Lecture 08 27/12/2011 Shai Avidan הבהרה: החומר המחייב הוא החומר הנלמד...

Lecture 08

27/12/2011Shai Avidan

מופיע: / לא המופיע זה ולא בכיתה הנלמד החומר הוא המחייב החומר הבהרה .במצגת

Today

• Hough Transform

• Generalized Hough Transform

• Implicit Shape Model

• Video Google

Hough Transform & Generalized Hough Transform

K. Grauman, B. Leibe

Hough Transform• Origin: Detection of straight lines in clutter

– Basic idea: each candidate point votes for all lines that it is consistent with.

– Votes are accumulated in quantized array– Local maxima correspond to candidate lines

• Representation of a line– Usual form y = a x + b has a singularity around 90º.– Better parameterization: x cos() + y sin() =

x

y

θ

ρ

x

y

K. Grauman, B. Leibe

Examples

– Hough transform for a square (left) and a circle (right)

K. Grauman, B. Leibe

Hough Transform: Noisy Line

• Problem: Finding the true maximum

Tokens Votesθ

ρ

K. Grauman, B. Leibe

Hough Transform: Noisy Input

• Problem: Lots of spurious maxima

Tokens Votesθ

ρ

K. Grauman, B. Leibe

Generalized Hough Transform [Ballard81]

• Generalization for an arbitrary contour or shape– Choose reference point for the contour (e.g. center)– For each point on the contour remember where it is located w.r.t. to

the reference point – Remember radius r and angle

relative to the contour tangent– Recognition: whenever you find

a contour point, calculate the tangent angle and ‘vote’ for all possible reference points

– Instead of reference point, can also vote for transformation The same idea can be used with local features!

Slide credit: Bernt Schiele

Implicit Shape Model

K. Grauman, B. Leibe

Gen. Hough Transform with Local Features

• For every feature, store possible “occurrences”

• For new image, let the matched features vote for possible object positions

K. Grauman, B. Leibe

3D Object Recognition• Gen. HT for Recognition

– Typically only 3 feature matches needed for recognition

– Extra matches provide robustness– Affine model can be used for planar

objects

Slide credit: David Lowe

[Lowe99]

K. Grauman, B. Leibe

View Interpolation

• Training– Training views from similar

viewpoints are clusteredbased on feature matches.

– Matching features between adjacent views are linked.

• Recognition– Feature matches may be

spread over several training viewpoints.

Use the known links to “transfer votes” to other viewpoints.

[Lowe01]

K. Grauman, B. Leibe

Recognition Using View Interpolation

K. Grauman, B. Leibe

Location Recognition

Training

16 K. Grauman, B. Leibe

Applications• Sony Aibo

(Evolution Robotics)

• SIFT usage– Recognize

docking station– Communicate

with visual cards

• Other uses– Place recognition– Loop closure in SLAM

Slide credit: David Lowe

Video Google

Indexing local features

• Each patch / region has a descriptor, which is a point in some high-dimensional feature space (e.g., SIFT)

K. Grauman, B. Leibe

Indexing local features

• When we see close points in feature space, we have similar descriptors, which indicates similar local content.

Figure credit: A. ZissermanK. Grauman, B. Leibe

Indexing local features

• We saw in the previous section how to use voting and pose clustering to identify objects using local features

K. Grauman, B. Leibe

Figure credit: David Lowe

Indexing local features• With potentially thousands of features per image,

and hundreds to millions of images to search, how to efficiently find those that are relevant to a new image?

– Low-dimensional descriptors : can use standard efficient data structures for nearest neighbor search

– High-dimensional descriptors: approximate nearest neighbor search methods more practical

– Inverted file indexing schemes

K. Grauman, B. Leibe

• For text documents, an efficient way to find all pages on which a word occurs is to use an index…

• We want to find all images in which a feature occurs.

• To use this idea, we’ll need to map our features to “visual words”.

K. Grauman, B. Leibe

Indexing local features: inverted file index

Visual words

K. Grauman, B. Leibe

• More recently used for describing scenes and objects for the sake of indexing or classification.

Sivic & Zisserman 2003; Csurka, Bray, Dance, & Fan 2004; many others.

Inverted file index for images comprised of visual words

Image credit: A. ZissermanK. Grauman, B. Leibe

Word number

List of image numbers

Bags of visual words• Summarize entire image

based on its distribution (histogram) of word occurrences.

• Analogous to bag of words representation commonly used for documents.

K. Grauman, B. LeibeImage credit: Fei-Fei Li

Video Google System1. Collect all words within query

region2. Inverted file index to find

relevant frames3. Compare word counts4. Spatial verification

Sivic & Zisserman, ICCV 2003

• Demo online at : http://www.robots.ox.ac.uk/~vgg/research/vgoogle/index.html

26 K. Grauman, B. Leibe

Query region

Retrieved frames

Visual vocabulary formation

Issues:• Sampling strategy• Clustering / quantization algorithm• What corpus provides features (universal

vocabulary?)• Vocabulary size, number of words

K. Grauman, B. Leibe

Sampling strategies

K. Grauman, B. LeibeImage credits: F-F. Li, E. Nowak, J. Sivic

Dense, uniformly Sparse, at interest points

Randomly

Multiple interest operators

• To find specific, textured objects, sparse sampling from interest points often more reliable.

• Multiple complementary interest operators offer more image coverage.

• For object categorization, dense sampling offers better coverage.

[See Nowak, Jurie & Triggs, ECCV 2006]

Clustering / quantization methods

• k-means (typical choice), agglomerative clustering, mean-shift,…

29 K. Grauman, B. Leibe