LINE HISTOGRAM

A Fast Method for Rotated Rectangular Area Histogramming

Zhiqiang Hou

, Sion Hannuna

, Xianghua Xie

and Majid Mirmehdi

Xi’an Jiaotong University, Shaanxi, P.R. China

Department of Computer Science, University of Bristol, Bristol, U.K.

Department of Computer Science, University of Swansea, Swansea, U.K.

Keywords:

Line histogram, Integral histogram, Efﬁcient histogramming.

Abstract:

We propose a novel approach to executing exhaustive histogram search, which incorporates a process to rotate

the template used in a computationally efﬁcient manner, e.g. for tracking applications where object rotation

will require template rotation. The method is particularly applicable to rectangular templates as any rotation

in the region of interest will greatly reduce the potential for a satisfactory match. We present a computational

analysis of our proposed method, followed by comparative experimental results.

1 INTRODUCTION

The histogram is an important tool in computer vision

and is used for a variety of purposes, such as image

segmentation (Puzicha et al., 1999; Tobias and Seara,

2002), image retrieval (Brunelli and Mich, 2001;

Huang et al., 1997), object detection (Laptev, 2009;

Viola and Jones, 2001; Viola and Jones, 2004) and

visual tracking (Comaniciu et al., 2003; Czyz et al.,

2007; Nummiaro et al., 2003; Perez et al., 2002).

This paper is concerned with efﬁcient histogram con-

struction for exhaustive image search, with ﬂexible

image regions such as rotated rectangles in arbitrary

directions. The proposed technique beneﬁts any al-

gorithm which extracts histograms from regions that

are rotating over time. For example, in aerial imag-

ing (Doretto and Yao, 2010), video and images tend to

be acquired at a ﬁxed altitude with minimal pan or tilt

taking place and the primary motionsproducing trans-

lation and rotation of the image plane. Another ex-

ample is in human pose estimation where body parts

are often modelled as cylinders which have corre-

sponding rectangular regions in the image plane, e.g.

Ramanan and Forsyth (Ramanan and Forsyth, 2003)

use colour histograms within this type of paradigm

to learn human appearance. The line histogram ap-

proach described here could speed up many such ap-

plications.

One of the major impediments in direct histogram

construction is its computational complexity, and

while an exhaustive search is guaranteed to ﬁnd the

global minimum, it is often avoided by performing lo-

calised searches, e.g., in particle ﬁltering (Czyz et al.,

2007; Nummiaro et al., 2003; Perez et al., 2002) and

mean shift (Comaniciu et al., 2003; Zhao and Tao,

2009), at the expense of accuracy, i.e. only local

minima are obtained (Porikli, 2005; Sizintsev et al.,

2008).

The integral histogram is rooted in computer

graphics, where Crow (Crow, 1984) ﬁrst introduced

the summed-area table method for texture mapping.

This inspired Viola and Jones (Viola and Jones, 2004)

to propose a new image representation called an in-

tegral image in order to efﬁciently extract features

from rectangular regions in images. The integral im-

age representation, which can be calculated in linear

time, is a cumulative function where each element

contains the sum of the pixel values above and to the

left of the location of the element. This representa-

tion was adopted by Porikli et al. (Porikli, 2005) to

construct the so called integral histogram (IH) for efﬁ-

cient histogram-based exhaustivesearch. For each bin

of the histogram, an integral image was constructed

to count the accumulative number of pixels falling

into the bin. The histogram of rectangular regions

was then efﬁciently obtained by accessing those in-

tegral images using simple arithmetic operations. Re-

gional statistics, such as covariance, can also be ef-

ﬁciently computed using integral histograms (Porikli

and Tuzel, 2006). Further computational improve-

ment can be achieved through, for example, adaptive

approximation (Muller et al., 2008).

126

Hou Z., Hannuna S., Xie X. and Mirmehdi M. (2012).

LINE HISTOGRAM - A Fast Method for Rotated Rectangular Area Histogramming.

In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, pages 126-134

DOI: 10.5220/0003760401260134

 SciTePress

(a) Original image (b) no rotation (CH, IH, or DH) (c) with rotation (LH)

Figure 1: Example of conventional histogram (CH) template match (or IH (Porikli, 2005) or DH (Sizintsev et al., 2008))

against the proposed method (LH).

Earlier works in efﬁcient median ﬁltering, such as

(Huang et al., 1979), also inspired the development

of efﬁcient exhaustive search algorithms. In (Huang

et al., 1979), Huang et al. made use of overlapping

pixels between adjacent windows to address the re-

dundancy along a row in computing the histograms

for median ﬁltering. However,no redundancy was ex-

ploited between rows. Perreault and H´ebert (Perreault

and Hebert, 2007) extended (Huang et al., 1979)’s

work by removing redundancies both within row and

between rows based on the principle of histogram dis-

tributivity, that is the histogram of two disjoint re-

gions is simply a summation of histograms of those

individual regions. The rectangular region of interest

was broken up into a union of its columns, each of

which maintained its own histogram. The histogram

for the region was then computed by summing those

adjacent column histograms. This work was followed

by Sizintsev et al. (Sizintsev et al., 2008) who con-

structed the distributive histogram (DH) based on the

principles laid in (Perreault and Hebert, 2007) and

used it for very fast, exhaustive histogram search for

object detection. They also showed that this distribu-

tivity can be useful in computing regional statistics,

such as mean and covariance matrices.

Recently, Wei and Tao (Wei and Tao, 2010) op-

timised histogram based searches by calculating the

objective function in an incremental fashion. Their

research complements Porikli et al.’s (Porikli, 2005)

IH and Sizintsev et al.’s (Sizintsev et al., 2008) DH

fast exhaustive searches. However, histogram con-

struction using the IH or DH methods is generally

carried out on regular rectangular regions, i.e. they

are explicitly designed for unrotated rectangular re-

gions. For example, in the case of IH, the integral

images for histogram bins are constructed as integra-

tion along image coordinates. This may force the ex-

haustive search to result in undesirable local minima,

since the region of interest is subject to arbitrary rota-

tions. A square shape is thus often used; however, this

may compromise the representativeness of the target

histogram since it can include more irrelevant regions

due to a sub-optimal bounding box. The DH suffers

from similar difﬁculties, since there is also no mecha-

nism in DH to take into account object rotations. The

histogram initialisation process of DH would have to

be repeated for each possible rotation, which is cum-

bersome to say the least. Here, we propose a method

that can handle arbitrary rotations, and can be used

to build on the localisation performance of IH and

DH to generate even more optimal matches, e.g. see

Fig. 1. Indeed, as it will be shown later, disregarding

object rotation can in fact lead to complete tracking

failure. Furthermore, rotational information is impor-

tant in determining orientation of objects, e.g. (Zhao

and Tao, 2009). In (Lienhart and Maydt, 2002), Lien-

hart and Maydt used the rotated summed area table

or integral image to compute histograms of rectangu-

lar regions with 45

◦

rotation. However, this strategy

is impractical and inefﬁcient for arbitrary rotations.

Moreover, the shape can take any arbitrary form.

Here, we present a simple, ﬂexible and efﬁcient

histogram-based exhaustive search method. We also

exploit the distributivity of histogram representation,

by using vertical or horizontal line integration to

obtain rotated histogram representation, instead of

conﬁning the process to regular rectangular regions.

Hence, we refer to our histogram representation as

the line histogram or LH. One signiﬁcant difference

between the proposed LH and IH is that the IH pre-

pares histogram initialisation using rectangular areas

whereas ours can use rows or columns to conveniently

form arbitrarily shaped regions. This leads to a sig-

niﬁcant advantage in handling non-rectangular region

histograms in a computationally cheap and memory

efﬁcient manner. However, without losing general-

ity and for the ease of comparison with IH and DH,

in this paper we use rotated rectangular area his-

tograms. The proposed method also allows adaptive

change of template size in exhaustive search without

re-initiating the histogram generation process as in the

DH method.

Note in this work we develop the LH in the spirit

of the works that introduced the IH (Porikli, 2005)

LINE HISTOGRAM - A Fast Method for Rotated Rectangular Area Histogramming

127

and DH (Sizintsev et al., 2008) where a template of

an object is available and one or more unseen frames

are searched to optimally locate the template - for ob-

ject detection or tracking purposes. The rest of the

paper is organized as follows. Section 2 describes

the proposed LH method. In Section 3, we present

a computational analysis of LH. Experimental results

are shown in Section 4 and we conclude the paper in

Section 5.

2 LINE HISTOGRAM

Image histograms provide a quantized representation

of an image’s intensity or colour distribution, the

granularity of which is determined by the number of

bins used. An important property is that histograms

for non-intersecting regions may be summed (Per-

reault and Hebert, 2007; Sizintsev et al., 2008) as

S(A∪ B) = S(A) + S(B) (1)

where S(.) is a histogram and A and B are two im-

age regions which may or may not be connected.

This property forms the foundation of the integral his-

togram and distributive histogram techniques and also

underpins the line histogram technique proposedhere.

When obtaining a single histogram for a whole

image, or subset of an image, it is optimal to generate

the distribution directly from the pixel data. However,

when performing a task that requires histograms to be

calculated for overlapping regions, e.g. in an exhaus-

tive search, signiﬁcant computational savings may be

gained by precomputing an image’s histogram. For

example, the IH (Porikli, 2005) extends the concept

of the integral image (Crow, 1984) by precomput-

ing histograms at every pixel location such that the

stored histogram at a given pixel describes the dis-

trbution of the subimage contained within the upper

left of that location. This allows an arbitrarily sized

and positioned histogram to be efﬁciently calculated

from a combination of four previously determined

histograms. The DH (Sizintsev et al., 2008) precom-

putes column histograms for a subset of an image,

such that it is speciﬁcally tailored to an exhaustive

search. The proposed LH method is, in some sense,

an extension of the DH in that column histograms are

also precomputed, but for full length columns, that

span the entire image.

Our LH approach has three phases: an exhaustive

search, followed by line histogram initialisation, and

ﬁnally rotational search. The exhaustive search gen-

erates similarity scores for each pixel location. Initial-

isation precomputes column histograms for the entire

image, with each location in a column containing the

Figure 2: Histogram initialisation.

histogram of all the pixels from the ﬁrst position to

the current position. For rotational search, the tem-

plate is rotated through 1

◦

→ 180

◦

and the orientation

and position yielding the best similarity score is se-

lected.

Exhaustive Search. The ﬁrst stage of the algo-

rithm is to perform an exhaustive search of the en-

tire image, retaining a subset of image locations most

closely matching the unrotated search template. The

DH is an extremely fast technique and is applied to

this end in our proposed LH method. The question

of how many close matches to retain for further at-

tention is not trivial and has thus far been determined

empirically. By enforcing a minimum distance be-

tween matches, based on the image size, it is possible

to ensure that all the matches are not so tightly clus-

tered that potential matches are overlooked. If only a

few matches are retained, or if they are localized to

a sub-area of the image, it is possible to initialise the

LH for small areas containing the matches. This po-

tentially offers additional computational savings. We

will touch on this again but later below LH initialisa-

tion is explained for the whole image. To perform his-

togram matching in general, there are many measures

that can be used, e.g. the L

norm, Bhattacharrya dis-

tance, Earth Mover’s distance, or χ

difference. Here,

we use the L

norm on 64-bin histograms.

Histogram Initialisation. Consider an image, P,

with M rows and N columns. The inititialized LH will

then be a M × N × B matrix, where B is the number

of bins. Starting at the ﬁrst row, histograms are calcu-

lated at each pixel location along each column, with

each location’s histogram describing the distribution

of the pixel located at that position and all those above

it on that column (see Fig. 2). In practice, this in-

volves performing a memory copy of the histogram

immediately above the current location and then in-

crementing the bin corresponding to the current pixel.

Note the histogram of the ﬁrst pixel marked p(1, n) in

column n is S(p(1, n)) and includes one pixel p(1, n),

the histogram of the second pixel marked p(2, n) in

column n is S(p(2, n)) and includes two pixels p(1, n),

ICPRAM 2012 - International Conference on Pattern Recognition Applications and Methods

128

(a) Unrotated template (b) Rotated template

, y

]

[

', y

, y

]

Figure 3: (a) and (b) Area histogram calculation for unrotated and rotated templates respectively, and (c) effect of rotating

template on horizontal displacement.

p(2, n), and the histogram of the m

pixel marked

p(m, n) in column n is S(p(m, n)) and includes m pix-

els. This process is repeated for each column in the

image so that location M in each column contains the

histogram for that entire column. This could be per-

formed for rows instead of columns, but for the sake

of clarity, columns are considered in the proceeding

discussion.

Rotational Search. Once the LH has been initial-

ized, (1) may be exploited to efﬁciently calculate

histograms for arbitrarily orientated and sized re-

gions. Fig. 3(a) illustrates a rectangular region, A,

subdivided into columns A

to A

. Each column’s

histogram is obtained by subtracting the histogram

stored immediately above the start of a column from

that at the last pixel in that column:

S(A

) = S(p(m+ s,n+ j)) − S(p(m, n+ j)) (2)

where (m, n) is the origin of the area histogram A, j =

1, . . . , t, and s is the length of column j. Next, the sub-

histograms, S(A

), are summed to yield the histogram

for A:

S(A) = S(A

)+S(A

)+· · · + S(A

) (3)

The discussion above refers to the unrotated rectangu-

lar template, but is equally applicable to a rotated one

in Fig. 3(b). All that is required are the start and end

points for each column across the template’s width.

In our implementation this is achieved by consider-

ing the line equations for the rectangle’s four sides at

◦

to 90

◦

when its centroid is at the origin. Start and

end points are computed for all orientations and these

may be used by simply adding the current search co-

ordinates to them.

3 COMPUTATIONAL ANALYSIS

The proposed LH method for rotated rectangular his-

tograms can offer signiﬁcant computational savings

over a naive approach where histograms are calcu-

lated from scratch, pixel by pixel. Combining his-

tograms requires that corresponding bin counts are

added or subtracted from one another. Hence, the

greater the number of bins used, the more com-

putationally expensive the LH technique becomes.

The naive approach does not involve combining his-

tograms, so is independent of bin count. It is, how-

ever, very sensitive to template size as the number of

operations required goes with the square of its length.

In simple terms, the LH approach offers the greater

savings for larger templates and fewer histogram bins.

We next consider the cost of generating his-

tograms for our rotated rectangular search templates.

The cost of calculating pixel by pixel conventional

histograms (CH) is independent of rectangle orienta-

tion because the cost is proportional to search area,

which is not a function of angle. For LH, the width

of the template and hence the number of columns re-

quired is dependent on the rectangle’s orientation (see

Fig. 3(c)). Note that for anticlockwise rotation by an

angle θ (0 < θ <

), the maximum width, w

rot

, of the

template is x

′

− x

′

. For rotation about the origin

′

− x

′

= (x

− x

)cosθ − (y

− y

)sinθ (4)

If w and h are the height and width of the search tem-

plate, (4) simpliﬁes to:

rot

= wcosθ+ hsinθ (5)

Note the sign has changed because (y

− y

) < 0. The

mean value of w

rot

is:

rot

Z π

wcosθ+ hsinθdθ (6)

which resolves to

(w+ h). Hence, for a unit length

square template the mean number of columns to be

considered, w

rot

, over a full

anticlockwise rota-

tion is the mean value of this function:

, which is

approximately 1.27. For more elongated templates,

LINE HISTOGRAM - A Fast Method for Rotated Rectangular Area Histogramming

129

e.g. where the height is 10 and the width 50, w

rot

around 38.2. This is important as it shows that less

column histograms have to be summed, on average,

than for the full width of the template, reducing cost.

Of course the conventional cost is also lower in this

case as the area is less.

Without loss of generality, consider a square im-

age P of size M × M and histogram with B bins, and

rectangular template T of size w× h. Using the same

entities operated in (Sizintsev et al., 2008), we set d

for division, f for ﬂoor and type conversion, and a

for addition or subtraction.The CH approach operates

on wh pixels for each template orientation and loca-

tion. Operations include: 1 division and 1 ﬂoor to

ﬁnd the histogram bin, and this bin is incremented us-

ing 1 addition. So the total computational cost of the

CH approach for a single orientation and location is

wh(d + f + a) and for multiple locations and orienta-

tions is

loc

angle

wh(d + f + a), (7)

where n

loc

and n

angle

are the number of locations and

angles examined respectively. The LH method re-

quires 1 histogram addition and 1 subtraction to gen-

erate histograms for each column and then w

rot

addi-

tions to combine them to produce the histogram for

the entire area. Hence for n

loc

locations and n

angle

angles the operations are:

loc

angle

rot

Ba (8)

However, there is also the LH initialisation cost. Ex-

cluding the cost of the memory copies, when moving

down each column, this is

(d + f + a) (9)

The costs deduced in the above discussion are sum-

marized in Table 1. Recall that w

rot

is a linear com-

bination of w and h so as they are increased LH be-

comes cheaper relative to CH. Conversely as B is in-

creased, the relative cost for LH goes up. Further-

more, to beneﬁt from the relative cheapness of LH for

rotation, n

loc

and n

angle

must be high enough to off-

set the initialisation cost of LH. In practical terms CH

and LH take the same time to execute, where B = 64,

w = 33, h = 19, n

loc

= 5, n

angle

= 180 and M = 277.

Note, the relative savings can be massively increased

by reducing M, initialising LH for a subset of the im-

age, or if many locations are being searched, reducing

B, using a more compact colour space representation,

e.g. HSV, which was used by Sizintsev et al (Sizintsev

et al., 2008), who set B to 16.

Histogram Memory Requirements. For an M × M

image and histogram representation with B bins, our

LH approach, like the IH, requires M

B units of mem-

ory. However, for small images with height < 256

pixels, it is only necessary to use unsigned chars for

each unit and unsigned short integers will always pro-

vide ample capacity for larger images. This contrasts

with the IH approach which can be subject to over-

ﬂow errors (Sizintsev et al., 2008) and requires 4 byte

integers as storage units. Furthermore, it is not always

necessary to initialise the LH for the entire image re-

gion so other potential avenues for reducing memory

requirement are available.

4 EXPERIMENTAL RESULTS

This section has two main objectives: ﬁrstly to

demonstrate how detection accuracy is improved us-

ing a rotating rectangular template and secondly to

show how and when the line histogram method is

computationally more efﬁcient than the conventional

approach. Fig. 4 shows the templates used in the var-

ious examples presented in this paper for reference.

a b c d

e f g

Figure 4: Templates: (a) Taxi sequence, (b) and (c) square

and rectangular templates, (d) and (e) for face tracking in

Girl and Villains, (f) and (g) for tracking multiple objects in

Road.

Fig. 5 presents two frames of the Taxi sequence

where the beneﬁts of employing a rotating template

is illustrated. The match maps in Figs. 5(b) and

5(f) clearly show two spatially disparate local minima

which leads to incorrect detection in Fig. 5(g) for the

unrotated histogram. Furthermore, note how the tem-

plate boundary completely encompasses the object of

interest in 5(d) for the proposed method, whereas in

Fig. 5(c) the ﬁt is less accurate without rotation, i.e.

as the result of IH or DH.

Fig. 6 compares the relevance of using rotated

templates for square and rectangular regions at sam-

ple rotations. The top row shows the conventional

output, i.e. again for IH, or DH, and the bottom row

presents the results for the proposed LH method. The

contrast in the results is far more striking when a rect-

angular region is being detected as there is no way

to effectively align elongated regions at different ori-

entations. The accuracy of the detection combined

with its discovered orientation can beneﬁt higher level

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130

Table 1: Comparison of computational cost.

Method sequencesInitialisation Rotated Template Histogram Calculation

CH 0 n

loc

angle

wh(d + f + a)

LH M

(d + f + a) n

loc

angle

rot

(a) Frame 26 (b) match map (c) Unrotated (d) Rotated

(e) Frame 39 (f) match map (g) Unrotated (h) Rotated

Figure 5: Sequence Taxi, comparing results on two different frames. Note the inaccuracy or loss of representation for the

conventional unrotated approaches.

(a) 25

◦

(b) 70

◦

(d) 80

◦

Figure 6: Finding a rotated object using square and rectangular templates at various rotations - top row: unrotated template

approaches (IH or DH), bottom row: LH.

recognition processes. Fig. 7 shows histogram sim-

ilarity distances at different rotation angles for the

square and rectangular templates in Fig. 6. Note

how far greater returns are gained for the rectangu-

lar template relative to the square template. The latter

shows maximum error at around 40

◦

whereas the for-

mer peaks at around 90

◦

In Fig. 8, the results of applying histogram detec-

tion to face tracking are shown in frames from two

different sequences, Girl and Villains. In both se-

quences superior alignment is achieved with LH’s ro-

tating template and the face orientation is revealed.

Figs. 8(i) and 8(j) illustrate how varying rotational

angle yields a minimal similarity distance for a ﬁxed

location for the frames used in Fig. 8. Further-

more, Table 2 lists the improved similarity scores and

agreement with handlabeled groundtruth using rotat-

ing templates in the two frames.

We have so far illustrated the beneﬁts of rotating a

rectangular search template when performing an ex-

haustive histogram-based search. Next, we demon-

strate empirically the savings made when calculat-

ing rotated histograms using the LH approach on a

3.2GHz CPU PC under Win XP, with 3GB RAM. All

the code was written in C++.

Table 3 shows the computational times for the var-

ious stages of an exhaustive search, including rota-

tion, for a single frame for different sequences and

LINE HISTOGRAM - A Fast Method for Rotated Rectangular Area Histogramming

131

Table 2: Comparison of groundtruth and predicted positions for unrotated and rotated templates. The similarity distance is

under the (L

norm) column

Image Groundtruth Method Predicted Angle L

norm

Girl (46,54) Unrotated (48,54) 0

◦

0.144

frame 69 Rotated (47,54) 27

◦

0.127

Villains (51,61) Unrotated (52,62) 0

◦

0.363

frame 14 Rotated (51,61) −45

◦

0.294

0 10 20 30 40 50 60 70 80 90

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

IH & DH

Rotation angle

Dissimilarity (L1)

10 20 30 40 50 60 70 80 90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

IH & DH

Rotation angle

Dissimilarity (L1)

Figure 7: The comparative histogram similarity results for the square (left) and rectangular (right) templates in Fig. 6 with

and without rotation.

(a) frame 69 (b) match map (c) Unrotated (d) Rotated: LH

(e) frame 14 (f) match map (g) Unrotated (h) Rotated: LH

−90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

Rotation angle

Dissimilarity (L1)

Best L1 at 27

(i) at pixel (47,54)

−85 −70 −55 −40 −25 −10 5 20 35 50 65 80

0.3

0.32

0.34

0.36

0.38

0.4

Best L1 at -45

Rotation angle

Dissimilarity (L1)

(j) at pixel (51,61)

Figure 8: Face tracking examples, sequences Girl and Villain, (top and middle rows, from left) original, histogram distance

map, unrotated result e.g. IH or DH, and LH’s rotated result. (bottom row) minimum dissimilarity measure for each frame.

template shapes. The number of locations searched,

loc

, is 5, the number of orientations examined, n

angle

is 180, and the number of bins, B, is 64. For each

of the four sequences, running times are provided for

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132

Table 3: Running time (in ms) comparisons for various templates.

Sequence Image size Template size DH search time Init. time Rotate time Total

Girl (CH) 128× 96 31× 45 1.78 0 64.41 66.19

Girl (LH) 128× 96 31× 45 1.78 2.45 9.11 13.34

Villains (CH) 128× 96 19× 35 2.26 0 30.98 33.24

Villains (LH) 128× 96 19× 35 2.26 2.55 6.10 10.91

Square (CH) 480× 360 47× 47 54.10 0 307.03 361.13

Square (LH) 480× 360 47× 47 54.10 51.22 26.68 132.00

Rectangle (CH) 320× 240 35× 19 25.50 0 24.73 50.23

Rectangle (LH) 320× 240 35× 19 25.50 20.71 5.16 51.37

(a) Frame 10 (b) Frame 28 (c) Frame 57 (d) Frame 66

Figure 9: Sequence Road, an example of tracking multiple objects.

rotated templates calculated in a pixel by pixel fash-

ion (CH) and using LH. Note that the DH search

time is the same for CH and LH as it is the optimal

method for ﬁnding candidate locations to apply rota-

tion. These results show excellent agreement with the

computational costs determined analytically in Sec-

tion 3 and summarized in Table 1. Larger images re-

quire longer LH initialisation times whilst larger tem-

plates are relatively expensive to calculate using CH.

For example, the ‘Girl’ sequence is processed ﬁve

times as quickly using LH as the image is small and

the template relatively large. Indeed, using LH in con-

junction with DH, a rate of 75fps is achieved. On the

other hand, for the ‘Rectangle’ sequence, LH and CH

take around the same time to execute as the image is

larger and the template smaller.

5 CONCLUSIONS

We proposed the Line Histogram, a new method to

compute a rotated histogram which is based on sub-

histograms along columns of a region. The method

is fast and can be used in real-time applications for

object detection and tracking, single, or multiple (e.g.

see Fig. 9). We outline its computational performance

analytically and through several experiments.

ACKNOWLEDGEMENTS

This paper is supported by National Natural Sci-

ence Foundation of P.R.China(60805015,61175029)

and Shaanxi Province Natural Science Founda-

tion(2011JM8015).

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