27/12/2011
Shai Avidan
.
תגצמב עיפומ אל / עיפומה הז אלו התיכב דמלנה רמוחה אוה בייחמה רמוחה : הרהבה

• Hough Transform
• Generalized Hough Transform
• Implicit Shape Model
• Video Google

Hough Transform & Generalized 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(

) =
 y

 y x
K. Grauman, B. Leibe x
ρ
θ

– Hough transform for a square (left) and a circle
(right)
K. Grauman, B. Leibe

ρ
Tokens
• Problem: Finding the true maximum
Votes
K. Grauman, B. Leibe
θ

ρ
Tokens
• Problem: Lots of spurious maxima
Votes
K. Grauman, B. Leibe
θ

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!
K. Grauman, B. Leibe
Slide credit: Bernt Schiele

Implicit Shape Model

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

• Gen. HT for Recognition [Lowe99]
– Typically only 3 feature matches needed for recognition
– Extra matches provide robustness
– Affine model can be used for planar objects
K. Grauman, B. Leibe
Slide credit: David Lowe

• Training
– Training views from similar viewpoints are clustered based 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.
K. Grauman, B. Leibe
[Lowe01]

Recognition Using View Interpolation
K. Grauman, B. Leibe

Training
K. Grauman, B. Leibe

• Sony Aibo
(Evolution Robotics)
• SIFT usage
– Recognize docking station
– Communicate with visual cards
• Other uses
– Place recognition
– Loop closure in SLAM
K. Grauman, B. Leibe 16
Slide credit: David Lowe

Video Google

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

• When we see close points in feature space, we have similar descriptors, which indicates similar local content.
Figure credit: A. Zisserman
K. Grauman, B. Leibe

• 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

• 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

Indexing local features: inverted file index
• 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

• 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.
K. Grauman, B. Leibe

Inverted file index for images comprised of visual words
Image credit: A. Zisserman
K. Grauman, B. Leibe
Word number
List of image numbers

• Summarize entire image based on its distribution
(histogram) of word occurrences.
• Analogous to bag of words representation commonly used for documents.
K. Grauman, B. Leibe
Image credit: Fei-Fei Li

1. Collect all words within query region
2. Inverted file index to find relevant frames
3. Compare word counts
4. Spatial verification
Sivic & Zisserman, ICCV 2003
• Demo online at : http://www.robots.ox.ac.uk/~vgg/ research/vgoogle/index.html
K. Grauman, B. Leibe 26
Query region

Issues:
• Sampling strategy
• Clustering / quantization algorithm
• What corpus provides features (universal vocabulary?)
• Vocabulary size, number of words
K. Grauman, B. Leibe

Sparse, at interest points
Multiple interest operators
Image credits: F-F. Li, E. Nowak, J. Sivic
Dense, uniformly Randomly
• 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]
K. Grauman, B. Leibe

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