Large Scale Discovery of Spatially Related Images Ondřej Chum and Jiří Matas Center for Machine...

Large Scale Discoveryof Spatially Related Images

Ondřej Chum and Jiří Matas

Center for Machine Perception

Czech Technical University

Prague

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Related Vision Problems

• Organize my holiday snapshots– Schaffalitzky and Zisserman ECCV’02

• Find images containing a given “object” (“window”)– Sivic ICCV‘03, Nister CVPR‘06, Jegou CVPR’07, Philbin CVPR‘07, Chum ICCV’07

• Find small “object” in a film– Sivic and Zisserman CVPR’04

• Match and reconstruct Saint Marco – Snavely, Seitz and Szeliski SIGGRAPH’06

• Find and match ALL spatially related images in a large database, using only visual information, i.e. not using (flicker) tags, EXIF info, GPS, ….

This Work

O.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

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Visual Only Approach

• Large database (100 000 images in our experiments)• Find spatially related clusters• Fast method, even for sizes up to 250 images• Probability of successful discovery of spatial relation of

images independent of database size


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Image Clustering and its Time Complexity

Standard Approach (using image retrieval):Quadratic method in the size of database D -- O(D2)the multiplicative constant at the quadratic term ~ 1 – quadratic even for small D

1. Take each image in turn2. Use a image retrieval system to retrieve related images3. Compute connected components of the graph

Proposed method1.Seed Generation – hashingcharacterize images by pseudo-random numbers stored in a hash table time complexity equal to the sum of variances of Poisson distributions linear for database size D ¼ 250

2. Seed Growing – retrieval complete the clusters only for cluster members c << D, complexity O(cD)


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Building on Two Methods• Fast (low recall) seed generation based on hashing• Thorough (high recall) seed growing based on image retrieval

Chum, Philbin, Isard, and Zisserman:Scalable Near Identical Image and Shot Detection

CIVR 2007

Chum, Philbin, Sivic, Isard, and Zisserman:Total Recall: Automatic Query Expansion

with a Generative Feature Model for Object RetrievalICCV 2007


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Image Representation

0

4

0

2

...

Feature detector SIFT descriptor [Lowe’04]

Visual vocabulary

Vector quantization

…0

1

0

1

...

Bag of words

Set of words


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Hypothesizing Seeds with min-Hash

A1 ∩ A2

A1 U A2

A1 A2

Image similarity measured as a set overlap (using min-Hash algorithm)

• Spatially related images share visual words• Problem: Robustly estimate set overlap of high dimensional sparse binary vectors in

constant time independent of the dimensionality (d¼105)• Set overlap probabilistically estimated via min-Hash• Similar approach as LSH (locally sensitive hashing)


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min-Hash

0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1

0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0

1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1

• According to some (replicable) key select a small number of non-zero elements

• Similar vectors should have similar selected elements• Key = generate a random number (a hash) for each dimension, choose

nonzero element with minimal value of the key

29 12 19

26 3 26

29 12 1

35 27 7

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Seed Generation: Probability of Success

An image pair forms a seed if at least one of k s-tuples of min-Hashes agrees.

Probability that an image pair is retrieved is a function of the similarity:

where s,k are user-controllable parameters of the method:s governs the size of the hashing table k is number of hashing tables

Successfully retrieved pair of images = at least one collision in one of the tables (equivalent to AND-OR)


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Probability of Retrieving an Image Pair

similarity (set overlap)

Near duplicate ImagesImages of the same object

and unrelated images

8.9 % (sim = 0.057)

5.1% (sim = 0.047)

13.9 % (sim = 0,066)100% (sim = 0.746)

100% (sim = 0.322)

99.5% (sim = 0,217)

prob

abili

ty o

f re

trie

val


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Spatially Related Images

18.9 % (sim = 0,074)5.1 % (sim = 0,047)

similarity (set overlap)

prob

abili

ty o

f re

trie

val (

log

scal

e)

13.9 %13.9 %

8.9 %8.9 % 5.1 %5.1 %

9.8 %9.8 % 7.2 %7.2 %

8.9 %8.9 %

13.9 %13.9 %

16.3 %16.3 %

10.7 %10.7 %

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10%7%

4%

5% 4%

Seed Generation

P (no seed) =

6%

94.00 %85.73 %68.88 %


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68.88 %

Seed Generation

P (no seed) = 55.13 %31.84 %1.94 %

Resemblance to RANSAC

Related image pair ~ an all inlier sample(there is no need to enumerate them all, one hit is sufficient)

Probability of retrieving an image pair ~ fraction of inliers

The number of related image pairs ~ how many times we can try


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At Least One Seed in Cluster

cluster size

P(n

o se

ed)

similarity0.050.060.07

= probability of retrieval6.2%10.4%16.1%

Estimate of the probability of failure plot against the size of the clusterassumption used in this plot: all images in the cluster are related


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backprojectfeatures

Growing the Seed• Application of Total Recall

– Combining average query expansion and transitive closure

– 3D geometric constraint (not only affine transformation)

– Tighter geometric constraints (10 pixel threshold)

queryenhanced query

Average query expansion (from possibly multiple coplanar structures)

Transitive closure crawl


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Summary of the Method

Unknown structuremin-Hash seeds

x

Spatial verificationQuery Expansion

Rejected seed

Missed cluster

Seed

Cluster skeleton

Failed retrieval

Images


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Experiment 1 Univ. of Kentucky Dataset

[Nister & Stewenius]

2550 clusters of size 4 – very small clusters

“partial” ground truth: “different” cluster share the same background

How many clusters have at least one seed?

CONTRAST – DIFFERENT TASKIf we were looking for ALL results not ANY (seed)

the standard retrieval measure on this dataset would be only 1.63 out of 4

46.9%


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Experimental Validation UKY dataset

cluster size

P(n

o s

eed

)

similarity0.050.060.07

= probability of retrieval6.2%10.4%16.1%

+

In University of Kentucky dataset“average” similarity slightly above 0.06


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Experimental Results on 100k Images

Hertford

Keble

Magdalen

Pitt Rivers

Radcliffe Camera

All Soul's

Ashmolean

Balliol

Bodleian

Christ Church

Cornmarket

Images downloaded from FLICKRIncludes 11 Oxford Landmarks with manually labelled ground truth


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Experimental Results on 100k ImagesSettings scalable to millions images, also finding small clusters

Settings scalable to billions images, only finding larger clusters

Timing: 17 min 13 sec + 16 min 20 sec = 0.019 sec / imageO.Chum, J. Matas: Large Scale Discovery of Spatially Related Images

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Application – Object Labelling

Factorizing the clusters using multiple constrains• Matches between images• Weak geometric constraints (coplanarity, disparity)• Photographer’s psychology – tends to take pictures of

single objects

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Automatic 3D Reconstruction


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Conclusions

• Novel method for fast clustering in large collections• Combines fast low recall method (seed generation) and

thorough (total recall) method for seed growing• Probability of finding a cluster rapidly increases with its

size and is independent of the size of the database• Can be incrementally updated as the database grows• Efficient: 0.019 sec / image on a single PC• Fully parallelizable

• A state of the art near duplicate detection comes as a bonus (as a part of seed generation)


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Thank you!

Thanks to Daniel Martinec, Michal Perďoch, James Philbin, Jakub Pokluda

Technical Report availablehttp://cmp.felk.cvut.cz/~chum/papers/Chum-TR-08.pdf


Large Scale Discovery of Spatially Related Images Ondřej Chum and Jiří Matas Center for Machine...

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