EFFICIENT MOTION DEBLURRING FOR INFORMATION

RECOGNITION ON MOBILE DEVICES

Florian Brusius, Ulrich Schwanecke and Peter Barth

Hochschule RheinMain, Unter den Eichen 5, 65195 Wiesbaden, Germany

Keywords:

Image processing, Blind deconvolution, Image restoration, Deblurring, Motion blur estimation, Barcodes,

Mobile devices, Radon transform.

Abstract:

In this paper, a new method for the identiﬁcation and removal of image artifacts caused by linear motion

blur is presented. By transforming the image into the frequency domain and computing its logarithmic power

spectrum, the algorithm identiﬁes the parameters describing the camera motion that caused the blur. The

spectrum is analysed using an adjusted version of the Radon transform and a straightforward method for

detecting local minima. Out of the computed parameters, a blur kernel is formed, which is used to deconvolute

the image. As a result, the algorithm is able to make previously unrecognisable features clearly legible again.

The method is designed to work in resource-constrained environments, such as on mobile devices, where it

can serve as a preprocessing stage for information recognition software that uses the camera as an additional

input device.

1 INTRODUCTION

Mobile devices have become a personal companion

in many people’s daily lives. Often, mobile applica-

tions rely on the knowledge of a speciﬁc context, such

as location or task, which is cumbersome to provide

via conventional input methods. Increasingly, cam-

eras are used as alternative input devices providing

context information – most often in the form of bar-

codes. A single picture can carry a large amount of

information while at the same time, capturing it with

the integrated camera of a smartphone is quick and

easy. The processing power of smartphones has sig-

niﬁcantly increased over the last years, thus allowing

mobile devices to recognise all kinds of visually per-

ceptible information, like machine-readable barcode

tags and theoretically even printed text, shapes, and

faces. This makes the camera act as an one-click

link between the real world and the digital world in-

side the device (Liu et al., 2008). However, to reap

the beneﬁts of this method the image has to be cor-

rectly recognised under various circumstances. This

depends on the quality of the captured image and is

therefore highly susceptible to all kinds of distortions

and noise. The photographic image might be over- or

underexposed, out of focus, perspectively distorted,

noisy or blurred by relative motion between the cam-

era and the imaged object. Unfortunately, all of those

problems tend to occur even more on very small cam-

eras. First, cameras on smartphones have very small

image sensors and lenses that are bound to produce

lower quality images. Second, and more important,

the typical single-handed usage and the light weight

of the devices make motion blur a common problem

of pictures taken with a smartphone. In many cases,

the small tremor caused by the user pushing the trig-

ger is already enough to blur the image beyond ma-

chine or human recognition.

Blurry image taken by user Preprocessing (blur removal)

4915355604303

Information recognition

Figure 1: Use of the image deblurring algorithm as a pre-

processing stage for information recognition software.

In order to make the information that is buried in

blurry images available, the artefacts caused by the

blur have to be removed before the attempt to extract

the information. Such a preprocessing method should

run in an acceptable time span directly on the de-

vice. In this paper, we present a method that identiﬁes

and subsequently removes linear, homogeneous mo-

tion blur and thus may serve as a preprocessing stage

for information recognition systems (see ﬁgure 1).

Brusius F., Schwanecke U. and Barth P..

EFFICIENT MOTION DEBLURRING FOR INFORMATION RECOGNITION ON MOBILE DEVICES.

DOI: 10.5220/0003321200070018

In Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory

and Applications (IMAGAPP-2011), pages 7-18

ISBN: 978-989-8425-46-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 RELATED WORK

In the last thirty-ﬁve years, many attempts have been

made to identify and remove artefacts caused by im-

age blur. Undoing the effects of linear motion blur

involves three basic steps that can be considered as

more or less separate from each other: Calculating

the blur direction, calculating the blur extent, and ﬁ-

nally using these two parameters to deconvolute the

image. Since the quality of the deconvolution is

highly dependent on the exact knowledge of the blur

kernel, most publications focus on presenting new

ways for blur parameter estimation. While some of

the algorithms are developed to work upon a series

of different images taken of the same scene (Chen

et al., 2007; Sorel and Flusser, 2005; Harikumar and

Bresler, 1999), the method in this paper attempts to

do the same with a single image.

2.1 Blur Angle Calculation

Existing research can be divided into two groups: One

that strives to estimate the blur parameters in the spa-

tial image domain and another that tries to do the

same in the frequency domain.

The former is based on the concept of motion

causing uniform smear tracks of the imaged objects.

(Yitzhaky and Kopeika, 1996) show that this smear-

ing is equivalent to the reduction of high-frequency

components along the direction of motion, while it

preserves the high frequencies in other directions.

Thus, one can estimate the blur angle by differen-

tiating the image in all directions and determining

the direction where the total intensity of the image

derivative is lowest. However, this approach works

best when the imaged objects are distinct from the

background, so that the smears will look like distinct

tracks. It also assumes that the original image has

similar local characteristics in all directions. Such

methods suffer from relatively large estimation errors

(Wang et al., 2009). They also need a lot of computa-

tion time and therefore are not applicable to real time

systems.

A more common approach is the blur direction

45°

Figure 2: Image of a barcode blurred by linear camera mo-

tion in an angle of 45° and the resulting features in its loga-

rithmic power spectrum.

identiﬁcation in the frequency domain. (Cannon,

1976) showed that an image blurred by uniform lin-

ear camera motion features periodic stripes in the fre-

quency domain. These stripes are perpendicular to

the direction of motion (see ﬁgure 2). Thus, know-

ing the orientation of the stripes means knowing the

orientation of the blur. In (Krahmer et al., 2006), an

elaborate overview of the diverse methods for esti-

mating linear motion blur in the frequency domain is

presented. One possibility to detect the motion an-

gle is the use of steerable ﬁlters, which are applied to

the logarithmic power spectrum of the blurred image.

These ﬁlters can be given an arbitrary orientation and

therefore they can be used to detect edges of a cer-

tain direction. Since the ripples in the image’s power

spectrum are perpendicular to the direction of motion

blur, the motion angle can be obtained by seeking the

angle with the highest ﬁlter response value (Rekleitis,

1995). Unfortunately, this method delivers very in-

accurate results. Another method of computing the

motion direction analyses the cepstrum of the blurred

image (Savakis and Easton Jr., 1994; Chu et al., 2007;

Wu et al., 2007). This is based on the observation that

the cepstrum of the motion blur point spread function

(PSF) has large negative spikes at a certain distance

from the origin, which are preserved in the cepstrum

of the blurred image. In theory, this knowledge can

be used to obtain an approximation of the motion an-

gle by drawing a straight line from the origin to the

ﬁrst negative peak and computing the inverse tangent

of its slope. However, this method has two major

disadvantages. First, it only delivers good results in

the absence of noise, because image noise will sup-

press the negative spikes caused by the blur. And sec-

ond, calculating the cepstrum requires an additional

inverse Fourier transform, which is computationally

expensive. A third approach is the use of feature

extraction techniques, such as the Hough or Radon

transform. These operations detect line-shaped struc-

tures and allow for the determination of their orien-

tations (Toft, 1996). The Hough transform, as it is

used in (Lokhande et al., 2006), requires a prelimi-

nary binarisation of the log spectrum. Since the high-

est intensities concentrate around the center of the

spectrum and decrease towards its borders, the bina-

risation threshold has to be calculated separately for

each pixel, which can become computationally pro-

hibitive. Another issue is that the stripes tend to melt

into each other at the origin and thus become indis-

tinct, which makes ﬁnding an adaptive thresholding

algorithm that is appropriate for every possible ripple

form a difﬁcult, if not impossible task (Wang et al.,

2009). The Radon transform is able to perform di-

rectly upon the unbinarised spectrum and is therefore

IMAGAPP 2011 - International Conference on Imaging Theory and Applications

much more practical for time-critical applications. As

a result, it delivers a two-dimensional array in which

the coordinate of the maximum value provides an esti-

mate of the blur angle. According to (Krahmer et al.,

2006), the Radon transform delivers the most stable

results. However, this method needs a huge amount

of storage space and computation time.

2.2 Blur Length Calculation

The estimation of the blur extent in the spatial image

domain is based on the observation that the derivative

of a blurred image along the smear track emphasises

the edges of the track which makes it possible to iden-

tify its length (Yitzhaky and Kopeika, 1996). Again,

this method highly depends on distinctively visible

smear tracks and is therefore very unstable. Most

of the algorithms estimate the blur length in the fre-

quency domain, where it corresponds to the breadth

and frequency of the ripples. The breadth of the cen-

tral stripe and the gaps between the ripples are in-

versely proportional to the blur length. To analyse

the ripple pattern, usually the cepstrum is calculated.

One way of computing the blur extent is to estimate

the distance from the origin where the two negative

peaks become visible in the cepstrum. After rotat-

ing the cepstrum by the blur angle, these peaks ap-

pear at opposite positions from the origin and their

distance to the y-axis can easily be determined (Chu

et al., 2007; Wu et al., 2007). Another way collapses

the logarithmic power spectrum onto a line that passes

through the origin at the estimated blur angle. This

yields a one-dimensional version of the spectrum in

which the pattern of the ripples becomes clearly vis-

ible, provided that the blur direction has been calcu-

lated exactly enough. By taking the inverse Fourier

transform of this 1-D spectrum, which can be called

the 1-D cepstrum, and therein seeking the coordinate

of the ﬁrst negative peak, the blur length can be esti-

mated (Lokhande et al., 2006; Rekleitis, 1995). As

with the angle estimation, these two methods have

their speciﬁc disadvantages: In the ﬁrst method, cal-

culating the two-dimensional cepstrum is a compara-

tively expensive operation, while the second method

is once again highly susceptible to noise.

2.3 Image Deblurring

Knowing the blur parameters, an appropriate PSF can

be calculated. This blur kernel then can be used to re-

construct an approximation of the original scene out

of the distorted image (Krahmer et al., 2006). Un-

fortunately, traditional methods like Wiener or Lucy-

Richardson ﬁlter tend to produce additional artefacts

of their own in the deconvoluted images (Chalkov

et al., 2008). These artefacts particularly occur at

strong edges and along the borders of the image.

Some methods have been developed to overcome that

issue, such as in (Shan et al., 2008), where a new

model for image noise is presented. However, these

methods always involve some sort of iterative optimi-

sation process, which is repeated until the result con-

verges towards an ideal. This makes them inappropri-

ate for the use in time-critical applications. Luckily,

there is no need to get rid of all the artefacts, as long

as the information contained in the image is recognis-

able. However, it has to be taken into account that the

deconvolution artefacts may still hinder or complicate

the recognition process.

3 THE IMAGE DEGRADATION

MODEL

In order to support the elimination or reduction of

motion blur, a mathematical model that describes this

degradation is needed. When a camera moves over a

certain distance during exposure time, every point of

the pictured scene is mapped onto several pixels of the

resulting image and produces a photography that is

blurred along the direction of motion. This procedure

can be regarded as some sort of distortion of the un-

blurred original image, i.e. the picture taken without

any relative movement between the camera and the

imaged scene. The distortion can be modelled as a lin-

ear ﬁlter function h(u,v) that describes how a point-

shaped light source would be mapped by the photog-

raphy and which is therefore called the point spread

function (PSF). Thus, the blurring of an original im-

age f (u,v) (see ﬁgure 3) equates to the linear convo-

lution ∗ with the adequate PSF (Cannon, 1976). In

the case of linear homogeneous motion blur, this PSF

is a one-dimensional rectangular function (Lokhande

et al., 2006). The PSF looks like a line through the

point of origin with the angle ϕ to the x-axis, equal

to the direction of motion, and the length L, equal to

the distance one pixel travels along this direction of

motion. The coefﬁcients in h(u,v) sum up to 1, thus

the intensity being

/L along the line and 0 elsewhere.

With the knowledge of the correct motion parameters,

the PSF can be calculated via

h(u,v) = (1)











if (u,v)

sinϕ

cosϕ

= 0 and u

+ v





0 otherwise .

EFFICIENT MOTION DEBLURRING FOR INFORMATION RECOGNITION ON MOBILE DEVICES

It has to be taken into account that in the majority

of cases, the undistorted original image is deranged by

additional, signal-independent noise. This noise can

be modelled as an unknown random function n(u,v),

which is added to the image. Hence, the blurred im-

age i(u,v) can be described as

i(u,v) = f (u,v)∗h(u,v) + n(u,v) . (2)

Because the convolution becomes a multiplication in

the frequency domain, the Fourier transform of the

blurred image equates to

I(m, n) = F(m,n) ·H(m,n) + N(m,n) . (3)

This multiplication could theoretically be reversed

by pixel-wise division, so with the knowledge of

the proper PSF, the undistorted original image could

be obtained through the inverse Fourier transform.

This procedure is often referred to as inverse ﬁlter-

ing (Gonzalez and Woods, 2008). However, this only

works properly under the assumption that there is zero

noise. In the presence of noise, only an approximation

F of the transformed original image can be obtained,

which equals to

F =

I(m, n)

H(m,n)

F(m,n) ·H(m,n) + N(m,n)

H(m,n)

= F(m,n) +

N(m,n)

H(m,n)

(4)

This shows that

F cannot be reconstructed without

the knowledge of the transformed noise function N.

In addition, the small coefﬁcients in H(m,n) make

the term

N(m,n)

/H(m,n) very large and superpose the ac-

tual original image beyond recognition (Gonzalez and

Woods, 2008). To avoid that, a method of inverse ﬁl-

tering is needed that explicitly takes the noise signal

into consideration. The Wiener deconvolution is such

a method, which is based on the well known Wiener

ﬁlter (Wiener, 1949) for noise suppression in signal

processing.

Figure 3: Motion blur can be modelled as a linear convolu-

tion with an appropriate PSF.

4 THE IMAGE DEBLURRING

ALGORITHM

In the algorithm presented in this paper, a given

blurred input image is analysed to determine the

direction and length of the camera movement that

caused the blur. These two motion parameters are

used to calculate a point spread function modelling

the blur. Regarding the blur as a linear convolution

of the original image with that blur kernel, it can be

removed by reversing this operation. The algorithm

focuses on efﬁcient computation and is therefore suit-

able for resource-limited environments.

First, in section 4.1 a preprocessing step, which

converts a relevant part of the respective greyscale

image to the frequency domain with FFT, is intro-

duced. Then, in section 4.2 the blur direction is deter-

mined by performing a Radon transform on the log-

arithmic power spectrum of the blurred image. The

power spectrum features some ripples in its centre,

which run perpendicular to the direction of motion.

The computation time of the Radon transform is sig-

niﬁcantly decreased by customising it to ﬁt the struc-

tural conditions of the spectrum. Next, in section 4.3

the blur length is estimated by measuring the breadth

of the central ripple within the log spectrum, which is

inversely proportional to the sought-after blur length.

This is done by collapsing the spectrum onto a line

that passes through its origin at an estimated blur an-

gle. Then the resulting one-dimensional log spec-

trum is analysed to ﬁnd the ﬁrst signiﬁcant local min-

imum. This approach does not require any further

costly Fourier transforms. In the last step in sec-

tion 4.4, the PSF is calculated and a simple Wiener

ﬁlter is used to deconvolute the image.

Figure 4 shows an overview of the algorithm. It

also denotes the additional costly segmentation of the

image that is required if instead of the Radon trans-

form the Hough transform is used to detect the blur

direction.

4.1 Preprocessing

Estimating the blur parameters requires some pre-

processing. First, the colour image obtained by

the smartphone camera is converted into an 8 bit-

greyscale picture. This can be done by averaging the

colour channels or by weighting the RGB-parts ac-

cording to the luminance perception of the human eye

(Burger and Burge, 2008).

(u,v) = 0.30 ·i

(u,v)+0.59 ·i

(u,v)+0.11 ·i

(u,v)

(5)

Next, a square section is cut out of the centre of the

image. For the FFT to be applicable, this size has to

IMAGAPP 2011 - International Conference on Imaging Theory and Applications

Preprocessing

Blurry input image

8 bit-grayscale image Square image area

Hough-Transformation

Radon-Transformation

Segmentierung

(White-Schwellwert)

Hough-Transformation

Radon-Transformation

Auswertung des Akkumulator-Arrays

Blur direction determination

Hough transform

Radon transform

Segmentation

(White thresholding)

Hough transform

Radon transform

Blur length

determination

1-D spectrum

Auswertung des Akkumulator-Arrays

Estimation of the

breadth of the central

peak



length L

Deconvolution

Auswertung des

Akkumulator-Arrays

Fourier transform of

original image and

point spread function

Calculation of the

point spread function

Wiener-filter

Inverse Fourier transform

Quadrant swap

Masking with Hanning

window

Fourier transform, quadrant swap & logarithmic power spectrum

Analysis of the accumulator array  angle φ

Figure 4: Overview of the image deblurring algorithm.

be a power of two. In practise, sizes of 512 ×512

and 256 ×256 pixels have shown to maintain a rea-

sonable balance between stable high quality results

and computational cost. The period transitions from

one image border to the next often lead to high fre-

quencies, which become visible in the image’s power

spectrum as vertical and horizontal lines. Since these

lines may distract from or even superpose the stripes

caused by the blur, they have to be eliminated by ap-

plying a windowing function before transforming the

image. The Hanning window offers a good trade-off

between forming a smooth transition towards the im-

age borders and preserving a sufﬁcient amount of im-

age information for the parameter estimation. For a

square image of size M, the Hanning window is cal-

culated as (Burger and Burge, 2008)

Hanning

(u,v) =

(

0.5 ·cos(πr

u,v

+ 1) if 0 ≤r

u,v

≤ 1

0 otherwise

with

u,v



−1





−1



(6)

After that step, the windowed image can be trans-

ferred into the frequency domain by performing a

FFT. To facilitate the identiﬁcation of particular fea-

tures of the Fourier spectrum, its power spectrum is

computed. In its basic form, the power spectrum is

deﬁned as the absolute value of the Fourier trans-

formed image. However, because the coefﬁcients of

the Fourier spectrum decrease rapidly from its cen-

ter towards the borders, it can be difﬁcult to identify

local differences. Taking the logarithm of the power

spectrum s(u,v) = log|I(m,n)| helps to balance this

rapid decrease. In order to obtain a centred version of

the spectrum, its quadrants have to be swapped di-

agonally. Since the interesting features are around

the centre of the spectrum, the following operations

can be performed upon a centred 256 ×256-window,

which reduces computation time.

4.2 Blur Direction Determination

As a result of the above operations, the power spec-

trum exhibits a pattern of stripes parallel to a line

passing through its origin at an angle θ, which cor-

responds to the motion angle ϕ as θ = −ϕ. Thus, es-

timating the direction of these stripes means knowing

the motion angle. To do so, a Radon transform is per-

formed. This is done by shooting a certain amount

of parallel rays for each possible angle θ through

the image, adding up the intensities of the pixels hit

by each ray and subsequently storing the sums in a

two-dimensional accumulator array. The high inten-

sity values along the sought-after stripes lead to local

maxima within this array, and the corresponding ar-

ray indices reveal the parameters (radius and angle)

of the detected lines. The precision of the algorithm

depends on how ﬁne the angle domain θ = 0 . . .π is

divided into a number of n

steps. 360 steps provide

an accuracy of 0.5°, which is sufﬁcient for image re-

construction and subsequent information extraction.

In the general case where the position of the

sought-after feature is unknown, there is no alterna-

tive but to try every possible distance for each angle

(see ﬁgure 6(a)). Yet with the previous knowledge

that the central stripe runs through the origin, the ra-

dius is always 0 and the complexity of the procedure

can be signiﬁcantly decreased. Theoretically, all what

has to be done is to shoot one ray per angle through

the origin of the spectrum and determine the angle

with the highest sum (see ﬁgure 6(b)).

Unfortunately, this method usually fails in prac-

tise. Periodic structures are common in e.g. barcodes

and high-contrast edges occur for example along the

border of a white sheet of paper photographed against

a dark background. In the spectrum they manifest as

EFFICIENT MOTION DEBLURRING FOR INFORMATION RECOGNITION ON MOBILE DEVICES

86°

94°

0° 22,5° 45° 67,5° 90° 112,5° 135° 157,5° 180°

Figure 5: The periodic structures of the barcode lead to ad-

ditional features in the power spectrum and create distract-

ing maxima in the Radon accumulator array.

additional lines (see ﬁgure 5). Since these distracting

parts tend to have very high frequencies, they can eas-

ily lead to wrong estimations. Therefore, a criterion is

needed which helps to separate the “wrong” features

from the “right” ones. Fortunately, the breadth of the

central stripe caused by the blur is inversely propor-

tional to the blur length. This means that for typical

cases of motion blur up to 50-70 pixels, the blur stripe

is much broader than the distracting other stripes. At

the same time, it is also more diffuse, meaning that

it spreads its energy over its breadth. The correct an-

gle can reliably be estimated by looking for maxima

within the expected breadth from the origin only (see

ﬁgure 6(c)). This is a nontrivial problem, because the

blur length and with it the expected breadth b are not

known. Since taking a value for b that is signiﬁcantly

larger than the actual breadth would lead to an in-

accurate estimation, the best result can be achieved

by choosing b according to the largest expected blur

length (which corresponds to the smallest expected

ripple breadth). The blur length is equal to the size

of the spectrum divided by the half of b. Hence, for

a length of 60 pixels, b equates to

of the spectrum

width.

(a) (b) (c)

Figure 6: Three different versions of the Radon transform.

The arrows denote the rays shot through the image for one

particular angle. In (a), every single possible radius is

taken into account, whereas (b) and (c) are individually cus-

tomised to the expected structure of the power spectra.

The result is an array with n

·b sums. Determin-

ing the correct blur angle out of this array is done by

searching for the w consecutive angles whose sums

add up to the highest total sum. Each of these sums

consists of b single values, according to the number

of rays sent through the image for each angle. Having

found these w angles, the maximum out of all w ·b

single values is determined. The angle to whose sum

this maximum value has contributed is the desired an-

gle of camera motion. A range of 3° has proven to

be sufﬁciently large to ensure that the correct angle is

selected, so that w can be calculated out of the angle

resolution n

w =

180

·3 (7)

4.3 Blur Length Determination

The blur length is also calculated by analysing the

logarithmic power spectrum of the blurred image.

Here, it is the breadth of the central ripple running

through the origin that has to be estimated. This

breadth is inversely proportional to the blur extent and

therefore can be used to calculate it. Unlike the ma-

jority of other algorithms, the estimation requires no

further Fourier transform. To determine the breadth

of the central stripe, a one-dimensional version of the

spectrum is calculated. This is done by collapsing

the intensity values of the spectrum onto a line run-

ning through the origin perpendicular to the blur rip-

ples. The intensity of each pixel is summed up in an

array according to its distance d from that line. In

order to do so, d has to be discretised ﬁrst. Since

simple rounding may lead to imprecise results, (Rek-

leitis, 1995) proposes another approach where the in-

tensities are proportionately divided into two array in-

dexes according to the decimal places of their dis-

tances from the projection line. He also suggests to

normalise the projected spectrum by dividing each

sum by the amount of pixels that went into it. That

way, the sums do not necessarily decrease towards

the borders of the array, because fewer pixels con-

tribute to them. In addition to these two improve-

ments, (Krahmer et al., 2006) proposes to mirror the

array in its centre and to add the values to the respec-

tive other side. Due to the fact that the blur ripples

should be symmetric, this suppresses noise and at the

same time clariﬁes the interesting features.

The resulting 1-D spectrum exhibits a prominent

peak in its centre which matches the central blur rip-

ple in the 2-D spectrum (see ﬁgure 7). The zeros, or

rather the gaps, between the individual stripes man-

ifest as local minima in the collapsed spectrum. To

identify the maximum in the centre of the spectrum,

a search to the right (either direction would be possi-

ble because of the symmetry) is performed until the

values become higher instead of smaller.

P(x

) < P(x

+ 1) (8)

Out of this ﬁrst local minimum x

, one easily can cal-

culate the breadth of the blur ripple by doubling its

IMAGAPP 2011 - International Conference on Imaging Theory and Applications

(a) (b)

Figure 7: The log power spectrum of a blurred image (a)

and the plot of its projected 1-D spectrum (b).

distance to the maximum. Unfortunately, this sim-

ple approach usually fails in the presence of noise.

With blur that has been developed under realistic con-

ditions, small deﬂections show up in the spectrum.

Thus, the collapsed spectrum is not monotonically de-

creasing up to the sought-after ﬁrst local minimum

and the approach described in (8) is bound to fail. To

solve this problem, we propose to deﬁne a distance s

within which the values must not become bigger than

at the potential minimum.

P(x

) < P(x

+ 1) < P(x

+ s) (9)

Since the parallel ripples in the spectrum become

smaller and more dense to the same degree the caus-

ing movement is faster, the choice of a proper value

for s is not an easy one. On the one hand, it has to

be larger than the maximal breadth of the noise de-

ﬂections it strives to suppress. On the other hand,

it has to be smaller than the minimal breadth of the

next ripple, which is half as broad as the one in the

centre. This means that s has to be individually com-

puted according to the characteristics of the present

spectrum. With increasingly larger blur lengths, the

values in the spectrum decline more rapidly towards

the sides. This is why the calculation of the slope m

between two points Q

= (x

) and Q

= (x

which both lie on the central peak, is a promising ap-

proach. To be on the safe side, we presume a maxi-

mal blur length of 100 pixels, which would make the

breadth of the entire peak

of the width

√

2M of the

spectrum. Hence, x

is set to be at the centre

√

and x

at a distance of

100

of the spectrum width from

there.

m =



−y

−x



P(x

) −P(x

)

100

√



(10)

The resulting slope m grows with increasingly

larger blur lengths. At the same time, the deﬂections

become smaller as the slope becomes steeper, which

means that smaller blur lengths are more susceptible

to noise than larger ones. Thus, for determining s, we

use the reciprocal of m, multiplied by an appropriate

correction factor f :

s =

· f . (11)

For a spectrum with a size of 512 × 512 pixels, we

found that dividing the slope by a correction factor of

5 worked best. Since the breadths of the peaks depend

on the size M of the projected power spectrum, this

results in a correction factor of f =

2560

s =

· f =

512 ·5

2560 ·m

. (12)

When the correct minimum x

has been found accord-

ing to equation (9), the breadth b of the peak is calcu-

lated as

b = 2 ·



−

√



. (13)

Because b is inversely proportional to the length L of

the camera motion, the reciprocal of b is used. L is

then calculated by dividing the size of the spectrum

by the half of b.

L =

(14)

It is possible that the algorithm fails to detect a local

minimum. This is mostly due to a faulty calculation

of the distance s or the collapsed spectrum exhibiting

no prominent peaks. The latter is the case when the

angle has not been estimated exactly enough in the

previous step, which leads to an incorrect projection

line orientation.

4.4 Deconvolution

Knowing the two blur parameters, an adequate PSF

can be calculated according to equation (1). Then

both the PSF and the original, unaltered image have

to be transformed into the frequency domain so that

the deconvolution can be carried out. The Wiener de-

convolution ﬁlter as it is presented in (Lokhande et al.,

2006) is given by

F =

∗

(m,n) ·I(m,n)

∗

(m,n) ·H(m,n) + K

, (15)

where H

∗

(m,n) is the complex conjugate of H(m,n)

and K is a constant that can be approximated by the

reciprocal image width

/B. In order to obtain the

reconstructed, deblurred image, the result eventually

has to be transformed back into the image domain.

Provided that the information in the pictured ob-

ject consists solely of monochrome elements, it might

be reasonable to binarise the reconstructed image.

Good results can be achieved with the thresholding

EFFICIENT MOTION DEBLURRING FOR INFORMATION RECOGNITION ON MOBILE DEVICES

algorithms of White (White and Rohrer, 1983) and

Bernsen (Sezgin and Sankur, 2004). Since most of the

locally-adaptive thresholding methods require a lot of

computation time, this method is better used in envi-

ronments that are not time critical. However, if the

photo is consistently lit so that a viable global thresh-

old can be found, the method of Otsu (Otsu, 1979)

might also be applicable.

5 EVALUATION

In order to evaluate how accurate and reliable the mo-

tion parameter estimation works, two different classes

of input data have been used. The ﬁrst category con-

sisted of images with artiﬁcially generated motion

blur. To do so, 11 different motifs had each been con-

voluted with 30 different PSFs. These PSFs had been

constructed from all possible combinations out of ﬁve

different, randomly chosen angles and six different,

likewise random lengths according to the deﬁnition

given by equation (1). This way, a total of 330 test

images were created. The original motifs comprised

real photography as well as completely digitally cre-

ated pictures, all of a size of 512 × 512 pixels.

Nine of the images showed different kinds of bar-

codes. The beneﬁt of artiﬁcially created blur is that

the exact motion parameters are known beforehand

and can therefore easily be compared to the ones de-

termined by the algorithm. Yet it can not predict

whether the method works for photos taken under real

conditions. Hence, the second class consisted of real,

unaltered photographs. For these pictures, ﬁve differ-

ent barcodes had each been photographed ﬁve times.

In order to simulate realistic conditions, they were

made using a smartphone camera, manually moving

the phone in different speeds and angles during expo-

sure time. The shots were also taken under different

light conditions in order to vary the shutter speed.

5.1 Artiﬁcial Blur

For the artiﬁcially blurred images, the angle estima-

tion continuously produced stable results. The algo-

rithm could estimate the angles up to an accuracy of

5° for 92.71% of the test images. In most of the cases

where the estimation delivered incorrect results, this

was caused by additional features in the power spec-

trum induced by periodic structures or high-contrast

edges. The accuracy of the angle estimation is to

some degree dependent on the intensity of the blur:

If the ray within which the Radon transform sums up

the intensity values is smaller than the stripe it strives

to detect, multiple maxima occur at adjacent angles.

Since shorter blur lengths lead to broader stripes, the

accuracy decreases with the blur length, as can be

seen in table 1. Only taking into account pictures with

blur lengths greater than 50 pixels leads to an increase

of the detection rates for 0.5° accuracy of 40% of the

images. Out of the pictures with blur lengths greater

than 30 pixels, nearly 100% could be detected cor-

rectly with an accuracy of 4°.

The blur length estimation also worked reliably,

provided that the angle had been calculated correctly.

In the case of an exact angle estimation in the range

of 0.5° around the desired value, 95.73% of the blur

lengths could be determined with an accuracy up to

5 pixels. As shown in table 2, this rate decreases to

79.43% for an angle estimation accuracy of 5°. Given

these numbers, the percentage of images where both

the angle and the length could be estimated with an

accuracy of up to 5° or 5 pixels, is 73.56%. Never-

theless, the high portion of correctly estimated blur

lengths with the exact knowledge of the blur angle

shows that the method for blur length estimation pre-

sented in this paper works well. The accuracy how-

ever decreases for greater blur lengths, which is once

again due to the breadth of the central ripple: In a

spectrum of the size of 256 pixels, it is 26 pixels broad

for a blur length of 20 pixels. If the blur length is dou-

bled to 40 pixels, the breadth is halved accordingly to

13 pixels. For a blur length of 80 pixels, the stripe is

merely 6 pixels broad. The breadth of the ripple con-

verges towards the resolution limit and the accuracy

with which it can be determined inevitably decreases.

5.2 Real Blur

To allow the veriﬁcation of the blur parameters es-

timated for photos taken under real conditions, the

angles of the ripples appearing in the images’ power

spectra were measured manually. The same was done

for the blur lengths using plots of the 1-D spectra.

Since the estimation of the blur length is impossi-

ble without the exact knowledge of the correspond-

ing blur angle, in cases where the angle estimation

had failed the spectra were recreated using the manu-

ally measured data. In other words, corrective actions

were taken in order to make separate statements about

the estimation accuracy of both parameters.

The test material presented here can only attempt

to provide evidence of the algorithm’s performance

under real conditions. On the one hand, the amount of

images is much smaller than that with the artiﬁcially

created blur. On the other hand, even the images taken

with a smartphone camera were likewise created “ar-

tiﬁcially”, since they all had been taken with the ex-

plicit intent to create linear motion blur. Yet, it can

IMAGAPP 2011 - International Conference on Imaging Theory and Applications

Table 1: Angle detection rates for angles with artiﬁcial blur.

accuracy up to

maximal blur length

all ≥ 25 px ≥ 30 px ≥ 40 px ≥ 50 px ≥ 70 px

0.5° 35.56% 41.82% 45.00% 48.48% 50.00% 47.27%

1.5° 64.13% 74.55% 79.09% 84.24% 87.27% 89.09%

2° 76.60% 86.55% 90.91% 94.55% 94.55% 94.55%

3° 86.32% 96.36% 97.27% 98.18% 97.27% 96.36%

4° 89.06% 98.55% 99.55% 99.39% 99.09% 98.18%

5° 92.71% 99.27% 99.55% 99.39% 99.09% 98.18%

7° 95.44% 99.64% 99.55% 99.39% 99.09% 98.18%

10° 95.44% 99.64% 99.55% 99.39% 99.09% 98.18%

∅ deviation 3.01° 1.36° 1.28° 1.25° 1.36° 1.82°

Table 2: Length detection rates for artiﬁcial blur.

accuracy up to

maximal accuracy of the angle estimation

0.5° 1.5° 2° 4° 5° 10° all

1 px 15.38% 17.54% 17.86% 18.77% 19.02% 19.43% 18.84%

2 px 49.57% 45.97% 46.03% 46.08% 47.21% 48.09% 46.20%

3 px 74.36% 66.35% 63.10% 61.43% 62.30% 62.74% 60.49%

4 px 95.73% 82.94% 78.57% 76.11% 76.39% 76.43% 73.56%

5 px 95.73% 84.83% 81.75% 79.18% 79.34% 79.62% 76.90%

7 px 99.15% 90.52% 86.51% 83.96% 83.93% 84.08% 81.76%

10 px 99.15% 92.89% 88.89% 87.71% 87.87% 87.90% 86.63%

∅ deviation 6.08 px 6.46 px 9.24 px 8.99 px 8.74 px 8.62 px 9.08 px

be stated that the method generally works for motion

blur caused by actual movement of a physical camera.

Table 3 shows that for 16 out of the 25 images, the

motion angle could be estimated with a 5°-accuracy,

which still is a detection rate of roughly 60%. The

lengths could be estimated accurately to 5 pixels in

14 out of 25 cases. When the exact angles from the

manual measuring were used, this rate increased to 22

out of 25 (88%).

5.3 Image Reconstruction

In the last step, the algorithm uses the determined mo-

tion parameters to remove the blur artefacts. The im-

ages in ﬁgure 8 clearly show that the reconstruction is

able to produce good results: Text that could not even

be identiﬁed as such becomes legible again, and indi-

vidual elements of the barcodes become clearly disti-

nguishable. Figure 8(b) shows that even with very

large blur lengths of around 70 pixels, still good re-

sults are possible. While the results are of course bet-

ter with the artiﬁcial blur, the naturally blurred images

also could be successfully deblurred in many cases.

To determine whether the deblurring allows for

increased detection rates of barcode scanners, some

test images were passed through the open source

ZXing-Decoder before and after the reconstruction.

Out of the artiﬁcially blurred images, 50 were chosen

where the barcode elements were distinctively visi-

ble. With these 50 images, the detection rates of the

ZXing-Decoder could be increased by 30.6%. An ad-

ditional binarisation of the resulting images using the

method of Bernsen could increase the success rate by

another 4.1%. There, among the images with less than

15 pixels blur length the increase was 41.7% in to-

tal. Extrapolated onto all images that could have been

EFFICIENT MOTION DEBLURRING FOR INFORMATION RECOGNITION ON MOBILE DEVICES

(a) Artiﬁcial blur. Angle: 22.5°, length: 25 pixels.

(b) Artiﬁcial blur. Angle: 74.5°, length: 70 pixels.

(d) Real blur. Angle: 63°, length: 16.52 pixels.

(e) Real blur. Angle: 156°, length: 11.38 pixels.

Figure 8: Images blurred by artiﬁcial ((a), (b), (c)) and real

((d), (e)) linear motion and their respective deconvolution

results.

Table 3: Comparison between the manual measuring and

the values determined by the algorithm for the 25 test im-

ages. Deviations of more than 5 pixels are highlighted.

angle angle length length

(manual) (algorithm) (manual) (algorithm)

100.0° 89.5° 14.22 px 14.63 px

180.0° 178.0° 17.96 px 18.29 px

38.0° 36.0° 34.13 px 36.57 px

90.0° 89.0° 21.79 px 22.26 px

32.0° 32.5° 26.95 px 28.44 px

150.0° 98.0° 11.38 px 11.38 px

90.0° 90.5° 25.6 px 25.6 px

42.0° 86.0° 8.46 px 9.31 px

1.0° 1.5° 20.9 px 85.33 px

63.0° 86.5° 16.0 px 16.52 px

91.0° 90.0° 9.23 px 46.55 px

7.0° 0.5° 15.28 px 8.53 px

156.0° 1.5° 11.38 px 11.38 px

62.0° 93.0° 10.04 px 11.64 px

59.0° 61.5° 14.42 px 14.22 px

178.0° 1.5° 14.22 px 14.63 px

91.0° 90.5° 15.75 px 15.06 px

12.0° 3.5° 6.4 px 4.92 px

140.0° 177.0° 14.03 px 4.92 px

171.0° 173.0° 8.83 px 8.83 px

179.0° 180.0° 9.23 px 20.48 px

174.0° 177.5° 15.28 px 18.96 px

75.0° 78.5° 8.53 px 2.67 px

142.0° 146.0° 14.42 px 14.63 px

45.0° 49.0° 14.63 px 15.52 px

recognised theoretically, this gives a rate of 8.1%.

Note, that even then the percentage of images on

which the reconstructed information is recognisable

with the naked eye is much higher. Obviously, the

scanning algorithm cannot handle the reconstructed

input images. This is most likely due to the additional

artefacts and diffuse edges caused by the deconvolu-

tion (Shan et al., 2008).

5.4 Performance

The algorithm has been implemented in Java in order

to conduct the experiments. It was ﬁrst run on a stan-

dard desktop PC (3 GHz Intel Pentium D with 2 GB

IMAGAPP 2011 - International Conference on Imaging Theory and Applications

RAM) using JavaSE 1.6 and then ported to JavaME in

order to test it on a real mobile device. In the test run,

the whole process (preprocessing, blur parameter es-

timation and deconvolution) took about 500 ms for all

images to be completed on the desktop computer. The

exact same calculation took a total of about 22 sec-

onds on a last generation mobile device (Sony Erics-

son k800i), which is more than 40 times longer. While

some parts (e.g. the windowing) ran about 23 times

slower on the smartphone than on the desktop PC, the

FFT took 90 times as long. For the FFT the compar-

atively much slower ﬂoating point arithmetic makes

itself felt. However, note that next generation hard-

ware offers higher integer performance, much better

ﬂoating point support, and faster Java run time envi-

ronments. An analysis on the desktop computer re-

vealed that the FFT by far required the longest CPU

time (36%), followed by the Radon transform (18%)

and the calculation of the power spectrum (8%). Since

the complexity of the FFT is O(M log M), dependent

on the image size M, this also determines the com-

plexity of the deblurring algorithm as a whole.

6 CONCLUSIONS AND FUTURE

WORK

In this paper, a novel method combining and adapting

existing techniques for the estimation of motion blur

parameters and the subsequent removal of this blur is

presented. The algorithm is suitable for the execu-

tion on resource-constrained devices such as modern

smartphones and can be used as a preprocessing phase

for mobile information recognition software.

The algorithm uses the logarithmic power spec-

trum of a blurred image to identify the motion pa-

rameters. It introduces a new, specially adjusted

and therefore time-saving version of the Radon trans-

form for angle detection where features are only

sought after within a certain distance around the ori-

gin. The blur length is detected by analysing a one-

dimensional version of the spectrum. No cepstrum

and hence no further FFT are required. The estimated

parameters are then used to form a proper PSF with

which the blurred image can be deconvoluted. To do

so, a Wiener ﬁlter is employed.

It was found that the motion angle estimation

worked with a 5° accuracy for 92.71% of 330 arti-

ﬁcially blurred images. The blur length determina-

tion delivered correct results with a maximum error

of 5 pixels in 95.73% of all cases. For images blurred

by real movement of an actual camera, these rates

amounted to roughly 60% and 88%, respectively. The

algorithm was implemented in Java to run on desk-

top computers as well as mobile devices. The algo-

rithm terminated within 500 ms on an standard desk-

top computer and took around 40 times longer on an

older smartphone. While sub second performance on

smartphones is not to be expected any time soon, exe-

cution time within a few seconds on modern hardware

should be attainable.

The application of the presented algorithm makes

some previously unrecognised barcodes to be recog-

nised by the ZXing decoder. However, the additional

artefacts caused by the deconvolution itself often hin-

ders the recognition in other cases. Yet, after the de-

convolution, completely blurred text become legible

again, and individual barcode features become clearly

distinguishable in many of the cases where decoding

failed. This gives reason to surmise that a success-

ful recognition might be possible if the decoders were

able to cope with the singularities of the reconstructed

images. Or, deconvolution methods that suppress the

emergence of artefacts could be explored.

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IMAGAPP 2011 - International Conference on Imaging Theory and Applications