Multi-Object Segmentation for Assisted Image reConstruction

Sonia Caggiano

, Maria De Marsico

, Riccardo Distasi

and Daniel Riccio

Master of Architecture and PhD, Digital Painting Restoration, Italy

Dipartimento di Informatica, Sapienza Universit

a di Roma, 00198 Roma, Italy

Dipartimento di Studi e Ricerche Aziendali (Mgmt IT), Universit

a di Salerno, 84084 Fisciano (SA), Italy

Dipartimento di Ingegneria Elettrica e Tecnologie dell’Informazione, Universit

a di Napoli “Federico II”,

80121 Campi Flegrei (NA), Italy

Keywords:

Image processing, Feature extraction, Feature-based indexing, Jigsaw puzzle, Cultural heritage.

Abstract:

MOSAIC is a tool for jigsaw puzzle solving. It is designed to assist cultural heritage operators in reconstructing

broken pictorial artifacts from their fragments. These undergo feature extraction and feature based indexing,

so that any fragment can be the key to queries about color distribution, shape and texture. Query results are

listed in order of similarity, which helps the user to locate fragments likely to be near the key fragment in

the original picture. A complete working protocol is provided to bring the user from the raw materials to a

working database. System performance has been assessed with both computer simulations and a real case

study involving the reconstruction of a XV century fresco.

1 INTRODUCTION

When a fresco or a piece of pottery shatters after some

traumatic event, reconstructing it from its fragments

is an as challenging as time-consuming and often te-

dious endeavour. Manual reconstruction requires ex-

treme amounts of time and resources, which are di-

rectly proportional to the number of fragments and

further grow as such fragments become smaller, till

to make the task downright impossible. What’s more,

in some cases the intrinsic fragility of the materials

imposes heavy constraints on the manipulation of the

pieces, which is necessary on the other hand to ver-

ify matches and correspondences. Fragility and un-

ease of handling are the most critical issues, and be-

come even more hindering when there is no reference

document representing the artwork, e.g., a fresco, as

a whole. The latter would not only support the re-

storer during the work but also reduce the number of

required matches, therefore decreasing the risk of fur-

ther degradation of the fragments.

In recent times, the use of advanced hardware as

well software resources has represented a dramatic

turning point. An interesting and recent example is

the reconstruction system implemented to work with

the artifacts found at the Roman archaeological site in

Tongeren, Belgium (Brown et al., 2010). An ad hoc

3D scanner has been set up for the acquisition of the

tridimensional shape of the fragments. The shapes are

submitted as input into an ad hoc software system that

matches the contours. However, the costs for such

sophisticated equipment (approximately 25,000 USD

for a scanner with suitable performance) are still quite

high when compared with the improvement in work-

ﬂow: in this speciﬁc case, 17 true matches were con-

ﬁrmed out of the 6103 candidate matches proposed

by the system, compared with 3 matches previously

found manually.

As a further example, Brown et al. implemented

a semi-automatic system for fresco reconstruction

at the Akrotiri excavation site in Thera, Santorini,

Greece (Brown et al., 2008). The main purpose was

to produce a practical, user-friendly software system

that could provide the archaeologists with some au-

tonomy in cataloging and trying to reconstruct ancient

frescos. In this case, too, the system is partly based on

3D data, but there is heavier use of 2D image process-

ing techniques such as extraction of features based on

color, shape and texture.

From a theoretical point of view, the problem of

reconstructing pictures or generic documents from

fragments is connected to jigsaw puzzle solving. Puz-

zles are grouped into two types: (a) apictorial puz-

zles (where fragment shape is the only kind of infor-

mation available or signiﬁcant) and (b) pictorial puz-

zles, where texture and color information is available

100

Caggiano S., De Marsico M., Distasi R. and Riccio D..

Multi-Object Segmentation for Assisted Image reConstruction.

DOI: 10.5220/0005274601000107

In Proceedings of the International Conference on Pattern Recognition Applications and Methods (ICPRAM-2015), pages 100-107

ISBN: 978-989-758-077-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

and can be meaningfully used. For both types, it has

been shown that providing an exact algorithmic so-

lution is an NP-complete problem: computing time

grows unmanageably (non-polinomially) with prob-

lem size (Chung et al., 1998). As a consequence,

when the number of fragments is large, the time re-

quired for an algorithmic solution can be prohibitively

long. However, things are different when we settle

for a non-exact solution: there are heuristic and ap-

proximate techniques that provide acceptably accu-

rate solutions in reasonable times. The available liter-

ature offers several solutions for both types of jigsaw

puzzles—and several applications as well, mostly in

the ﬁelds of cultural heritage and ancient document

reconstruction.

Freeman and Gardner were among the ﬁrst to face

the problem of apictorial jigsaw puzzles (Freeman

and Garder, 1964). Their approach was based on

ﬁve fundamental puzzle properties: orientation (not

known a priori), connectivity (presence or absence of

internal “holes”), perimeter shape (known/unknown a

priori), uniqueness (does the problem have one solu-

tion only?), radiality (type of juncture between frag-

ments). Fragment contours are represented as chain

codes whose length is used as a heuristic for reducing

the dimension of the search space. Papaodysseus et

al. tackle this problem in the speciﬁc context of wall

painting reconstruction (Papaodysseus et al., 2002).

Their paper is particularly interesting because it fo-

cuses on speciﬁc real-world issues that arise when

dealing with wall paintings: lack of information about

the original aspect of the painting, lack of uniqueness,

and especially the presence of very small fragments—

dealt with by the introduction of non-connectedness

(“holes”) to account for the loss of some of the pieces.

The technique for correspondence veriﬁcation and

matching is based on local curve matching and is able

to cope with missing information.

It is possible to obtain more effective solutions by

exploiting all available information in a better way.

For this reason, most techniques that are actually used

in cultural heritage reassembly applications regard the

problem not as an apictorial, but as a pictorial puz-

zle. For instance, works such as (Chung et al., 1998)

and (Sagiroglu and Ercil, 2006) use color and tex-

ture information, respectively. However, their actual

testing has been limited to problems involving a rela-

tively small number of fragments. On the other hand,

Nielsen et al. devised a technique that uses no infor-

mation pertaining to single pieces, relying instead on

features of the whole represented pictorial scene. The

reported results for this technique show low error mar-

gins: the solution to a 320-fragment problem only had

23 pieces out of place—an error margin of 7.2%. This

example shows that not only shape, but all available

information can be quite useful to obtain the highest

possible accuracy: in this particular case, a good so-

lution was obtained by color and texture information

alone.

Summing up, the virtual reconstruction of picto-

rial fragments is an intrinsically hard problem, and ap-

proximate solutions are often all we can get. For this

reason, a number of sophisticated techniques drawn

from image processing are being included in more ad-

vanced systems. The most promising ones are based

on local texture analysis, chrominance analysis and

contour analysis on single fragments. Methods based

on the whole scene depicted are quite powerful, when

the original appearance is known or can be at least

partially inferred, and can provide further features to

consider. All these techniques can be used to produce

multimodal representations that allow users to reﬁne

the solution progressively, adding detail and informa-

tion to the features of the solution search space.

The present paper proposes a system for the seg-

mentation and indexing of pictorial fragments: Multi-

Object Segmentation for Assisted Image reConstruc-

tion (MOSAIC). MOSAIC supports the rebuilding of

a fresco from fragments by a human operator. No in-

formation about the original appearance of the whole

artwork is assumed to be available. The system has

been tested on a real case study: the reconstruction of

a fresco from fragments found in the St. Trophimena

church in Salerno (Italy).

2 OPERATING CONTEXT

MOSAIC was expressly designed to support fresco

recomposition from fragments. Its architecture in-

cludes a protocol for image acquisition and process-

ing, so the single fragments can be cataloged and user

queries can be answered. A workspace is provided;

here, among the other actions, the user can virtually

rotate, translate and search for similar fragments. Fig-

ure 1 illustrates the system architecture schematically.

Figure 1: Architecture of the MOSAIC system.

Multi-ObjectSegmentationforAssistedImagereConstruction

101

During image acquisition, the real fragments are

laid in a white tray, whose bottom is covered by a

dark grey foam. The tray is placed inside a box for

object photographic acquisition, which is made by a

white curtain and two lateral spotlights. Beside the

tray there is a colorimeter, used to detect the possi-

ble need for automatic color corrections. A picture of

the tray is captured with a suitable device (in the spe-

ciﬁc case, an 8-Mpixel Canon camera), orthogonally

pointed from a height of 90 cm (35.4 in).

2.1 Segmentation

Segmentation is a delicate phase that has signiﬁcant

inﬂuence over the rest of the procedure: several things

can go wrong. The purpose of this operation is to sep-

arate each fragment, so that individual features can be

extracted. In the ﬁrst segmentation step, namely bina-

rization, the image is turned into B/W with no shades

of gray. Turning the original color photo into a binary

image might appear to be a trivial task, but it is not

so. If using naive thresholding on the raw images, we

have found that no single threshold value is effective

across all trays. Too low a value is ineffective at sepa-

rating one piece from another, while too high a value

yields pieces with “holes” inside them. In some cases,

a morphological ﬁll operation is able to ﬁll such holes,

but in other cases the piece comes out as two sepa-

rate fragments, and this cannot be repaired. An exam-

ple of problematic binarization is shown in Fig. 2 (a)

and (b).

Figure 2: Effect of threshold parameter t

on the segmenta-

tion of a tray image: (a) too low; (b) too high; (c) optimal

value t

= 0.1; (d) connected components detected after bi-

narization.

Since the naive approach on the raw images is in-

effective, the actual process of binarization needs to

amplify the difference between the fairer pixels (frag-

ments) and the darker ones (background foam—quite

dark but not exactly black).

The original image is represented in RGB space.

The single channels are stored in three separate ma-

trices r, g, and b. Two new matrices are then created:

M and m. The element M(i, j) of the new matrix M is

equal to the maximum over the three channels, i.e. the

maximum among r(i, j), g(i, j) and b(i, j)—therefore

each pixel in the new image represented by M con-

tains the largest (brightest) component of the origi-

nal image. The element m(i, j) of the new matrix m

is equal to the mean of r(i, j), g(i, j) and b(i, j)—

therefore the image represented by m is a greyscale

version of the original image. From M and m, the en-

hanced image I is built as follows. First,

I (i, j) ← M (i, j) ·

m(i, j) −δ

. (1)

The value δ in Eq. (1) is an experimentally determined

offset, which is a constant over all images. In our spe-

ciﬁc case, δ = 50. This is close to the mean lumi-

nance value of all pixels in the tray (both fragments

and background). The pixel values in I are then scaled

by dividing them by their mean value

I (i, j) ← I (i, j) /

I . (2)

The new I is then turned into a 0–1 binary image by

thresholding according to the binarization threshold

value t

I (i, j) ←

(

0, if I (i, j) < t

1, if I (i, j) ≥ t

. (3)

We now explain the rationale for the operations just

described. The grayscale image m and the maximum

component image M are pointwise multiplied in or-

der to enhance the pixels where both m and M have

larger values. The resulting image is then divided by

its mean value to perform a sort of normalization of

the pixel values, so that the value of the threshold t

used for binarization does not depend on the partic-

ular image anymore. A value of t

= 0.1 has been

found to be effective for all tray images in our pool.

The ﬁnal result of binarization can be seen in Fig. 2

(c).

The binary image just obtained becomes the input

to an algorithm for detecting connected components.

Ideally, each fragment should be one connected com-

ponent and vice versa, as in Fig. 2 (d). After a frag-

ment shape is extracted from the binary image, a mor-

phologic ﬁll operator is applied in order to ﬁll exist-

ing gaps or holes. Then speciﬁc information about

the newfound fragment is computed: area, perimeter,

orientation. The binary connected component will be

used as a mask to retrieve the fragment from the orig-

inal image by a pixel-wise logical AND operation.

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2.2 Feature Extraction

The module following segmentation deals with fea-

ture extraction, so the fragments can be indexed and

conveniently retrieved. The features used for indexing

and retrieval are the shape(s) depicted on the fragment

and a spatiogram—which describes the spatial distri-

bution of color. Such extracted features allow a user

to search the fragment database in order to retrieve

fragments similar to a given “key” fragment on the

basis of similar color, similar shape, or similar spatial

color distribution.

2.2.1 Color

Information about color is represented by a spa-

tiogram of the fragment (Birchﬁeld and Rangarajan,

2005). Brieﬂy, a spatiogram is a histogram where

the count of occurrences of each color is augmented

with are the mean vector and covariance matrices,

respectively, of the coordinates of the pixels con-

taining that color. In a way similar to histograms,

spatiograms allow simple manipulations—especially

comparisons between image areas—without the need

to work out geometric mappings between the areas in-

volved. However, these augmented data structures do

further contain some spatial information about color

distribution. This spatial information provides in-

creased matching accuracy.

2.2.2 Shape

The information extracted regards the predominant

shapes of pictorial elements from a fragment, based

on the color of the shapes. The pixels ﬁrst undergo a

clustering procedure based on color. Shape informa-

tion results from the analysis of the clusters in each

fragment. Color clustering is performed by a mean-

shift based method (Comaniciu and Meyer, 2002).

Such methods are non-parametric and fairly insensi-

tive to noise or similar low-level disturbances. More-

over, in mean-shift based clustering, the number of

clusters is not predetermined. As it turns out, in most

cases the result obtained is over-segmented for our

purposes. This is exempliﬁed in Fig. 3.

In order to correct over-segmentation, a threshold-

ing “color radius” t

is determined, and the resulting

distinct RGB colors that lie at a distance less than t

are coalesced into a single color by re-labeling. In

our speciﬁc case, the effective value the threshold has

been determined experimentally at t

= 32. Cluster-

ing accuracy is signiﬁcantly improved by this correc-

tion, as can bee seen comparing Fig. 3 (c) and (d).

Within a single fragment, each color cluster is

considered independently. The pixels belonging to

Figure 3: Shape extraction: (a) the original fragment; (b) af-

ter color clustering, original colors; (c) false colors show

oversegmentation; (d) thresholding and re-labeling; (e) ex-

tracted shapes.

one cluster (and then appearing to the system as

being of the same color) are fed to an algorithm

for connected component detection in order to de-

termine the shapes represented. This process is de-

picted in Fig. 3 (e). Each detected connected compo-

nent is in turn processed independently. The smaller

components—those whose area is less than 4% of the

total fragment area—are discarded as not signiﬁcant

(small color holes, noise, as well as processing de-

fects in binarization, segmentation, color clustering,

or detection of connected components). Each frag-

ment F

is thus characterized by a variable number s

of shapes S

, i = 1 ...s

, whose surface area equals at

least 4% of the total fragment surface. These compo-

nents undergo contour detection so their shapes can

be geometrically described. Since this processing is

performed on a per-fragment basis, and since the fol-

lowing analysis is performed on single shapes in the

fragment, in order to simplify the notation we will

drop from now on the subscript identifying fragment

and shape. Shape S is analyzed through its contour

C. However, a further consideration is still needed

before proceeding. Not all components correspond

to relevant shapes, even if their area is over the 4%

threshold: some of them are just stains and contribute

nothing but noise to the system. Therefore, it is neces-

sary devise some relevance criteria to assign a higher

weight to relevant shapes than to stains. In order to as-

sess relevance in this context, contour smoothness is a

useful criterion. The underlying assumption, which is

supported by experts, is that the contour of a stain or

blemish is most often more jagged than the smoother

contour of a pictorial element. An example is pro-

Multi-ObjectSegmentationforAssistedImagereConstruction

103

vided in Fig. 4. On the other hand, they still contribute

to the spatiogram, therefore their possible color infor-

mation content is not lost in any case. According to

this, the shape processing continues as follows.

=0.682

=0.849

Figure 4: Smoothness ranks shape contours along the

jagged/smooth axis.

The contour C of a shape is represented as an or-

dered sequence of n

points:

C = {P

,...,P

}, (4)

where the contour step count n

differs from shape

to shape. Given a point P

in C, let us consider an-

other contour point P

k+l

located l steps further along

the same path, so that the path from P

to P

k+l

has

step count l, which also corresponds to the lowest

distance between them. Let d(·,·) be the Euclidean

distance between any two points. The smoothness

for the subpath beginning at P

and spanning l points

k,l

= {P

k+1

,...,P

k+l

} is computed as

ω(k, l) = d(P

k+l

)/l . (5)

The actual value used for smoothness calculation de-

pends on n

and is l =

4log

. The smoothness

for the whole contour C is given by

ω(C) =

∑

k=1

ω(k, l). (6)

It assumes values in [0,1] and is used as a weight in

matching operations, as will be shown shortly.

Each shape is represented as a triple

S = hv,ω,ci. (7)

In this characterization, v = (v

,...,v

) is the vector

of the ﬁrst 7 central moments of the shape. For a thor-

ough discussion of central moments and some of their

applications to pattern recognition, see (Hu, 1962;

Mercimek and Mumcu, 2005). The two remaining

elements in the triple, ω and c, are the shape smooth-

ness and mean color value, respectively. A fragment

containing s

shapes is therefore characterized by

such triples.

In order to compare two shapes S

= hv

,ω

and S

= hv

,ω

i, we compute their similarity as

the normalized dot product of their moment vectors

(i.e., the cosine of the angle between them), weighted

by the product of their smoothness values:

sim(S

) = ω

· v

. (8)

The similarity between two fragments F

and F

given by the maximum shape-to-shape similarity:

sim(F

) = max

S ∈ F

T ∈ F

sim(S,T ) .

However, the most common type of query has a sin-

gle shape S as the key and goes through each frag-

ment indexed in the database looking for shapes with

high values of similarity to S. The similarity score as-

signed to a fragment is the maximum similarity score

achieved by a shape it contains. Smaller shapes are

discarded as not relevant. In a query based on shape,

the fragments are returned in decreasing order of sim-

ilarity to S.

3 THE SYSTEM INTERFACE

MOSAIC has a graphical user interface (GUI) that

allows the operator to create a work session where

the virtual fragments can be handled and reconstruc-

tion can be performed by retrieving relevant frag-

ments through queries based on shape, color or a com-

bination thereof. The interface is shown in Fig. 5.

A freshly created work session appears as a blank

workspace where fragments can be brought in. Here

is an outline of the main functionalities offered by the

interface.

Figure 5: MOSAIC: The graphical user interface and the

workspace.

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104

• Workspace Management. Fragments can be

picked from the database, manually or via queries,

and brought into the workspace. Unneeded frag-

ments can be removed.

• Manipulation. The computer system operator

can translate or rotate fragments, similarly to an

archaeologist or other cultural heritage specialist

actually working with physical pieces.

• Search. It is possible to query the system by se-

lecting a fragment from the workspace. The query

can address a number of features, among which a

speciﬁc pictorial shape among those represented

in the fragment, the whole set of shapes repre-

sented, color distribution, texture (both shape and

color are relevant), and more.

4 EXPERIMENTAL RESULTS

Given the nature of the MOSAIC system, assessing

its performance quantitatively is signiﬁcantly harder

than merely providing a qualitative judgment; there-

fore, a custom experiment has been designed. The

main objective was that of evaluating precision/recall

achieved by MOSAIC when attempting to retrieve the

fragments near a given one. This reﬂects the intended

use of the system by a human operator trying to recon-

struct shattered pictorial artworks. The chosen pic-

ture is a representation from the late XV century: the

Madonna della Misericordia or Madonna delle pietre,

by an unknown author, shown in Fig. 6. The original

size is 140×90 cm. The acquisition was performed at

300 ppi, 24 bit RGB, yielding 1185 × 1566 pixels.

Figure 6: The image chosen for quantitative performance

assessment, with a detail of some of the fragments.

The picture was divided into irregularly shaped

small pieces, and the smallest ones were discarded

to simulate true fragmentation resulting from a trau-

matic event. The process produced about 2900 pieces

of sizes ranging from roughly 2 × 2 cm to 8 × 8 cm,

which were entered into MOSAIC and indexed.

It is reasonable to assume that adjacent pieces of-

ten tend to have similar textural features, so searching

for similar features should return fragments lying in

the same picture area as the key fragment used for

querying. Vice versa, in our context, given a key frag-

ment, the user wants to retrieve the fragments that lied

close to it in the original, pristine “canvas”, and it is

possible to assume that they present a similar texture.

Therefore, jigsaw puzzle solution can be simpliﬁed

by picking fragments from this smaller subset rather

than from the full set. In order to verify the effec-

tiveness of the indexing process, in this test setting

each fragment was characterized with the canvas co-

ordinates of its barycenter, computed assuming uni-

form mass distribution. Of course, this is not pos-

sible in real situations, since the problem to solve is

exactly related to the fact that we do not know the

original position of the fragments. During reconstruc-

tion, we might only recover the position of the already

identiﬁed ones, but only if we have an image of the

original artwork. However this was useful to analyze

some issues. Given a key fragment A used as a query,

let its barycenter be P

; a fragment B retrieved by

the system is deemed to be “close enough”—that is,

signiﬁcant—if its barycenter P

falls within a circle

of radius t

centered in P

Since the geometry of the problem is based on

pixel units, the choice of a good value for the

threshold t

is strongly dependent on image scaling/

resolution. For this reason, the value of t

is ex-

pressed as the product of a proportionality factor δ in

the range [0,1] times a representative length quantify-

ing the image resolution, namely the diagonal length

, in our case 1964 pixels. Experiments have been

performed with δ = 0.02, δ = 0.05 and δ = 0.1, with

resulting values of t

= 39, t

= 98 and t

= 196 pix-

els respectively. Each fragment was used as the key

to a MOSAIC query. The average precision and recall

curves over all fragments are plotted in Fig. 7.

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

Recall

Precision

δ=0.02

δ=0.05

δ=0.1

Figure 7: Average precision/recall curves for MOSAIC with

δ = 0.02, δ = 0.05 and δ = 0.1.

Multi-ObjectSegmentationforAssistedImagereConstruction

105

The diagram shows that smaller values of δ gen-

erally yield better retrieval. The main reason is that,

for any given key fragment, the results of interest are

usually conﬁned to a small space neighborhood of

the key rather than spread around widely. However,

there is an intrinsic problem issue that harms preci-

sion and recall. Looking at Fig. 6, it can be seen

that there are fairly extended regions with homoge-

nous features. For example, the whole halo area has

nearly homogeneous textural and chromatic features.

As a consequence, any two fragments belonging to

that area will be “close” in the feature space, while

actually lying at a potentially large distance in the re-

constructed picture.

4.1 A Real Life Case

The MOSAIC system has also been put to the test

in a real case study involving reconstruction from

6419 fresco fragments found during restoration work

at the St. Trophimena Church site in Salerno. Un-

fortunately, no information was available about the

original appearance of the frescoes: virtual recon-

struction was the only option to recover at least parts

of the original work without adding further damage

to the fragments. Examples of actual use are shown

in Fig. 8, depicting a reconstruction in progress, and

Fig. 9, illustrating a shape-based query.

Lack of information about the “real” solution to

this jigsaw puzzle makes it impossible to obtain an

objective measure of the solution obtained by using

the system in this real-world case, but a qualitative

assessment of its effectiveness is possible. Detailed

feedback from the end users conﬁrmed the substantial

usefulness of such a system.

Figure 8: A query, its result, and a partial reconstruction

made from some of the fragments returned.

In Fig. 8, each label has two values. The ﬁrst is

the tray where the fragment lies, while the second is

the serial number inside that tray. As the illustration

shows, it is not uncommon for pieces close to each

other in the original picture to end up in quite distant

trays when they are picked up from the original site

or during cataloging.

Figure 9: Query by shape: strips.

5 CONCLUSIONS

MOSAIC (Multi-Object Segmentation for Assisted

Image reConstruction) is a system for the computer

aided reconstruction of pictorial artworks from their

fragments. The fragments are cataloged and indexed

based on relevant features such as color and shape.

Queries can be formulated through the GUI by select-

ing a fragment or a single shape represented on a frag-

ment. The results, sorted by similarity, provide can-

didates for puzzle solving in the area of the relevant

fragment. This can speed up the process signiﬁcantly

and improve the quality of the reconstruction. The

system has been tested ﬁrst via computer simulation

in a setting where the solution was known a priori,

and later in a real world situation, where the solution

was unknown. Domain experts have provided pre-

cious feedback for tuning the system; future work is

planned involving more detailed interaction with ar-

chaeologists and cultural heritage operators to better

understand their needs and offer improved support.

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