IMAGE RETARGETING USING STABLE PATHS

H

´

elder P. Oliveira

Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

Jaime S. Cardoso

INESC Porto, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

Keywords:

Image processing, Image retargeting, Image resizing, Stable paths.

Abstract:

Media content adaptation is the action of transforming media ﬁles to adapt to device capabilities, usually

related to mobile devices that require special handling because of their limited computational power, small

screen size and constrained keyboard functionality. Image retargeting is one of such adaptations, transforming

an image into another with different size. Tools allowing the author to imagery once and automatically retarget

that imagery for a variety of different display devices are therefore of great interest. The performance of these

algorithms is directly related with the preservation of the most important regions and features of the image.

In this work, we introduce an algorithm for automatically retargeting images. We explore and extend a recently

proposed algorithm on the literature. The central contribution is the introduction of the stable paths for image

resizing, improving both the computational performance and the overall quality of the resulting image. The

experimental results conﬁrm the potential of the proposed algorithm.

1 INTRODUCTION

Increasingly, our computing and communications in-

frastructure is evolving to support images and video.

The recent diversity and versatility of mobile dis-

plays, such as PDAs and cellular phones, have en-

larged the importance of adaptation of images for

these devices. Traditional image manipulation tech-

niques, such as scaling and cropping, lead to a degra-

dation of image quality and important loss of informa-

tion when automatically applied to images with mul-

tiple objects. In such techniques, valuable image area

in the target image may be wasted with unimportant

regions between important features. Content aware

retargeting algorithms try to change the image size

while preserving the most important information in

it.

In this work we present a novel scheme to resize

an image. Our algorithm repeatedly carves out multi-

ple lines simultaneously. To do this, we draw on the

work by Avidan and Shamir on seam carving (Avidan

and Shamir, 2007). Analogous to their approach, we

identify low energy seams that are carved out from

the image. The seams are not restricted to be straight

but rather follow the contours of low-gradient regions

in the image. In this work we extend and explore

their approach in two main directions. Firstly, the

use of stable paths instead of the shortest path im-

proves the computational performance of the method

by selecting multiple seams simultaneously. Further-

more, this option also has the advantage of spread-

ing more evenly the removed seams on the image,

improving the overall quality. Secondly, the design

of the weights on the graph resulting from the image

is generalized to depend nonlinearly on the gradient

value. Moreover, we also distinguish, in terms of cost,

pair of pixels 4-neighbourhood-connected from pix-

els only connected under 8-neighbourhoods. This im-

provement in the weight design enhances further the

ﬁnal performance.

After reviewing the state of the art in image re-

targeting, we introduce in Section 3 the concept of

stable paths in a graph and present a computationally

efﬁcient algorithm for determining them. The exper-

imental work reported at the end of the communica-

tion includes a thorough testing on real images, where

the original method in (Avidan and Shamir, 2007) is

compared with the extensions proposed in this work.

40

P. Oliveira H. and S. Cardoso J. (2009).

IMAGE RETARGETING USING STABLE PATHS.

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 40-47

DOI: 10.5220/0001785900400047

Copyright

c

SciTePress

2 RELATED WORKS

Before describing in detail the proposed method for

image retargeting it is instructive to examine the cur-

rent state of the art.

A non-photorealistic algorithm was proposed

in (Setlur et al., 2005) to adapt automatically images

for small sized displays with different sizes and/or as-

pect ratios, while preserving the important features in

the image. This is achieved by ﬁrst decomposing the

image in a background layer and foreground objects.

Then, all important zones are temporally cropped and

the other parts are removed from the image. The ﬁ-

nal image is obtained by pasting the important zones,

with the rest of the image obtained by resizing some

parts using inpainting (Harrison, 2001).

In (Liu and Gleicher, 2005) and (Liu and Gleicher,

2006) the authors propose a method for image and

video retargeting, respectively. Their method presents

a tradeoff between image resizing and image crop-

ping. The method consists on ﬁnding the Region-of-

Interest (ROI) of the image and constructing a novel

Fisheye-View warp that applies a linear scaling func-

tion in each dimension of the image. Basically, in this

method the information on the ROI is preserved and

the rest of the image is warped. In the video applica-

tion they use a combination of the image and saliency

maps to ﬁnd the ROI. After this operation, cropping,

virtual pan and shot cuts are used to resize the image.

In (Gal et al., 2006) is presented a method for in-

homogeneous 2D texture mapping by a feature mask

to the general problem of warping, that preserves

some parts of the image speciﬁed by the user. The

feature-aware texture warping is done by applying a

formulation based on Laplacian editing technique.

An automatic non-uniform global warping was

employed by (Wolf et al., 2007) in a problem of video

retargeting. The algorithm starts by analyzing the

frame to detect important zones and then shrinks less

important regions. The analysis of the frames is based

on local saliency, and object and motion detection.

The technique of cropping the important zones

and then resizing them to obtain the desired aspect

ratio was applied in (Tao et al., 2007) to a problem

of video retargeting. In (Chen and Sen, 2008) the au-

thors use graph cuts to ﬁnd and remove low gradient

sheets, for video summarization applications.

An approach for the summarization of visual data

for images and videos is proposed in (Simakov et al.,

2008). The authors propose a measure to quantify

how “good” is a visual summary. This measure can

be applied to compare two images or two videos se-

quences with different sizes. This is useful to im-

prove some objective function within an optimiza-

tion process, to generate good visual summaries or to

compare quantitatively and evaluate visual summaries

produced by different methods.

An important work in image retrieving was re-

cently presented by Avidan (Avidan and Shamir,

2007), and improved by Rubinstein (Rubinstein et al.,

2008) for video retargeting. In (Avidan and Shamir,

2007) the authors create an operator called seam carv-

ing that permits the reduction and enlarging of im-

ages. A seam was deﬁned as an optimal 8-connected

path of pixels between opposing margins of the im-

age, where optimally is determined using an image

energy function. The algorithm preserves the image

structure by removing more low energy pixels than

high energy pixels. The computation of the optimal

seam is based on an efﬁcient dynamic programming

algorithm. In (Rubinstein et al., 2008) the authors

extend the work for video. There, the dynamic pro-

gramming had to be replaced by graph cuts, suitable

for 3D volumes. A novel energy function was also in-

troduced, improving the visual quality of both videos

and images.

The principal problem of the algorithm in (Avidan

and Shamir, 2007; Rubinstein et al., 2008) is related

with the lower performance when applied to images

with big sizes. The algorithm is slow because only

one line is discarded per iteration.

3 A STABLE PATH APPROACH

FOR IMAGE RESIZING

In the work to be detailed, the image grid is consid-

ered as a graph with pixels as nodes and arcs con-

necting neighbouring pixels. The weight of each arc,

w(p, q), is a function of pixels values and pixels rela-

tive positions. A path from vertex (pixel) v

1

to vertex

(pixel) v

n

is a list of unique vertices v

1

, v

2

, . . . , v

n

, with

v

i

and v

i+1

corresponding to neighbour pixels. The to-

tal cost of a path is the sum of each arc weight in the

path

∑

n

i=2

w(v

i−1

, v

i

).

A path from a source vertex v to a target vertex u

is said to be a shortest path if its total cost is minimum

among all v-to-u paths. The distance between a source

vertex v and a target vertex u on a graph, d(v, u), is the

total cost of a shortest path between v and u.

A path from a sub-graph Ω

1

to a sub-graph Ω

2

is

said to be a shortest path between Ω

1

and Ω

2

if its

total cost is minimum among all v ∈ Ω

1

-to-u ∈ Ω

2

paths. The distance from a sub-graph Ω

1

to a sub-

graph Ω

2

, d(Ω

1

, Ω

2

), is the total cost of a shortest

path between Ω

1

and Ω

2

:

d(Ω

1

, Ω

2

) = min

v∈Ω

1

,u∈Ω

2

d(v, u). (1)

IMAGE RETARGETING USING STABLE PATHS

41

3.1 Algorithm Outline

For completeness and to help introducing the pro-

posed method, we summarize here the method

in (Avidan and Shamir, 2007), in which we build on.

The presentation will rely on height reduction only;

the necessary adaptations for width reduction or im-

age enlarging should be clear at the end.

To reduce the height of an image by one pixel,

one needs to remove one and only one pixel in each

column. Moreover, in order to prevent discontinuities,

the removed pixels should be connected. Therefore,

we are allowed to remove only any connected path

from the left to the right margins, without zig zagging

back and forth (Avidan and Shamir, 2007). Formally,

let I be an N

1

×N

2

image and deﬁne an admissible

path to be

s = {(x, y(x))}

N

1

x=1

, s.t. ∀x |y(x) −y(x −1)|≤ 1,

where y is a mapping y : [1, ··· , N

1

] → [1, ··· , N

2

].

That is, an admissible path is an 8-connected path of

pixels in the image from left to right, containing one,

and only one, pixel in each column of the image.

In (Avidan and Shamir, 2007) the authors propose

to remove the path with least energy. Toward that

end a weight (= energy) is deﬁned for each arc con-

necting neighbour pixels; then the optimal path is the

minimum-cost path connecting the two lateral mar-

gins. This optimal path can be found using dynamic

programming. The ﬁrst step is to traverse the image

from the second column to the last column and com-

pute the cumulative minimum cost C for all possible

connected staff lines for each entry (i, j):

C(i, j) = min

C(i −1, j −1) + w(p

i−1, j−1

; p

i, j

)

C(i −1, j) + w(p

i−1, j

; p

i, j

)

C(i −1, j + 1) + w(p

i−1, j+1

; p

i, j

)

,

where w(p

i, j

; p

l,m

) represents the weight of the edge

incident with pixels at positions (i, j) and (l, m). At

the end of this process,

min

j∈{1,···,N

2

}

C(N

1

, j)

indicates the end of the minimal connected path.

Hence, in the second step, one backtrack from this

minimum entry on C to ﬁnd the path of the optimal

staff.

3.1.1 Design of the Weight Function

It is important to call the attention for the ﬁrst im-

provement over (Avidan and Shamir, 2007). In (Avi-

dan and Shamir, 2007), the authors deﬁne a weight

(energy) on each pixel. In here we put the weight

on the arc connecting two neighbour pixels. Had we

deﬁned the arc’s weight as the average of the pixels’

weight, our formulation would resume to the previ-

ous. But by putting the weight on the arc we have

now the ﬂexibility to distinguish a path over an arc

connecting 4-neighbour pixels from an arc connect-

ing 8-neighbour pixels, penalising the latter over the

former. The weight of each arc is a function of pixels

values and pixels relative positions.

In this work we set

w(p

i, j

; p

l,m

) =

f (p

i, j

, p

l,m

)

if p

i, j

, p

l,m

are 4-neighbours

√

2 f (p

i, j

, p

l,m

)

if p

i, j

, p

l,m

are 8-neighbours

Note that is important to set f (p

i, j

, p

l,m

) strictly

greater than zero so that

√

2 f (p

i, j

, p

l,m

) is strictly

greater than f (p

i, j

, p

l,m

).

3.2 Stable Paths on a Graph

1

Assume one wants to decrease the height of the image

by several pixels. This can be approached by succes-

sively ﬁnding and removing the shortest path from the

left to the right margin of the image. A preferable so-

lution would be to ﬁnd multiple paths in a single itera-

tion. The stable path method allows us to do precisely

that.

Before moving to the formal deﬁnition of a stable

path on a graph, it is instructive to motivate the con-

cept by considering a hypothetical, simpliﬁed 9 ×10

image. The graph corresponding to such image is rep-

resented in Figure 1. The design of the weight func-

tion will be considered next; for now, it sufﬁces to

know that black pixels represent pixels with low cost

(energy), likely resulting from points with low gradi-

ent.

The shortest path between the left and right mar-

gins (sub-graphs Ω

1

and Ω

2

) is the path correspond-

ing to the fourth row, entirely through black pixels.

By following the strategy just delineated, one could

reduce the height by four pixels in four iterations, se-

quentially. Nonetheless, although only one path cor-

responds to the shortest path, it is visible multiple ‘al-

most optimal’ paths. The stable path concept provides

a means to ﬁnd all of such paths simultaneously.

Deﬁnition. A path P

s,t

is a stable path between re-

gions Ω

1

and Ω

2

if P

s,t

is the shortest path between

s ∈ Ω

1

and the whole region Ω

2

, and P

s,t

is the short-

est path between t ∈Ω

2

and the whole region Ω

1

.

1

A ﬁrst incursion into stable paths is already present

in (Cardoso et al., 2008), in the context of medical imag-

ing; here we provide, arguably, a cleaner presentation.

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

42

Figure 1: Stable paths on a toy example.

Note that the concept of stable path is valid for

any graph and any two sub-graphs in general. The

computation of the stable paths on the toy example of

Figure 1 provides the three paths gray-highlighted in

the ﬁgure.

In Figure 2(b) the shortest paths between each

point on the left margin and the whole right margin

are traced. Likewise, Figure 2(c) shows the shortest

paths between each point on the right margin and the

whole left margin. The set of stable paths between

both margins result as the set of paths present in both

ﬁgures, as illustrated in Figure 2(d).

Although the computation of the stable paths may

be expensive in general graphs, the computation in

the graph derived from an image under the setting

adopted in Section 3.1 has only roughly twice the

complexity of the shortest path computation pre-

sented in the same Section. Noticing that the proce-

dure delineated in Section 3.1 actually gives the short-

est path between the whole left margin Ω

1

and each

point on the right margin Ω

2

, the ﬁrst step on the com-

putation of the stable path corresponds verbatim to

the computation of the shortest path presented on Sec-

tion 3.1. In a second step one repeats the same proce-

dure, traversing now the graph from the right column

to the left. At the end of this process, if the two end-

points of a direct and reverse path coincide, we are in

the presence of a stable path.

Noticing that the two steps of computing the short-

est paths in both directions can done in parallel and

most personal computers are nowadays dual cores, the

computation of the stable paths takes essentially the

same time as the shortest path computation. Finally,

when the number of stable paths is less than the num-

ber of lines to be removed, one just repeats the proce-

dure after removing the stable paths found; when the

number of stable paths is larger than the necessary,

one just keeps the shortest stable paths. While the de-

scription has focused on height reduction, the same

mechanism applies for width reduction or image en-

(a) Original image. (b) Shortest paths from each

pixel in the left column and

the whole right column, su-

perimposed on the original

image.

(c) Shortest paths from each

pixel in the right column and

the whole left column, super-

imposed on the original im-

age.

(d) Resulting stable paths.

Figure 2: Exempliﬁcation of stable paths for Figure 2(a).

(a) Original image. (b) Original image stable

paths superimposed.

Figure 3: Staff lines for Figure 3(a).

larging, totally in line with the adaptations in (Avidan

and Shamir, 2007).

Summing up, two main advantages accrue from

IMAGE RETARGETING USING STABLE PATHS

43

the replacement of the sequential search of the short-

est path by the search of stable paths: multiple lines

can be computed in a single iteration, saving on the

computational time; the stable path approach tends to

spread the lines over the image, as observed in Fig-

ure 2 and Figure 3.

Indeed, while the shortest paths tend to be all clus-

tered in a single, gradient-free zone of the image, the

stable paths are usually found in several zones of the

image.

4 RESULTS

The proposed methodology was applied to a set of 36

images. Only the luminance information was used in

the analysis. The weight of an arc is based on the

energy of the incident pixels. Like in (Avidan and

Shamir, 2007), the energy function is derived from

the gradient information. Our gradient model is based

on the Sobel operator. The Sobel operator is applied

on the x and y directions; from the computed values,

E

x

and E

y

, the magnitude of the gradient is estimated

as E =

q

E

2

x

+ E

2

y

, as exempliﬁed in Figure 4. Al-

though more general setting could have been adopted,

we ﬁxed the weight of an arc as monotonically in-

creasing function of the average energy of the inci-

dent pixels (or

√

2 times that value, for 8-neighbour

pixels): f (p

i, j

, p

l,m

) =

ˆ

f (

E

i, j

+E

l,m

2

) .

(a) Original image. (b) Gradient image.

Figure 4: Gradient based on the Sobel operator.

Weights were assigned based on an power law:

ˆ

f (E) = δ + 255

E

255

n

, δ, n ∈ ℜ

The parameters δ and n were experimentally tuned,

yielding δ = 32 and n = 2. For comparison purposes

(a) Original image. (b) Resized image using the

linear shortest path method.

(c) Resized image using the

linear stable path method.

(d) Resized image using the

nonlinear stable path method.

Figure 5: Results of the different resizing methods when

applied to image E.

we also evaluated the linear weight (n = 1). Five dif-

ferent methods are experimentally compared:

1. Linear Shortest Path. A slightly improved ver-

sion of the method in (Avidan and Shamir, 2007),

with the incorporation of the δ > 0 parameter, to

ensure that the cost of 8-neighbour pixels is larger

than 4-neighbour pixels. This method discards a

single line per iteration.

2. Linear Stable Path. Based on stable paths to dis-

card multiple line per iteration but using the linear

weight function (n = 1).

3. Nonlinear Shortest Path The method of (Avidan

and Shamir, 2007) discarding a single line per it-

eration but using the nonlinear weight function

(n = 2).

4. Nonlinear Stable Path. Based on stable paths to

discard multiple line per iteration and using the

nonlinear weight function (n = 2).

5. Scaling. Standard scaling, with Lanczos ﬁltering.

The new size of each image was subjectively cho-

sen to make visible differences between the different

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

44

Table 1: Results obtained using different resize methods.

Image Height Discarded Lines

Number Iterations

Linear and nonlinear

Linear stable path Nonlinear stable path

shortest path

A 230 35 35 20 (57%) 12 (34%)

B 230 35 35 14 (40%) 5 (14%)

C 288 80 80 42 (53%) 42 (53%)

D 230 10 10 10 (100%) 6 (60%)

E 300 80 80 58 (73%) 49 (61%)

F 200 30 30 21 (70%) 13 (43%)

G 300 60 60 26 (43%) 25 (42%)

H 300 75 75 44 (59%) 41 (55%)

I 230 80 80 51 (64%) 53 (66%)

J 230 110 110 75 (68%) 61 (55%)

K 230 60 60 30 (50%) 34 (57%)

L 180 60 60 37 (62%) 29 (48%)

M 220 60 60 27 (45%) 16 (27%)

N 1536 150 150 46 (31%) 6 (4%)

O 1944 100 100 29 (29%) 15 (15%)

P 800 100 100 48 (48%) 14 (14%)

Q 600 70 70 34 (49%) 30 (43%)

R 800 90 90 33 (37%) 27 (30%)

S 355 80 80 58 (73%) 10 (13%)

T 274 70 70 43 (61%) 38 (54%)

U 400 100 100 41 (41%) 36 (36%)

V 402 70 70 31 (44%) 23 (33%)

W 290 30 30 10 (33%) 4 (13%)

X 375 30 30 29 (97%) 27 (90%)

Y 504 70 70 32 (46%) 21 (30%)

Z 411 130 130 59 (45%) 56 (43%)

AA 332 35 35 18 (51%) 22 (63%)

AB 350 110 110 60 (55%) 63 (57%)

AC 375 50 50 31 (62%) 25 (50%)

AD 385 50 50 27 (54%) 14 (28%)

AE 300 65 65 30 (46%) 33 (51%)

AF 480 50 50 20 (40%) 19 (38%)

AG 324 40 40 36 (90%) 23 (58%)

AH 504 150 150 24 (16%) 15 (10%)

AI 319 150 150 57 (38%) 8 (5%)

AJ 428 150 150 38 (25%) 27 (18%)

Average (53%) (39%)

methods. The results can be found in the Table 1. The

percentage values are the fraction of iterations neces-

sary by the stable path algorithms relative to the to-

tal number of iteration required by the shortest path

methods (that matches the number of removed lines).

It can be observed that the proposed algorithm has

a very interesting performance. The use of the stable

paths reduced the number of iterations and the corre-

sponding computational complexity. The simultane-

ous use of a nonlinear weight function and the stable

path method reduced further the number of iterations

required to resize the image.

In a second experiment we evaluated the impact

on quality of the use of stable paths to resize images.

It is important to conﬁrm if we are trading off quality

for computational performance.

In Figures 5 and 6 it is presented the results ob-

tained with the linear shortest path method and the

linear and nonlinear stable path method. It is possible

to observe that the stable path method attain a better

quality; the principal visual improvement can be seen

on people appearance.

From the analysis of the results reported in Fig-

ure 7, it is possible to conclude that the nonlinear

weight function presents a better behaviour than the

linear weight. The principal visual impact can be seen

on the horizon of the scenery. Furthermore, is pos-

sible to observe, by comparing Figure 7(c) and 7(d),

that the stable path algorithm outperforms the shortest

path algorithm. The resized image using our method

IMAGE RETARGETING USING STABLE PATHS

45

(a) Original image. (b) Resized image using the

linear shortest path method.

(c) Resized image using the

linear stable path method.

(d) Resized image using

the nonlinear stable path

method.

Figure 6: Results of the different resizing methods when

applied to image V.

(a) Original image. (b) Resized image using the

linear shortest path method.

(c) Resized image using

the nonlinear shortest path

method.

(d) Resized image using the

nonlinear stable path method.

Figure 7: Results of the different resizing methods when

applied to image J.

seems more natural: in Figure 7(c) the sky is very

compacted when compared with Figure 7(d).

In Figures 8 and 9 we can observe that our al-

gorithm can be simultaneously faster and with better

quality than the version in (Avidan and Shamir, 2007),

both on small sized images and big sizes image, re-

spectively.

(a) Original image. (b) Resized image using the

linear shortest path method.

(c) Resized image using

the nonlinear shortest path

method.

(d) Resized image using the

nonlinear stable path method.

Figure 8: Results of the different resizing methods when

applied to image AI.

(a) Original image. (b) Resized image using the

linear shortest path method.

(c) Resized image using

the nonlinear shortest path

method.

(d) Resized image using the

nonlinear stable path method.

Figure 9: Results of the different resizing methods when

applied to image N.

The lack of metrics to perform this evaluation ob-

jectively, led us to create a panel of observers to evalu-

ate subjectively the output of the different algorithms.

Besides conﬁrming the results already demonstrated,

an interesting conclusion was that, in some images,

the traditional rescaling continues to be preferable.

5 CONCLUSIONS

We presented an algorithm for content-aware image

resizing. The proposed method is an improvement

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

46

over an already established method in the literature.

We exploit the concept of stable paths to enhance both

the computational speed and the quality of the result-

ing image. The generalization of the weight function

of the graph derived from the image further improved

the quality results. Though the experimental results

have focused on image reduction only, the method is

straightforwardly applied to image enlarging, image

ampliﬁcation and object removal. We intend now to

generalize and adapt the concept of stable paths for

video retargeting.

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