. The steps are:

3D-3D Alignment of Mesh Models to Mesh Data

• Older Work: match 3D features such as 3D edges and junctions or surface patches

• More Recent Work: match surface signatures

• Older Work: match 3D features such as 3D edges and junctions or surface patches

• More Recent Work: match surface signatures

The Spin Image Signature

P is the selected vertex.

X is a contributing point of the mesh.

α is the perpendicular distance from X to P is surface normal.

β is the signed perpendicular distance from X to P’s tangent plane.

Spin Image Construction

Spin Image Matching ala Sal Ruiz

Spin Images Object Recognition

Offline: Compute spin images of each vertex of the object model(s)

2D-3D Alignment

View Classes and Viewing Sphere

The space of view points can be partitioned into a finite set of characteristic views.

•Each view class represents a set of

view points that have something

in common, such as:

1. same surfaces are visible

2. same line segments are visible

3. relational distance between pairs of them is small

3 View Classes of a Cube

TRIBORS: view class matching of polyhedral objects

RIO: Relational Indexing for Object Recognition

Object Representation in RIO

• 3D objects are represented by a 3D mesh and set of 2D view classes.

• Each view class is represented by an attributed graph whose nodes are features and whose attributed edges are relationships.

• For purposes of indexing, attributed graphs are stored as sets of 2-graphs, graphs with 2 nodes and 2 relationships.

RIO Features

RIO Relationships

Graph and 2-Graph Representations

Relational Indexing for Recognition

Preprocessing (off-line) Phase

Matching (on-line) phase

The Voting Process

RIO Verifications

1. The matched features of the hypothesized object are used to determine its pose.

2. The 3D mesh of the object is used to project all its features onto the image.

3. A verification procedure checks how well the object features line up with edges on the image.

THE END

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