USING THE DISCRETE HADAMARD TRANSFORM TO DETECT

MOVING OBJECTS IN SURVEILLANCE VIDEO

Chanyul Kim and Noel E.O’Connor

CLARITY: Centre for Sensor Web Technologies

Dublin City University, Glasnevin, Dublin, Ireland

Keywords:

Discrete Hadamard Transform, Moving object detection, Edge.

Abstract:

In this paper we present an approach to object detection in surveillance video based on detecting moving edges

using the Hadamard transform. The proposed method is characterized by robustness to illumination changes

and ghosting effects and provides high speed detection, making it particularly suitable for surveillance appli-

cations. In addition to presenting an approach to moving edge detection using the Hadamard transform, we

introduce two measures to track edge history, Pixel Bit Mask Difference (P B M D ) and History Update Value

(H U V ) that help reduce the false detections commonly experienced by approaches based on moving edges.

Experimental results show that the proposed algorithm overcomes the traditional drawbacks of frame differ-

encing and outperforms existing edge-based approaches in terms of both detection results and computational

complexity.

1 INTRODUCTION

Moving object detection in video sequences is an im-

portant research area since it can be viewed as a lower

level vision task necessary to achieve higher level

event understanding. It is a critical task for appli-

cations such as video surveillance, trafﬁc monitoring

and video compression e.g. region of interest (ROI)

coding. In this paper we propose a computationally

efﬁcient moving object detection algorithm based on

moving edge detection using the Discrete Hadamard

Transform (DHT) that is particularly suited to real-

time surveillance scenarios.

Within the literature we can consider the follow-

ing main approaches to object detection in surveil-

lance scenarios: frame differencing, background sub-

traction, optical ﬂow and pre-trained statistical ap-

proaches. Statistical training methods require many

training samples and typically require signiﬁcant

computational complexity to obtain good immunity

to noise (Wang and Suter, 2006). Optical ﬂow meth-

ods allow accurate detection of moving objects that

are free of ghosts, but they can have problems with il-

lumination changes. Such approaches are often com-

plex and not suitable for real-time systems, although

there has been some work on achieving real-time op-

eration (Jongcheol et al., 2005; Bruhn and Schnorr,

2006). The background subtraction method, some-

times referred to as background removal, is a popular

approach, where each video frame is compared to a

background model and signiﬁcant deviations from the

model are considered to be moving objects. Back-

ground models include recursive and non-recursive

methods (classiﬁcation terms suggested by Cheng

and Kamth (Cheung and Kamath, 2004)). Back-

ground subtraction should be able to adapt to grad-

ual or sudden illumination changes and local changes

such as shadows. In order to handle non-stationary

background objects, such as waving trees and image

changes due to camera motion, complex algorithms

are needed. Many background subtraction algorithms

are surveyed in (Shireen et al., 2008). Frame differ-

encing, sometimes referred to temporal differencing,

is the most computationally efﬁcient approach, but is

prone to producing poor results. The difference frame

is binarised by thresholding at some pre-determined

value to obtain changed regions of the video. How-

ever, the appropriate threshold is dependent on the

scene as well as illumination that may change over

time. This means that the threshold value should be

512

Kim C. and E.O’Connor N. (2009).

USING THE DISCRETE HADAMARD TRANSFORM TO DETECT MOVING OBJECTS IN SURVEILLANCE VIDEO.

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 512-518

DOI: 10.5220/0001800205120518

 SciTePress

calculated dynamically based on image content, so

experimentally choosing a value is usually not appro-

priate for automatic systems.

Since the primary objective of our work is com-

putational efﬁciency and ease of implementation for

real-time systems, we target a frame differencing ap-

proach, but one based on image edges. Our approach

does not critically depend on a particular threshold

thereby avoiding some of the drawbacks of traditional

frame differencing approaches. To achieve computa-

tional efﬁciency, we propose an edge detection algo-

rithm based on the Discrete Hadamard Transform in-

stead of conventional methods such as Sobel, Canny

and Prewitt operations which often introduce signif-

icant complexity for background modeling (Shireen

et al., 2008). Furthermore, our block-based approach

lends itself to efﬁcient memory usage and robust pro-

cessing.

The remainder of the paper is organised as fol-

lows. Section 2 describes related work and the moti-

vation for our approach. Section 3 describes the over-

all architecture as well as the details of the proposed

method. Experimental results are presented in Sec-

tion 4. Section 5 contains the conclusions.

2 RELATED WORK

Frame differencing uses the video frame at time t − 1

as the background model for the frame at time t. The

unchanged part is eliminated in the difference im-

age (difference map) with only the changed areas re-

tained. Frame differencing is sensitive to noise and

variations in illumination and fails to identify the in-

terior pixels of a large, uniformly-colored moving ob-

ject (Shireen et al., 2008; Radke et al., 2005). It is

well known that object detection using single frame

differencing, while computationally much simpler

than other techniques, is more liable to generate large

areas of false foregrounds known as ghosts (Archetti

et al., 2006). An appropriate threshold value for lo-

calising the moving objects can be set empirically or

adaptively. In the former case, the threshold value

is ﬁxed for all pixels in the frame and determined

experimentally based on a large database (Durucan

and Ebrahimi, 2000). In the latter case, the threshold

value is adapted by pre-deﬁned rules (Costantini et al.,

2001; Otsu, 1979). To mitigate against the critical de-

pendency on thresholds, Cavallaro proposed using a

Sobel edge detector between the current and the ref-

erence image to leverage information edges that are

immune to noise and are not changed by illumination

variations (Cavallaro and Ebrahimi, 2001). Julius et

al. also proposed edge based moving object detection

for surveillance applications to obtain robustness to

illumination changes (Julius et al., 2007). Their ap-

proach measured the difference between edge pixels

to match and classify edges. Chaohui et al. also pre-

sented a moving object algorithm based on frame dif-

ferencing and edge detection (Chaohui et al., 2007),

and their approach is most similar to that proposed

in this paper. In their proposed method, no thresh-

old value is applied in the binarisation process but

only used for counting non-zero pixels in the moving

mask. However, their approach introduces computa-

tional complexity due to the presence of the following

steps: (1) an image ﬁlter to reduce noise; (2) calcula-

tion of the amplitude and direction of the gradient of

each pixel; (3) application of thinning to obtain edges

one pixel in width; (4) application of the threshold

(simple or complex).

3 THE PROPOSED APPROACH

The proposed moving object detection method con-

sists of three components, edge detection, moving

edge detection and post-processing. An edge is de-

tected by classifying coefﬁcients of the DHT to avoid

the computational burden of using conventional edge

detection algorithms. The moving edges are extracted

by frame differencing the edge map and calculating

and tracking the transitions of edge patterns in the

same 2 × 2 block. Finally, moving objects are ob-

tained by a post-processing step that includes region

marking and morphological operations.

3.1 Discrete Hadamard Transform

The two-dimensional Hadamard transform can be

written in matrix and series form as;

F(u, v) =

[ f(x,y)]H

(1)

[ f(x,y)]H

(2)

∑

N−1

x=0

∑

N−1

y=0

f(x, y)(−1)

s(x,y,u,v)

(3)

where s(x, y, u, v) ≡

∑

n−1

i=0

(u)x

+ g

(v)y

, y

, u

, v

) is the binary representation of the

(x, y,u, v), (x, y) and (u, v) are row and column

position in pixel and DHT domain, and

≡ u

n−1

≡ u

n−1

+ u

n−2

≡ u

n−2

+ u

n−3

n−1

≡ u

+ u

USING THE DISCRETE HADAMARD TRANSFORM TO DETECT MOVING OBJECTS IN SURVEILLANCE VIDEO

513

Non-

Edge

Figure 1: Edge classiﬁcation patterns in a 2× 2 pixel block;

patterns are denoted as numbers according to edge direction

(horizontal, vertical, diagonal and negative diagonal).

We use the ordered version of the DHT so that se-

quency is an increasing function of the number of

rows (or columns). A conservationof energy property

exists between the spatial domain and the Hadamard

domain. It is useful as a criterion for classifying edges

(as described later in Eq (5)). A 2× 2 DHT is used to

classify edge patterns in this paper.

3.2 Edge Detection based On DHT

Coefﬁcients

Edge patterns are assigned identifying numbers by

classifying different patterns of pixels in a 2×2 block

as shown in Figure 1. Let the coefﬁcients of the

Hadamard transform in a 2 × 2 image block be de-

noted as F(u, v). We ﬁrst calculate the following:

χ = max(|F(1, 0)|,|F(0, 1)|, |F(1, 1)|) (4)

D =









F(1,0)

F(0,1)

+ 0.5



if F(0, 1) 6= 0

2 otherwise

(5)

where [] is a round function.

P (i), i =











0 if (χ ≤ τ)

1 if (χ > τ

D = 2

F(1,0) > 0)

2 if (χ > τ

D = 2

F(1,0) < 0)

3 if (χ > τ

D = 1

F(1,1) > 0

F(1,0) > 0)

4 if (χ > τ

D = 1

F(1,1) < 0

F(1,0) < 0)

5 if (χ > τ

D = 1

F(1,1) < 0

F(1,0) < 0)

6 if (χ > τ

D = 1

F(1,1) < 0

F(1,0) > 0)

7 if (χ > τ

D = −1

F(1, 1) < 0

F(1,0) < 0)

8 if (χ > τ

D = −1

F(1, 1) > 0

F(1,0) > 0)

9 if (χ > τ

D = −1

F(1, 1) > 0

F(1,0) > 0)

10 if (χ > τ

D = −1

F(1, 1) > 0

F(1,0) < 0)

11 if (χ > τ

D = 0

F(0,1) > 0)

12 if (χ > τ

D = 0

F(0,1) < 0)

(6)

For a non-edge region (assigned P (0) as shown

in Figure 1), the non zero position coefﬁcients

(F(1, 0), F(0, 1),F(1, 1)) should be zero. However,

the non-zero position coefﬁcients increase according

to edge strength. Therefore if χ is greater than a pre-

deﬁned threshold value (τ), the block is classiﬁed as

an edge block, otherwise as a non-edge block. We set

this pre-deﬁned noise threshold to ten in this paper.

This means that when the difference of pixel values

is greater than ten, we consider this block as an edge.

Pattern P (i) is obtained via Eq (5) and the properties

of the Hadamard transform, as shown in Eq (6), where

τ is a pre-deﬁned threshold value and

is a logical

AND operation. In Eq (6), D indicates the direction

of the edge. P (5), P (6) and P (9), P (10) are the one-

pixel shifted edges of P (3), P (4) and P (7), P (8) re-

spectively.

Figure 2 illustrates a comparison of the result of

edge detection using Canny edge detection (Canny,

1986) and the proposed method. The Canny opera-

tor has the feature of high precision localisation of a

single edge, but when the background of the scene is

complicated, too many edges will be detected. An ac-

curate result requires that well-matched thresholding

values be calculated, and this causes additional com-

putational complexity. The proposed edge detection

algorithm suffers sensitivity to noise and some edge

lines are disconnected due to noise and block-based

processing. Despite this, the proposed edge detection

algorithm has two advantages over Canny edge de-

tection: (1) it does not need to set critical threshold

values and to perform a ﬁltering operation (instead

of using a ﬁlter, noise effects are eliminated via the

moving object detection algorithm described in Sec-

tion 3.3); (2) the block based approach provides for

memory efﬁciency and low complexity.

3.3 Moving Edge Detection

After edge detection, the blocks corresponding to

moving edges are determined. As an object moves in

the scene it covers and uncovers background around

its borders and possibly deforms. These phenomena

result in a change of the edge characteristics within

blocks on the object’s boundary. This can be used

to detect moving edge blocks from frame to frame.

There are 3 possibilities to consider: (1) edge to non-

edge (2) non-edge to edge (3) edge direction chang-

ing.

Within a frame differencing framework, the ﬁrst

possibility above will result in ghost edges that should

be removed if they can be detected. In the ideal case,

the other possibilities above will result in real moving

edges but in practice there will be a lot of noise. To

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

514

(a) (b) (c)

Figure 2: (a) The 1500

frame of the dataset3 camera1 sequence of PETS2001; (b) edge detection using the Canny detector

with a high threshold of 190, a low threshold of 110 and a 3× 3 Sobel mask; (c) our proposed edge detection approach.

Figure 3: The example of P B M D between P (1) and other

patterns.

reduce the effect of noise, the history of the edge is

examined and processed in our proposed method. We

introduce the Pixel Bit Mask Difference (P B M D )

as an observation factor. P B M D is the number of

different bits between assigned edge patterns. It is

increased based on the strength of the noise that po-

tentially results in a bit change. P B M D can be cal-

culated as follows (where black and white pixels in

Figure 1 are set to 0 and 1 respectively):

P B M D =

∑

(u,v)∈{0,1}

P (i)

(u,v)

⊕ P ( j)

(u,v)

(7)

where ⊕ is a XOR bit operation, P (i)

(u,v)

, P ( j)

(u,v)

are mask bits of P (i) and P ( j). For example,

P B M D is calculated as ’1’ (meaning there is one bit

difference) between P (1) and P (3), P (6), P (8), P (9)

by comparing the pixel bit masks as shown in Fig-

ure 3. The P B M D between P (1) and P (0) (non-

edge block) should be controlled in a different way

by setting a maximum value of P B M D (i.e. by set-

ting α to ‘1’ as shown in Figure 3.

The differencing between edges in temporal se-

quences sometimes generates false alarms if edges

vary in the background. This is an inevitable con-

sequence of frame differencing methods. We intro-

duce a compensation method for false alarms using

the History Update Value (H U V ) based on P B M D .

H U V is observed at each frame and compared to the

P B M D to classify moving edges from all possible

candidate edges. When the current block has the same

edge pattern from the past frame, the H U V is zero.

This means that any edge pattern appearing in this

block except the same edge pattern from the previous

.

Static Candidate

Patterns

Moving Edge

Candidate Patterns

Figure 4: An example of detecting moving edges by observ-

ing the relationship between P B M D and H U V , B

is a

2×2 block m in the i

frame. β = 0.8.

frame is considered as a moving edge. On the con-

trary, the higher number of H U V represents much

noise existence from the past frames, only restricted

edge patterns are decided as a moving edge. H U V

can be obtained by using Eq (8). Figure 4 shows the

process to detect moving edges using P B M D and

H U V at β of 0.8. The 2x2 block is decided that has

a moving edge by comparing H U V in the previous

frame and the current P B M D .

H U V (i) = β × H U V (i− 1) + (1 − β) × P B M D (i)

(

P B M D (i+ 1) > H U V (i) moving block

P B M D (i+ 1) ≤ H U V (i) non moving block

(8)

where P B M D (i), H U V (i) are the P B M D and

H U V values of a block in the i

frame and β is a

weighted constant satisfying the condition β ∈ [0, 1].

In summary, the overall moving edge detection al-

gorithm can be explained as follows.

1. Obtain average pixel differences between frames

t and t − 1 (ZS

= (F(0, 0)

− F(0, 0)

t−1

)). If ZS

is larger than a pre-deﬁned value (τ

⋆

), a block is

considered a candidate moving block, otherwise

non-moving block.

2. If ZS

> τ

⋆

, P B M D and H U V are calculated. If

P B M D (t) > H U V (t − 1), this block is consid-

ered as a moving block, the value of the H U V is

updated with Eq (8).

3. When moving edge blocks are obtained, moving

USING THE DISCRETE HADAMARD TRANSFORM TO DETECT MOVING OBJECTS IN SURVEILLANCE VIDEO

515

edge pixels are marked as the whole 2 × 2. This

has the effect of generating a sub-sampled moving

edge binary image.

Figure 5: (a) 520

, 530

, 540

frames of PETS2006

dataset; (b) edge map detected by the proposed method; (c)

moving edge extraction result; (d) region marking based on

moving edges; (e) AND operation between marked regions

and edges using Canny operator; (f) after morphological

closing.

The entire process is illustrated in Figure 5(a)–(c).

3.4 Post-Processing

After separating moving edges, we need to locate the

object so as to get the position and the shape of mov-

ing objects. We propose a simple three step procedure

to extract location and shape. All post-processing is

applied to the down sampled image obtained automat-

ically, leading to very efﬁcient processing.

1. A 4 × 4 window scans the whole image in raster

scan order and ﬁnds a region containing moving

edges. Figure 5(d) shows how the marked region

area can contain missed moving edges.

2. There are many algorithms to ﬁll a contour bound-

ary such as connected components algorithms and

neighbor searching. The proposed method uses an

AND operation performed between a marked re-

gion and the edges in the original image obtained

using a Canny operator. This does not generate

signiﬁcant computational complexity since it acts

only on the marked region. The result is depicted

in Figure 5(e).

3. The morphologicalclosing operation is applied on

the moving edge binary mask to ﬁll small missing

edges. Closing is able to eliminate salt and pepper

noise, narrow cracks, small holes and ﬁll the gaps

in the contour. The closing of A by B, A • B =

(A⊕ B) ⊖ B, is simple dilation of A by B followed

by erosion of the result by B. Figure 5(f) shows

the output image after morphological closing.

4 EXPERIMENTAL RESULTS

Our experiments aimed at evaluating the moving ob-

ject detection algorithm’s ability to deal with illu-

mination changes, in avoiding ghost effects and as-

sessing its complexity. All processing is performed

on the Y component of the YUV signal. All tests

are performed on an Intel Core(TM)2 Duo 3.0GHz

with 2GB RAM using Window XP version 2002 with

service pack 2 written in ANSI C++. The pop-

ular and commonly available surveillance datasets,

namely CAVIAR

and PETS

, were used to evalu-

ate the performance of the proposed method. The

proposed method is compared with two frame differ-

encing low complexity methods. The ﬁrst uses adap-

tive thresholding based on observing histograms as

described in (Otsu, 1979). The second is the edge-

based frame differencing and thresholding approach

of Chaohui (Chaohui et al., 2007). We qualitatively

illustrate our approach in Figure 6 using 3 different

scenarios. Figure 6(a) has no moving objects, and

only features luminance changes. Figure 6(b) shows

a moving object that has uniform luminance in its in-

ternal and boundary area, so that some edges do not

appear. Figure 6(c) represents a fast moving object

that generates the ghost effect. The simple frame dif-

ferencing approach suffers under luminance changes

and also introduces the ghost effect as seen in Fig-

ure 6(d). The edge based approach of Chaohui has

good quality compared to frame differencing, but it

also suffers false alarms due to variation of edges in

successive frames, as shown in Figure 6(e). The pro-

posed method gives good results with no false alarms

since our approach uses not only frame differencing

but also tracks the history of edges.

In order to have a quantitative evaluation of the

performance, we use recall and precision, to quantify

how well each algorithm matches the ground truth

suggested by Cheung and Kamath (Cheung and Ka-

math, 2004). To adapt the quantitative method to the

proposed method, we only compared moving edge

available at http://homepages.inf.ed.ac.uk/rbf/CAVIAR

available at http://www.cvg.rdg.ac.uk/slides/pets.html

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

516

pixels and not all object pixels. Our modiﬁed metric

can be deﬁned by Eq (9)(10).

Recall =

# of moving edges detected in the ground truth

# of edge pixels in the ground truth

(9)

Precision =

# of moving edges detected in the ground truth

# of moving edges detected in a whole frame

(10)

Figure 6: (a)(b) & (c) Sample test sequences used to illus-

trate performance for illumination changes, ghosting and

fast moving objects; (d) results based on frame differenc-

ing, threshold ; (e) Chaohui’s approach ; (f) the proposed

method.

Figure 7: (a) Original scene (b) Edge map detected by the

Canny detector in the ground truth; (c), (d) & (e) Moving

edges detected by (Otsu, 1979), (Chaohui et al., 2007) and

our method : recall =

103

496

234

496

351

496

(f), (g) & (h)Detected

moving edges in the entire frame for each approach.

For clarity, the evaluation process is illustrated in Fig-

ure 7 for the different moving object detection algo-

rithms considered. The ground truth region is high-

lighted Figure 7(b) and shows the edges generated

by the Canny edge detector within this region. The

frame differencing and thresholding method gener-

ates ghosts that produce multiple edges as shown

in Figure 7(f). This points to a potential problem

with our proposed Recall metric, whereby approaches

prone to ghost effects will results in artiﬁcially high

Recall values (due to the presence of more mov-

ing edges). For this reason, we exclude the sim-

ple frame differencing approach from the quantita-

tive evaluation and focus only on our method and

that of Chaohui. The calculated Recall is depicted in

Figure 7(c)(d)(e). Figure 8 shows Precision and Re-

call graphs for both approaches for 100 frames of the

CAVIAR sequence. The proposed method shows the

high performance(large µ) and independence of im-

age contents(small σ). The improvement of our ap-

proach over Chaohui’s is mainly due to the lack of

false alarms it produces – as is clearly illustrated in

Figure 7(g) & (h).

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

Chaohui's method

Proposed method

Recall

Precision

Figure 8: Recall and Precision for 100 frames of the

CAVIAR sequence; µ is a average value and σ is a standard

deviation.

Table 1: Performance analysis of the computational com-

plexity of different approaches. T is the total time(seconds)

for 500 frames.

Time (sec)

Frame differencing (Otsu, 1979) 5.4

Chaohui’s method (Chaohui et al., 2007) 2.4

The proposed method 1.1

Finally, we compare computational complexity with

Chaohui’s method. We use from the 830

to the

1229

frame (500 frames in total) of the “Walk-

ByShop1front” sequence of CAVIAR in 384 × 288

resolution. The proposed method shows higher de-

tection speed than other fast detection algorithms as

illustrated in Table 1. The improveddetection speed is

mainly as a result of the fact that the proposed method

uses an efﬁcient edge detection algorithm rather than

other conventional approaches and the fact that post-

processing is performed on the down-scaled image.

USING THE DISCRETE HADAMARD TRANSFORM TO DETECT MOVING OBJECTS IN SURVEILLANCE VIDEO

517

5 CONCLUSIONS

In this paper, we present edge based moving ob-

ject detection using the Hadamard transform. The

Hadamard transform is a computationally efﬁcient

tool because it consists of only subtractions and

adders. We propose a moving object detection al-

gorithm based on this new edge detection approach.

The edge pattern of a 2 × 2 block is classiﬁed by ob-

serving the coefﬁcients of the Hadamard transform.

P B M D and H U V are deﬁned in order to detect

moving blocks by observing the history of edges. The

block-based approach provides potential to save on

memory usage and data processing.

The proposed method targets reducing complex-

ity while addressing the main problems encountered

by frame differencing such as illumination changes

and ghost effects. We have followed this approach

since we believe that edge features are potentially su-

perior to other types of features – they are robust to

sudden illumination changes and computationally ef-

ﬁcient because edge information is stored in binary

form. However, we acknowledge that the proposed

edge detection algorithm suffers discontinuity of edge

shape that mainly arises due to slow moving objects.

This could potentially be recovered by using the U

and V components based on a uniform colour as-

sumption for objects, and we plan to investigate this

in future work.

ACKNOWLEDGEMENTS

Authors would like to acknowledge the support of

Samsung Electronics and Science Foundation Ireland

under grant 07/CE/I1147.

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