Bag-of-Words
Object Bag of ‘words’
Image matching • Brute force approach:
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• 250,000 images→~ 31 billion image pairs – 2 pairs per second→1 year on 500 machines
• 1,000,000 images→500 billion pairs – 15 years on 500 machines
Image matching
• For city-sized datasets, fewer than 0.1% of image pairs actually match
• Key idea: only consider likely matches
• How do we know if a match is likely?
• Solution: use fast global similarity measures – For example, a bag-of-words representation
Object Bag of ‘words’
Origin 1: Texture recognition
Universal dictionary
Julesz, 1981; Cula & Dana, 2001; Leung & Malik 2001; Mori, Belongie & Malik, 2001; Schmid 2001; Varma & Zisserman, 2002, 2003; Lazebnik, Schmid & Ponce, 2003
Origin 2: Bag
• Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)
words models
Origin 2: Bag
• Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)
words models
US Presidential Speeches Tag Cloud
http://chir.ag/phernalia/preztags/
Origin 2: Bag
• Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)
US Presidential Speeches Tag Cloud
words models
http://chir.ag/phernalia/preztags/
Origin 2: Bag
• Orderless document representation: frequencies of words from a dictionary Salton & McGill (1983)
US Presidential Speeches Tag Cloud
words models
http://chir.ag/phernalia/preztags/
Origin 2: Bag
John likes to watch movies. Mary likes too. John also likes to watch football games
{“John”: 1, “likes”: 2, “to”: 3, “watch”: 4, “movies”: 5,
“also”: 6, “football”: 7, “games”: 8, “Mary”: 9, “too”: 10}
[1, 2, 1, 1, 1, 0, 0, 0, 1, 1] [1, 1, 1, 1, 0, 1, 1, 1, 0, 0]
words models
Bag of words
Works pretty well image retrieval, recognition and matching
face, flowers, building
Images as histograms of visual words
• Inspired by ideas from text retrieval – [Sivic and Zisserman, ICCV 2003]
visual words
Quiz: What is BoW for one image?
• A histogram of local feature vectors in an image
• A visual dictionary
• The feature vector of a local image patch
• A histogram of local features in the collection of images
Bag of features: outline 1. Extractfeatures
Bag of features: outline
1. Extractfeatures
2. Learn “visual vocabulary”
Bag of features: outline
1. Extractfeatures
2. Learn “visual vocabulary”
3. Quantize features using visual vocabulary
Bag of features: outline
1. Extractfeatures
2. Learn “visual vocabulary”
3. Quantize features using visual vocabulary
4. Represent images by frequencies of “visual words”
Quantize: approximate by one whose amplitude is restricted to a prescribed set of values.
Compute SIFT descriptor
1. Feature extraction
Normalize patch
Detect patches [Mikojaczyk and Schmid ’02]
[Mata, Chum, Urban & Pajdla, ’02] [Sivic & Zisserman, ’03]
Slide credit:
1. Feature extraction
2. Learning the visual vocabulary
2. Learning the visual vocabulary
Clustering
Slide credit:
2. Learning the visual vocabulary
Visual vocabulary
Clustering
Slide credit:
K-means clustering
• Want to minimize sum of squared Euclidean distances between points xi and their nearest cluster centers mk
D(X,M)= (x −m )2 ik
clusterk pointiin cluster k
Algorithm:
• Randomly initialize K cluster centers
• Iterate until convergence:
• Assign each data point to the nearest center
• Recompute each cluster center as the mean of all points assigned to it
K-means clustering
https://en.wikipedia.org/wiki/
File:K-means_convergence.gif
From clustering to vector quantization
• Clustering is a common method for learning a
visual vocabulary or codebook
• Unsupervised learning process
• Each cluster center produced by k-means becomes a codevector
• Codebook can be learned on separate training set
• Provided the training set is sufficiently representative, the codebook will be “universal”
• The codebook is used for quantizing features
• A vector quantizer takes a feature vector and maps it to the index of the nearest codevector in a codebook
• Codebook = visual vocabulary
• Codevector = visual word
Example visual vocabulary
Fei-Fei et al. 2005
Image patch examples of visual words
Sivic et al. 2005
3. Image representation
Large-scale image matching
11,400 images of game covers (Caltech games dataset)
• Bag-of-words models have been useful in matching an image to a large database of object instances
how do I find this image in the database?
Large-scale image search • Build the database:
– Extract features from the database images
– Learn a vocabulary using k- means (typical k: 100,000)
– Compute weights for each word
– Create an inverted file mapping words→images
Weighting the words
• Just as with text, some visual words are more discriminative than others
the, and, or vs. cow, AT&T, Cher
• the bigger fraction of the documents a word
appears in, the less useful it is for matching
– e.g., a word that appears in all documents is not helping us
TF (term frequency)- IDF(inverse document frequency) weighting
• Instead of computing a regular histogram distance, we’ll weight each word by it’s inverse document frequency
• inverse document frequency (IDF) of word j =
number of documents
number of documents in which j appears
TF-IDF weighting
• To compute the value of bin j in image I:
term frequency of j in I x inverse document frequency of j
Inverted file • Each image has ~1,000 features
• We have ~1,000,000 visual words
→each histogram is extremely sparse (mostly zeros)
• Inverted file
– mapping from words to documents
Inverted file
• Can quickly use the inverted file to compute similarity between a new image and all the images in the database
– Only consider database images whose bins overlap the query image
Spatial pyramid: BoW disregards all information about the spatial layout of the features
Compute histogram in each spatial bin
Slide credit: D. Hoiem
Spatial pyramid
[Lazebnik et al. CVPR 2006]
Slide credit: D. Hoiem
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