Exploring Residual and Spatial Consistency for Object Detection

Hao Wang, Ya Zhang and Zhe Xu

Institute of Image Communication and Information Processing

Shanghai Jiao Tong University, Shanghai, China

Keywords:

Visual Object Detection, Wide Baseline Matching, Local Image Feature, Spatial Consistency.

Abstract:

Local image features show a high degree of repeatability, while their local appearance usually does not bring

enough discriminative pattern to obtain a reliable matching. In this paper, we present a new object matching

algorithm based on a novel robust estimation of residual consensus and ﬂexible spatial consistency ﬁlter. We

evaluate the similarity between different homography model via two-parameter integrated Weibull distribution

and inlier probabilities estimates, which can select uncontaminated model to help eliminating outliers. Spatial

consistency test was encoded by the geometric relationships of domain knowledge in two directions, which is

invariant to scale, rotation, and translation especially robust to the ﬂipped image. Experiment results on nature

images with clutter background demonstrate our method effectiveness and robustness.

1 INTRODUCTION

With the increasing popularity of image applications

on internet such as Google Image and Flickr, consid-

erable attention has been directed to image detection

and classiﬁcation in multimedia research communi-

ties. However, accurate object recognition remains a

challenging problem, because the target object may

be small in size with cluttered background, or it is

signiﬁcantly different from the query image in color,

scale, and orientation.

Among existing methods, the bag-of-features

model (Sivic and Zisserman, 2003; Lazebnik et al.,

2006) has been a popular technique because of its

simplicity and effectiveness. This method quantizes

local image descriptors into distinct visual words for

scalable image indexing and searching. With the in-

verted index of visual words, one not only avoids stor-

ing and comparing high dimensional local descrip-

tors, but also reduces the number of candidate images

because only images sharing common words with the

query image are considered. To improve the pre-

cision of the matching, a visual word may be aug-

mented with compact information from its original

local descriptor, including a Hamming code (Jegou

et al., 2008), descriptor scale and angle, and the dis-

tance (in descriptor space) to its neighboring visual

words.

Geometric veriﬁcation such as RANSAC is a cru-

cial step after retrieval from the inverted index. Many

extensions of RANSAC have been proposed in or-

der to improve the accuracy of the matching. Multi-

GS (Chin et al., 2010) accelerates hypothesis sam-

pling by guiding it with information derived from

residual sorting. The LO-RANSAC (Chum et al.,

2003) method introduces an inner RANSAC loop into

the main RANSAC algorithm such that hypotheses

may be generated from the set of inliers. Guided-

MLESAC (Tordoff and Murray, 2005) and PROSAC

(Chum and Matas, 2005) focus on sampling more

conﬁdent keypoint matches. The above two meth-

ods are essentially guided only by the prior inlier

probabilities and do not conduct conditional sam-

pling to further improve efﬁciency. GroupSAC (Ni

et al., 2009) focuses on sampling groups of data ob-

tained using image segmentation. SCRAMSAC (Sat-

tler et al., 2009) introduces a spatial ﬁltering step such

that matches with similar local geometry are consid-

ered. ARRSAC (Raguram et al., 2008) performs a

partially breadth-ﬁrst veriﬁcation such that the num-

ber of hypotheses may be modiﬁed according to the

inlier ratio estimation while still bounding the run-

time.

In recent years, spatial context have been proven

to be useful for enhancing the discriminative power

of individual local features. Features that are close to

each other are grouped to form a visual phrase. Visual

phrase is formed by two different methods. The ﬁrst

type of methods mainly relies on object segmentation

or region detection, which ﬁnds spatial context of ob-

ject locating area by detecting contour (Russell et al.,

2006; Wu et al., 2009). An example of such meth-

191

Wang H., Zhang Y. and Xu Z..

Exploring Residual and Spatial Consistency for Object Detection.

DOI: 10.5220/0004746801910197

In Proceedings of the 9th International Conference on Computer Vision Theory and Applications (VISAPP-2014), pages 191-197

ISBN: 978-989-758-004-8

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

ods is bundled-feature which groups features in local

MSER regions described by SIFT into a local group

to increase the discriminative power of local features

(Zhang et al., 2011). However, object need to be seg-

mented accurately. Otherwise the visual phrase will

be far away from the correct area. The second type of

methods selects the visual phrase at a ﬁxed area, such

as geometry-preserving visual phrases that capture

long-range spatial layouts of the words (Sivic and Zis-

serman, 2009). They were generating a higher-level

lexicon, i.e. visual phrase lexicon, where a visual

phrase is a meaningful spatially co-occurrent pattern

of visual words (Jiang et al., 2011; Li et al., 2011).

In (Lowe, 2004), local spatial consistency from some

spatial nearest neighbors is used to ﬁlter false visual-

word matches.

In this work, we propose a novel robust estimation

of residual consensus and ﬂexible spatial consistency

ﬁlter for object matching. Speciﬁcally, we evaluate

the similar structure from different homography mod-

els in two aspects. Firstly, We extend RANSAC to

model residuals distribution using two-parameter in-

tegrated Weibull which is between a power-law and

a Gaussian distribution. Secondly, we calculate the

normalized overlap of sorted residuals obtained from

hypothesis generation. For spatial consistency ﬁl-

ter, previous literatures usually describe the relative

spatial positions between each feature pair along the

horizontal (X-axis) and vertical (Y-axis) directions or

measuring angles only in one direction. However, we

measure spatial consistency using geometric relation-

ships of globally point distribution in both clockwise

and counterclockwise, which is invariant to scale, ro-

tation, and translation especially robust to ﬂipped im-

age.

2 RESIDUAL AND SPATIAL

CONSISTENCY

The SIFT feature is one of the most robust and distinc-

tive features (Kalantidis et al., 2011). SIFT feature

descriptor is invariant to uniform scaling orientation,

and partially invariant to afﬁne distortion and illumi-

nation changes. Local interest points are extracted

by DOG detector and described by 128-dimensional

SIFT descriptor. A bag of visual words (BOW) is

obtained by quantizing high-dimensional local im-

age descriptors through clustering. An inverted index

structure is used for retrieval and each visual word has

an entry in the index that contains the list of images in

which the visual word occurs. Additionally, the tf-idf

weight is used to distinguish different matched fea-

tures. However, this structure ignores geometric re-

lationships among visual words due to quantization.

Geometric veriﬁcation such as RANSAC becomes an

important post-processing step for getting reasonable

retrieval precision, especially for distorted images.

Given a set of tentative correspondences, a minimal

subset of size m is randomly sampled to hypothesize

a geometric model. Then the model is veriﬁed by

the remaining correspondences. This process is iter-

ated until a termination is met. Despite the effective-

ness of RANSAC, false matching might still appear

in a real application. An extension of the RANSAC

is proposed by adding an optimization procedure to

solve this problem. We compute the similarity be-

tween different homography model via residual or-

dering distribution, which can select uncontaminated

model to help eliminating outliers. Spatial consis-

tency test was encoded by the geometric relationships

of domain knowledge in both clockwise and counter-

clockwise, which is measured by relative orientation

and distance order. The use of spatial conﬁguration

of local features aims at reducing the number of mis-

matches in the correspondence set.

2.1 Residual Consensus

Residual ordering distribution is useful for distin-

guishing between contaminated models and uncon-

taminated models. Naturally, residual errors obtained

from uncontaminated models are approximate simi-

lar with each other. Thus, potential patterns can be

discovered by evaluating the similarity between these

structures to help ﬁnding the optimal models.

Formally, given a set of N input data. Under the

hypothesize-and-verify framework, a model is ﬁtted

by a minimal sample. Let R

= {r

, r

, ..., r

} be ab-

solute residuals corresponding to the input data. We

then ﬁnd the permutation S

= {λ

, λ

, ...λ

} such

that the residuals are sorted in increasing order. We

deﬁne the intersection set Θ

i, j

as,

i, j

= S

1:n

, (1)

where S

1:n

denote the subset containing the ﬁrst n

points of S

and S

1:n

ﬁnds the number of overlap

elements from S

1:n

and S

1:n

. We also give the normal-

ized overlap θ

i, j

|Θ

i, j

|, (2)

Intuitively, Similar models should have the most

overlap of small value residuals. To verify this

method for distinguish uncontaminated and contam-

inated models, an example is shown to illustrates this

intuition explained. In details, we generate 400 ho-

mography hypotheses on the real images and select

VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications

192

the uncontaminated models to compare with the ran-

dom models. Fig.1(a) plots the normalized overlap

i, j

of sorted residuals from uncontaminated mod-

els and random models, respectively. Fig.1(b) shows

a block diagonal pattern of θ

i, j

(1 ≤ i, j ≤ 400), in

which, the points are scattered according to their

structure membership. The results show that, the val-

ues for an inlier concentrate mostly on other inliers

from the same distribution, while for a outlier the

value are generally low and appear to be randomly

distributed.

0 50 100 150 200 250

0.2

0.4

0.6

0.8

Norm. overlap

Uncontaminated Model

Random Model

(a) (b)

Figure 1: (a) Normalized overlap vs. subset size n for un-

contaminated models and random models. (b) The corre-

sponding matrix of size 400*400 with subset is set to 80.

We use a statistical model as an another means to

characterize the qualitive differences between mod-

els. By observing the data, the distribution of resid-

uals is usually between a power-law and a Gaussian

distribution, can be well modeled by a two-parameter

integrated Weibull distribution,

p(x) =

2γ

βΓ(

)

exp{−

}, (3)

where x is the residuals of geometric model. γ > 0

denotes the peakness of the distribution. β > 0 repre-

sents the scale parameter of the distribution. Γ(x) is

the complete Gamma function.

Γ(x) =

∞

x−1

exp(−t)dt, (4)

Given the observed data X = x

, x

, ...x

. The best

ﬁt is obtained when model parameters maximize the

log-likelihood function, in which case their respective

derivatives should equal zero.

∂

∂β

lnL

(β, γ|X) = −

∑

i=1

= 0, (5)

∂

∂γ

lnL

(β, γ|X) =

(γ− 1+ Ψ(

ln(γ) +

∑

i=1

(6)

Ψ(γ) =

dγ

lnΓ(γ) =

dγ

Γ(γ)

, (7)

The parameter is obtained by eliminating from

Eq.(6):

f(γ, X) = −

∑

i=1

∑

i=1

∑

i=1

+1+

ln(γ) +

Ψ(

) = 0.

(8)

Eq.(6) is solved using standard iterative proce-

dures, for example, the Newton-Raphson. Fig.2(a)

displays the ﬁtting result using an integrated Weibull

distribution. The residual is subtracted by median be-

cause we want the peak of probability density is lo-

cated on where residual equal zero. As in Fig.2(b),

we can see that the two parameters of models build

up a 2-D map and the most uncontaminated mod-

els come from the intensive area. Therefore, we can

use this property to capture uncontaminated models.

Given discrete data points from 2-D map, the center of

the intensive area is located using mean-shift method

(Comaniciu and Meer, 2002). Here, the mean-shift

path toward the mode follows a smooth trajectory, and

the angle between two consecutive vectors being al-

ways less than 90 degrees. The search procedure can

be interpreted as kernel density estimation for the po-

sition of the model distribution points. Moreover, we

deﬁne an elliptical area lying on the center of the 2-D

map, such that, the major axis l

parallel to scale axis

and minor axis l

parallel to shape axis. In this case,

the models within the elliptical area are kept for spa-

tial consistency test and unpromising hypotheses can

be quickly ﬁltered out .

0 20 40 60

0.005

0.01

0.015

Residual

Probability density

(a)

0 50 100 150 200

0.5

1.5

scale

shape

uncontaminated models

contaminated models

(b)

Figure 2: (a) Residual distribution is ﬁtted by an integrated

Weibull model. (b) The parameter map of uncontaminated

models and contaminated models.

2.2 Spatial Consistency Analysis

Given an image I, we extract a set of visual words

U(I) = {u

} with center coordinates (x

, y

) and

V(I) = {v

} is another visual word. In an image pair

ExploringResidualandSpatialConsistencyforObjectDetection

193

, I

), all the point correspondences are established

by visual words. Thus, we obtain a correspondence

set C,

C = {(u

, v

)|u

∈ U ∧ v

∈ V}. (9)

We deﬁne a matching score M(I

, I

), which con-

sists of a membership term M

, I

) and a geometric

, I

M(U,V) = M

(U,V) + λM

(U,V), (10)

where λ is a weighting parameter. For membership

term, we compute inlier scores to deﬁne the member-

ship term M

(U,V).

Our geometric term performs a weak geometric

veriﬁcation between training image I

and query im-

age I

using relative ordering, and we incorporate ori-

entation conﬁguration into distance conﬁguration. In

detail, the minimal value of two kinds of conﬁgura-

tion is the ﬁnal value,

(U,V) = min(M

(U,V), M

(U,V)), (11)

where, M

(U,V) is orientation conﬁguration term

and M

(U,V) is distance conﬁguration term. As in

Fig.3, the centroid of all the features is located as a

reference point. Starting from zero degree, the whole

visual words position is scanned clockwise. As the

angle increases, each visual word is assigned a num-

ber with ascending order. Note that the visual word

from testing image has the same number as training

one if they are the matching pair. The inconsistency

is accumulated by the difference of neighbor number

between training image and testing image,

(U,V) = −

∑

δ(O

] > O

i+1

]), (12)

where D is a pre-deﬁned geometric sorting order, and

δ(O

] > O

i+1

]) is an indicator function that mea-

sures the consistency between the order i < i+ 1 (be-

fore matching) and the order O

] > O

i+1

] (after

matching). In other words, we penalize geometric in-

consistency of the visual word matching between two

images and put a weight to inconsistency avoid for

weak discrimination by small difference. In order to

match ﬂipped image, the minimal inconsistency is set

as ﬁnal scores from clockwise and counterclockwise

image scan,

(U,V) = min(M

(U,V), M

(U,V)), (13)

where M

(U,V) is computed by a geometric veriﬁca-

tion via clockwise, and M

(U,V) by a counterclock-

wise geometric veriﬁcation. For spatial consistency

ﬁlter with distance, the only differencebetween orien-

tation is that we compare the distance from reference

point to the position of visual words.





















(a)





















(b)





















(c)

Figure 3: The ordering constraint for local features. (a)

Correct matches preserve the relative orientation orders; (b)

Wrong matches results in inconsistent relative orientation

orders; (c) Wrong matches results in inconsistent relative

distance orders.

2.3 Algorithm

Consider the residual consensus aforementioned, a

statistical rest that evaluates the similarity between

distributions can give the optimal homographymodel.

Speciﬁcally, we ﬁrst measure the fraction of models

by Weibull distribution intensivearea which is located

using mean-shift method. Then we restrict all fur-

ther processing to correspondences where this frac-

tion surpasses a threshold T by inlier probabilities

estimates, resulting in a reduced set of models. our

approach combines the robust estimation of residual

consensus and spatial consistency ﬁlter in a uniﬁed

framework. The details of algorithm are shown in Al-

gorithm 1.

Generally, image retrieval system uses criteria

whether the absolute matching number exceeds a cer-

tain threshold to decide the ﬁnal matching results.

However, taking into account the different complex-

ity of the images and different number of features,

which lead to more correspondence generating in im-

ages with large number features. In that case, even if

the query image does not have the object, the features

of the object still have high probabilities to match

the other parts of the image. In our approach, we

use the total number of features as penalty factor to

eliminate this problem. Note that the importance of

inliers is different because of residuals of geometric

model have diverse values. The residual with small

values is more important for correspondence selec-

tion, because they have high probabilities to become

true inliers. We follow MLESAC(Maximum Likeli-

hood SAC) (Torr and Zisserman, 2000) to deﬁne the

VISAPP2014-InternationalConferenceonComputerVisionTheoryandApplications

194

Algorithm 1: Residual and spatial consistency.

1. Hypothesis generation

k = 0

while k < k

max

Randomly sample minimal subset of m points.

Estimate model parameters θ

end while

2. Residual consensus

Sort residuals, store sorted index S

and residual er-

rors

for all models S

in {M

, M

, ...M

i−1

} do

Fit integrated Weibull distribution to sorted

residuals.

The most intensive area S

∗

is located using

mean-shift method.

Store models come from this area.

Compute intersection Θ

i, j

for M

and M

, and

normalize to θ

i, j

if θ

i, j

> T for some n then

Store K uncontaminated models and ﬁnd the

model with large number inliers.

end if

end for

3. Spatial Consistency

Gain orientation and distance between visual word

via position and centroid.

Compute inconsistency M

(U,V) using different

permutation.

loss function. It models inliers error as unbiased

Gaussian distribution and outlier error as uniform dis-

tribution.

3 EXPERIMENTAL RESULTS

In this section, experiments were conducted to

demonstrate the effectiveness of the proposed resid-

ual and spatial consistency method on real image

datasets. Yannis et al. [16] built the FlickrLo-

gos dataset by downloading real-world images from

Flickr containing 27 logos covering various aspects of

life. The 27 logo classes is Adidas, Apple, BMW, Cit-

roen, Coca-Cola, DHL, Fedex, Ferrari, Ford, Google,

Heineken, HP, Intel, McDonalds, Mini, Nbc, Nike,

Pepsi, Porsche, Puma, RedBull, Sprite, Starbucks,

Texaco, Unicef, Vodafone, and Yahoo. The dataset

selected 40 images per class from Flickr, and every

selected image include at least one instance of the

brands logo. All 1080 images were annotated with

bounding boxes. The annotated logo was partitioned

into 2 subsets: The training set has 30 randomly se-

lected images from the 40 images per brand, and the

rest were the test set. To further verify the scalabil-

ity and effectiveness of our approach, we add 500

crawled Flickr images with noting logos and 230 with

logos to the test set.

Baseline. We use Trademark Matching (Bagdanov

et al., 2007) approach with RANSAC as the base-

line approach, which is denoted as “RANSAC”. The

method is a compact representation of trademarks and

video frame content based on SIFT feature points,

which is state-of-the-art logo detection methods, and

has been used in commercial application. In the

paper, a visual vocabulary of 2M visual words is

adopted. In fact, we have experimented with differ-

ent visual codebook sizes, and have found the 2M vo-

cabularies yield the best overall performance for the

baseline.

Comparisons. Another two compared algorithms are

improved versions of baseline by adding different ge-

ometry consistency. The ﬁrst one is Hamming Em-

bedding [3] by adding a hamming code to ﬁlter out

matched features that have the same number of quan-

tized visual words but have a large hamming distance

from the query feature. We denote this method as

“HE.” The second one is accelerate hypothesis sam-

pling by guiding it with information derived from

residual sorting [6], which is denoted as “Multisac”.

In this paper, we set a fraction of inliers T to 0.95

in Residual consensus evaluation. For pairs of uncon-

taminated models, we found that when subset n close

to the true inlier ratio, θ

i, j

is approaching T. For pa-

rameter of elliptical area, we set the value of l

and l

to 40 and 0.25. We look for K good models to provide

robustness structure. In our experiments, setting K =

3 was sufﬁcient in practice. We empirically exam-

ine the ratio of optimal RANSAC score and geomet-

ric inconsistency. The parameter is set in the range

of λ = [0, 0.5, ..., 2.5]. For each varying of λ, we run

the residual and spatial consistency approach. Table 1

shows that λ = 1.0 is the most effective value. Param-

eters γ and σ are set to 0.7 and 0.3 for Loss function.

Table 1: Comparing the performance for varying λ.

λ 0 0.5 1.0 1.5 2.0 2.5

Accuracy 73.41 75.95 76.42 74.57 72.49 70.52

Performance results when varying the number of

training images are presented in Fig.4. To vary the

number of training images, we split the training set

into 5 random subsets of 5 images per class. Fig.5

shows performance comparison with Recall and Pre-

cision curves. We can see that our approach leads

to a better detection performance compared with the

other algorithms. Fig.6 displays the matching re-

sults between the same objects. It can be observed

ExploringResidualandSpatialConsistencyforObjectDetection

195

10 15 20 25 30

# of training samples per class

Accuracy

Multisac

RANSAC

Proposed

Figure 4: Compare with other method on different training

samples per class.

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

Recall

Precision

Multisac

RANSAC

Proposed

Figure 5: Precision and Recall curve comparison.

that most of matched ones locate on the object. As

a reminder, these curves are generated by varying

the matching threshold and computing the following

values:(TP:True Positive, FP:False Positive, FN:False

Negative)

Recall(%) =

TP+ FN

× 100,

Precision(%) =

TP+ FP

× 100,

(14)

4 CONCLUSIONS

In this paper, we present a new object matching algo-

rithm based on robust estimation of residual consen-

sus and ﬂexible spatial consistency ﬁlter. For resid-

ual consensus, we model residuals distribution using

two-parameter integrated Weibull which is between a

power-law and a Gaussian distribution. Then we esti-

mate a series of inlier probabilities, which are updated

on the ﬂy. For spatial consistency ﬁlter, we measure

spatial consistency using geometric relationships of

global point distribution in both clockwise and coun-

terclockwise, which is invariant to scale, rotation, and

translation especially robust to ﬂipped image. Exper-

iments on clutter background images show that the

Figure 6: Sample matching results from the same objects.

proposed method leads to improvements in the per-

formance of object detection system.

ACKNOWLEDGEMENTS

This research was supported by the High Technol-

ogy Research and Development Program of China

(2012AA011702, 2011AA01A107).

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