INTERACTIVE IMAGE SEGMENTATION WITH

INTEGRATED USE OF THE MARKERS AND THE

HIERARCHICAL WATERSHED APPROACHES

Bruno Klava and Nina Sumiko Tomita Hirata

Institute of Mathematics and Statistics, University of S

ao Paulo, Rua do Mat

ao, 1010, S

ao Paulo, Brazil

Keywords:

Segmentation, Interactivity, Watershed from markers, Hierarchical watershed.

Abstract:

The watershed transform is a well-known approach for image segmentation. Watershed from markers and

hierarchical watershed are derived from the watershed transform and are suitable for interactive image seg-

mentation: in the former, the user can edit markers and control the segmentation result; in the latter, the user

can select an image partition from a nested set of partitions. We investigate and propose ways to transition

from one approach to other. Such transitions can be used to integrate both approaches in such a way that

allow us to make full use of the strengths of both. We present examples that illustrate the use of the proposed

transitions in conjunction with several interaction possibilities from both approaches.

1 INTRODUCTION

Segmentation is an important stage in almost every

problem involving digital image analysis. The goal

of the segmentation process is to partition the spatial

domain of the image, delimiting the regions of interest

that correspond to the target objects of the analysis in

question.

Since it is not always possible to facilitate the

segmentation process, systems developed to automat-

ically segment images are usually restricted to spe-

ciﬁc domains. Even for a particular application pur-

pose, formal speciﬁcation of the parameters of a seg-

mentation algorithm can be very difﬁcult. In many

cases, in order to obtain a satisfactory result, a post-

processing of the partition (obtained through auto-

matic techniques) is necessary. Moreover, the concept

of a good partition may depend on the purpose of its

use and may be highly subjective.

Interactive segmentation systems are appropriate

to deal with several of these issues. The user can man-

age the segmentation process, having full control over

the level of detail of the desired partition.

The watershed transform (Beucher and Meyer,

1993) is a well-known segmentation tool from math-

ematical morphology. There are two approaches suit-

able for interactive segmentation:

• the watershed from markers approach reduces the

segmentation problem to ﬁnding a set of markers

for the regions of interest. The desired partition

can be obtained by interactively handling the set

of markers;

• the hierarchical watershed generates a nested par-

titions set, with partitions of the image at several

resolution levels. The user can navigate through

the hierarchy in order to select a partition with the

desired level of detail for each region of interest.

In the hierarchical watershed approach, the under-

lying structure is the region adjacency graph (RAG)

of an initial ﬁne partition. While pixels correspond

to the atomic units in images, in the hierarchical ap-

proach the atomic units are the regions of the ﬁnest

partition. Thus, in any partition derived from the hier-

archy, all resulting regions are unions of some primi-

tive regions.

The formal deﬁnition of watershed on graphs

made possible a unifying treatment for segmenta-

tion, regardless of the atomic unit considered (Meyer,

2001b). We say that partitions are at region level pre-

cision if the graph considered is the RAG, whereas

they are at pixel level precision if the graph consid-

ered is the 4 or 8-adjacency graph of the pixels.

Since the number of nodes in the RAG is consid-

erably smaller than the number of pixels in the image,

most of the operations on the hierarchy or its under-

lying RAG can be performed very efﬁciently. Several

interaction possibilities have been considered in the

context of the hierarchical approach (Meyer, 2001b;

186

Klava B. and Sumiko Tomita Hirata N. (2009).

INTERACTIVE IMAGE SEGMENTATION WITH INTEGRATED USE OF THE MARKERS AND THE HIERARCHICAL WATERSHED APPROACHES.

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, pages 186-193

DOI: 10.5220/0001794301860193

 SciTePress

Marcotegui and Zanoguera, 2002; Hahn and Peitgen,

2003). These works introduce ideas to interactively

handle the hierarchical structure, some in conjunction

with markers operating on the RAG.

However, if one desires to place contours beyond

those at the border of the primitive regions, it is im-

portant that the watershed from markers also operates

at pixel level precision. Another feature that may be

interesting is computing markers corresponding to a

given partition obtained from operations performed

on the hierarchy. Such markers may be edited and

the corresponding partition be reﬁned as desired, or

they can be used as a training data by systems aiming

to automatically generate markers for a given applica-

tion.

In this work we study how to make transitions be-

tween the hierarchical and the markers approaches.

Such transitions would be useful to integrate both ap-

proaches in such a way as to allow switching back and

forth between them, and thus making full use of the

interaction possibilities from both approaches.

Since markers can be considered on the RAG or

on the pixel adjacency graph, transitions between both

approaches may imply change in the precision. Tran-

sitions from region to pixel level precision can be

made without information loss. However, transition

in the opposite direction may result in information

loss (not all partitions that are possible in pixel level

precision are possible in the region level precision).

This paper is organized as follows. In Section 2

we recall some basic concepts and results from pre-

vious works needed to present our results. In Section

3 are the main contributions of this work. We dis-

cuss how to map a partition of the hierarchy to an

equivalent set of markers and, conversely, the parti-

tion corresponding to a set of markers to a hierarchy

that contains it as one of the partitions. In particu-

lar we show that if the markers corresponding to a

given partition are computed on the RAG, then the

exact recovery of the partition with pixel level pre-

cision can not be guaranteed, but the possible dif-

ferences between the original and the recovered par-

titions are well characterized. In Section 4 we de-

scribe how the proposed transitions can be used in

an interactive segmentation environment, in conjunc-

tion with some interaction possibilities from both ap-

proaches. These interaction features have been im-

plemented in the SegmentIt software tool, available at

http://watershed.sourceforge.net/. Examples illustrat-

ing the use of these features are presented. Finally,

in Section 5 we summarize the contributions of this

work.

2 PRELIMINARIES

2.1 Watershed

The watershed transform is a robust segmentation

tool, since the watershed lines produced are very close

to the object boundaries. Its most intuitive formula-

tion is a ﬂooding simulation. The image (usually a

gradient image such as the morphological gradient,

instead of the original image) is considered as a to-

pographic surface, and a hole is made in each of its

regional minima. Then, the surface is submerged at

a constant speed (uniform ﬂooding) making the water

arise through its holes. When fronts of water com-

ing from different minima are about to merge, a dam

is built to avoid it. The ﬂooding process continues

until only the dams, which stands for the watershed

lines, are visible over the water surface. This ap-

proach, known as classical watershed, has an over-

segmentation problem, due to the fact that gradient-

like images are very sensitive to noise and texture,

which results in a catchment basin (a region of the

partition) for each regional minima. Each catchment

basin from the classical watershed is called a primi-

tive catchment basin.

In order to reduce this over-segmentation prob-

lem, one can use the watershed from markers. This

approach is exactly the same as the classical water-

shed, except that the holes at the surface are made in

a selected set M of markers instead of at the regional

minima.

2.2 Graphs

A weighted graph G = (V, E, w) consists of a set V of

vertices and a set E of edges, E ⊆ V ×V , weighted by

a cost function w. Two vertices u and v are said ad-

jacent if (u, v) ∈ E. N(u) denotes the neighborhood

of u: N(u) = {v ∈ V : (u, v) ∈ E}. A path π(u, v)

from u to v is a sequence hu = v

, v

, . . . , v

= vi

of vertices such that (v

, v

i+1

) ∈ E, 1 ≤ i < n and

6= v

, 1 ≤ i < j ≤ n. The concatenation of the paths

and π

is denoted by π

· π

. A path from u to v

with minimum cost according to a cost function f

represented by π

∗

(u, v). π

∗

(M, v) denotes a minimum

cost path from a set M, M ⊆ V , to the vertex v, that

is, f

(π

∗

(M, v)) = f

(π

∗

, v)), for some m

∈ M,

and f

(π

∗

, v)) ≤ f

(π

∗

, v)), ∀m

∈ M. A graph

= (V

, E

, w) is a subgraph of G = (V, E, w), de-

noted by G

⊆ G, if V

⊆ V , E

⊆ V

×V

and E

⊆ E.

A graph G

= (V

, E

) spans a graph G = (V, E) if

⊆ G and V

= V . A forest of G is an acyclic sub-

graph of G. A tree is a connected component of a for-

est. A tree T is a minimum spanning tree (MST) of

INTERACTIVE IMAGE SEGMENTATION WITH INTEGRATED USE OF THE MARKERS AND THE

HIERARCHICAL WATERSHED APPROACHES

187

a graph G if T ⊆ G, T spans G, and the sum of its

edges weights is minimum (considering all possible

spanning trees of G).

2.2.1 Images as Graphs

Digital images can be modeled as graphs with differ-

ent precision levels: pixels and regions.

Pixel Adjacency Graph (PAG). An image I is

viewed as a weighted graph G

= (V, E, w), where V

is the set of the image pixels, E is derived from V

and a connectivity relation (usually 4-connectivity or

8-connectivity), and w is a dissimilarity function (in

our case, w(u, v) = max{∇(u), ∇(v)}, where ∇(p) is

the intensity of the pixel p in the gradient image).

Region Adjacency Graph (RAG). An image I is

viewed as a weighted graph, whose vertices repre-

sent the primitive catchment basins (CB) associated

to each regional minimum of I. An edge is created for

each pair of adjacent CBs, weighted by the minimum

pass value between them, that is:

w(CB

,CB

) = min

∈CB

∈N(p

)

{w(p

, p

)}. (1)

2.3 Image Foresting Transform

Under the image foresting transform (IFT) framework

(Falc

ao et al., 2004), the watershed transform is for-

mulated as a graph optimization problem: it corre-

sponds to the creation of a shortest-path forest (SPF),

in which exists a minimum cost path from each ver-

tex to the set of markers, or seeds. The cost function

considered is the max-arc path-cost f

max

(hv

, . . . , v

i) = max

1≤i<n

{w(v

, v

i+1

)} (2)

The resulting SPF deﬁnes a partition (each set

of trees with same label in the forest corresponds

to a catchment basin). We denote this partition by

IFT -W S(G, M), where G is the input graph and M is

the set of markers (distinct marker vertices can have

the same label associated to them).

2.4 Hierarchical Watershed

The nested set of partitions of the hierarchical water-

shed approach is derived from an MST of the RAG,

suppressing some of its edges: if the edge between

two vertices is not suppressed, they belong to the

same region of interest (ROI). The coarser partition of

the hierarchy is given by the MST without any edge

being suppressed, corresponding to only one ROI.

The ﬁnest partition is obtained when all the edges are

suppressed, corresponding to the classical watershed

partition. The other partitions of the hierarchy can be

obtained suppressing all the edges whose weights are

greater than a threshold value or through local oper-

ations (merge and reﬁne) over the hierarchy, as de-

scribed in (Zanoguera et al., 1999).

The navigation through the hierarchy of partitions

in user real time is possible using a data structure

known as the tree of critical lakes (TCL) (Meyer,

1996). It is derived from an MST of the RAG and

it makes it possible to run through the MST edges or-

dered by their weights.

Other hierarchies can be derived from the MST

of the RAG assigning different weights to its

edges through synchronous ﬂooding, as described in

(Meyer, 2001a). The synchronous ﬂooding can rank

regions according to their contrast and/or size, gener-

ating hierarchies with partitions that are usually more

interesting than the one obtained by uniform ﬂooding.

2.5 Tie-zone Watershed

As the watershed transform can have distinct opti-

mal solutions, the tie-zone watershed (Audigier et al.,

2005) aims to provide a unique and optimal solution

associated to a graph G and a set of seeds M: it assigns

each vertex of G to a CB if in all possible solutions it

belongs to this CB. Otherwise, the vertex is said to

belong to a tie-zone, denoted by T Z-W S(G, M).

3 SWITCHING BACK AND

FORTH BETWEEN THE

WATERSHED APPROACHES

In this section we investigate how to switch between

the watershed from markers and the hierarchical wa-

tershed approaches. More speciﬁcally, given a par-

tition P selected in the hierarchical set of partitions

of an image I, we would like to ﬁnd a set of mark-

ers M such that IFT -W S(G, M) = P, where G can

be a PAG or a RAG, depending on the desired pre-

cision level. Conversely, given a set of markers M

and its corresponding partition P = IFT -W S(G, M),

we would like to ﬁnd a hierarchical set of partitions

that includes P.

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

188

3.1 From Hierarchical to Markers

Approach

This problem is addressed using the concept of mini-

mal seed set (MSS). The MSS problem is the inverse

of the segmentation by watershed problem: given a

partition obtained by watershed, it consists in ﬁnding

a minimal set of seeds that is enough to obtain the

same partition by the watershed (Lotufo and Silva,

2002). The MSS is built by ﬁrst computing the so

called non-redundant receptive regions (NRRR) of

each ROI and then choosing one seed in each NRRR.

Each seed receives the same label of the ROI to which

it belongs. The MSS can be computed either in a RAG

or in a PAG (Audigier and Lotufo, 2007).

Given a partition P selected in the hierarchy, the

MSS in the corresponding RAG can be computed

straightforwardly because the hierarchy is constructed

based on the RAG. Let M denote the resulting set

of markers. If watershed is applied on the RAG

with markers M, partition P can be recovered ex-

actly. Similarly, if we compute the MSS of P in

, the resulting set of markers M

exactly recovers

P, i.e., IFT -W S(G

, M

) = P, as M

guarantees that

T Z-W S(G

, M

) = ∅.

These observations suggest computing markers ei-

ther on the RAG or in the PAG: on the RAG if region

level precision sufﬁces and on the PAG if pixel level

precision is required. However, the markers M

com-

puted on the PAG tend to be located at the borders of

the ROIs as shown in Figure 1. This ﬁgure shows the

NRRRs of each ROI. Recall that M

must include at

least one pixel of each NRRR.

In contrast, the markers M computed on the RAG

tend to be compact and located more at the center

of each ROI, making them more suitable for user

edition. In Figure 2(a) we show the markers com-

puted on the RAG for the same partition of Figure

1(b). However, if markers M computed on the RAG

are considered on the PAG G

, the resulting parti-

tion P

= IFT -W S(G

, M) may differ from the orig-

inal partition P, as shown in Figure 2(b).

Experimentally, we have observed that the differ-

ences between the original partition P and the recov-

ered one P

are located close to the borders. This ev-

idence made us to conjecture that differences are lo-

cated in the tie-zone. In fact, it can be show that P

(the partition selected in the hierarchy) is also an op-

timal solution of IFT -W S(G

, M). This implies that

the differences between P and P

necessarily belongs

to the tie-zone TZ-W S(G

, M). The proof is presented

in the following proposition.

Lemma 1. For any path π

RAG

= hCB

,CB

, . . . ,CB

in the RAG of I there is a path π

PAG

(a) RAG (b) Selected partition P

Figure 1: NRRRs computed in G

are located close to the

border of the ROIs: (a) RAG edges superimposed on the

primitive CBs, where the MST edges are in black. (b) A

partition P, selected on the hierarchy suppressing the edges

with weight greater than 150. (c)-(e) NRRRs of each ROI

of P, computed in G

(a) Marker set M (b) Obtained partition P

Figure 2: Markers computed in the RAG: (a) Markers of the

MSS of P (each ROI has one NRRR, containing all of its

pixels). (b) Partition P

obtained by applying the watershed

on the PAG. The difference between P and P

is marked

with an x.

, . . . , r

i with same cost (according to f

max

)

in G

, where r

is an arbitrary pixel of the regional

minimum of the catchment basin CB

Proof. For each pair (CB

,CB

i+1

) in π

RAG

, consider

, p

), p

∈CB

and p

∈CB

i+1

, as the pair of pixels

that determined the weight of the edge that connects

to CB

i+1

on the RAG of I (see (1)).

The path π

PAG

is constructed by linking r

to r

i+1

INTERACTIVE IMAGE SEGMENTATION WITH INTEGRATED USE OF THE MARKERS AND THE

HIERARCHICAL WATERSHED APPROACHES

189

for 1 ≤ i < n, by connecting r

to p

and r

i+1

to p

by the non-decreasing paths contained in the SPF ob-

tained by the IFT-WS when all regional minima are

used as markers (classical watershed).

Proposition 1. Let P = {P

, P

, . . . , P

} be a par-

tition of the image I obtained from the hierarchi-

cal watershed. Consider a set of markers M =

, M

, . . . , M

}, computed on the RAG of I, where

is the marker associated to P

, that is, for i =

1, . . . , n:

⊆ P

and M

∩ R 6= ∅, ∀R ∈ NRRR(P

) (3)

where NRRR(P

) denotes the set of non-redundant re-

ceptive regions of P

, computed on the RAG of I. Then,

P is an optimal solution of IFT -W S(G

, M).

Proof. Let P

= {P

, P

, . . . , P

} be an arbitrary op-

timal solution of IFT -W S(G

, M). If ∃p such that

= L

(p) 6= L

(p) = λ

, then it sufﬁces to show

that f

max

(π

∗

, p)) = f

max

(π

∗

, p)), where M

and M

are the markers with labels λ

and λ

, re-

spectively.

Without loss of generality, suppose that α = 1 and

β = 2. From the optimality of P

max

(π

∗

, p)) ≤ f

max

(π

∗

, p)). (4)

The MSS is computed in such a way that there is

no tie-zone, which implies that:

max

(π

∗

,CB)) < f

max

(π

∗

,CB)), (5)

i 6= j, ∀CB ∈ P

In particular, denoting by V the CB to which p be-

longs,

max

(π

∗

,V )) < f

max

(π

∗

,V )). (6)

From Lemma 1 it follows that:

max

(π

∗

,V )) = f

max

(π

∗

, r

)) (7)

From (7) and (6), we have that:

max

(π

∗

, r

)) < f

max

(π

∗

, r

)) (8)

Let v

be the ﬁrst pixel of V in π

∗

, p) (see Figure

3). By the choice of v

max

(π

∗

, p)) (9)

= f

max

(π

∗

, v

) ·π

∗

, p))

= max{ f

max

(π

∗

, v

)), f

max

(π

∗

, p))}

= max{ f

max

(π

∗

, v

)), f

max

(π

∗

, r

)),

max

(π

∗

, p))}

= max{ f

max

(π

∗

, v

)), f

max

(π

∗

, r

)), ∇(p)}

= max{ f

max

(π

∗

, r

)), ∇(p)}

(

)

(

)

(

)

(

)

(

)

(

)

(

)

Figure 3: Proof scheme.

As π

∗

, p) is an optimum cost path, it follows that:

max

(π

∗

, p)) (10)

≤ f

max

(π

∗

, r

) ·π

∗

, p))

= max{ f

max

(π

∗

, r

)), f

max

(π

∗

, p))}

= max{ f

max

(π

∗

, r

)), ∇(p)}

Replacing 8 and 9 in 10:

max

(π

∗

, p)) (11)

≤ max{ f

max

(π

∗

, r

)), ∇(p)}

≤ max{ f

max

(π

∗

, r

)), ∇(p)}

= f

max

(π

∗

, p))

Then,

max

(π

∗

, p)) ≤ f

max

(π

∗

, p)) (12)

From 12 and 4, we conclude that

max

(π

∗

, p)) = f

max

(π

∗

, p)). (13)

3.2 From Markers to Hierarchical

Approach

Given a partition P obtained from a set of markers M,

we would like to build an hierarchy that includes P.

In order to do that, two issues need to be considered.

First, as the primitive CBs are considered atomic

in the hierarchy, no partition of the hierarchy con-

tains borders beyond those located at the border of the

primitive CBs. When working with pixel level preci-

sion, if P contains borders that crosses some primitive

CB, then P can not be represented in the hierarchy. If

there are such borders, a possible approach is to set

the same label for all the pixels within each CB, for

example, the most frequent label among them.

Furthermore, it is also necessary that each set of

primitive CBs with same label (that actually make up

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

190

a ROI) is a connected set considering the edges of the

spanning tree of the RAG from which the hierarchy is

constructed. If this is not true, an hierarchy that in-

cludes the desired partition cannot be built. In order

to accomplish this, instead of considering an arbitrary

MST of the RAG, we derive a spanning tree (not nec-

essarily an MST) of the RAG in the following man-

ner:

1. consider an MST for each ROI (set of primitive

CBs with same label), obtaining a spanning forest

of the RAG;

2. complete the spanning forest with edges of mini-

mum weight among the edges of the RAG not yet

used, obtaining a spanning tree of the RAG.

When constructing the TCL, instead of using

all the edges of the spanning tree ordered by their

weights, the edges of the spanning forest obtained at

the ﬁrst step must be used before the edges added at

the second step.

4 INTERACTIVE

SEGMENTATION TOOL

In this section we describe an interactive segmenta-

tion tool that allows switching back and forth between

the two watershed approaches based on the transitions

described in the previous section. Examples illustrat-

ing the use of these transitions in conjunction with

interaction possibilities from both approaches are pre-

sented.

4.1 Interaction Possibilities

1. Construction of hierarchy of partitions using

uniform ﬂooding or synchronous ﬂooding, with

the following criteria:

• depth (ranking regions by their contrast)

• area (ranking regions by their size)

• volume (ranking regions by their contrast and

size)

The user can navigate through the hierarchy using

a slider control that selects a threshold value for

the weight of the edges to be suppressed in the

hierarchy.

As the selection of a threshold value affects the

entire partition, two local operations (merge and

reﬁne) can be used on the hierarchy to affect only

a desired region of the current partition, as illus-

trated in a simpliﬁed hierarchy in Figure 4.

(a) Original image

(b) Finest partition

A B C D E

(c)

A B C D E

(d)

A B C D E

(e)

Figure 4: Obtaining partitions navigating through the TCL:

(d) Region G split in D and E. (e) Regions F and C merged

in H.

Note that the selection of the threshold value and

the local operations are done on the RAG. Once

the hierarchy is constructed, these operations are

executed in user real time.

2. Automatic generation of markers to partitions

selected from the hierarchy, as described in Fig-

ure 3.1. After switching from the hierarchy to the

markers approach, the user can reﬁne the partition

at a pixel level precision. For example, to separate

cells as shown in Figure 5(d).

(a) (b)

Figure 5: Segmenting using hierarchy and markers:

(a) Original image. (b) Partition selected on the hierarchy.

ments at pixel level precision.

3. Edition of markers using a brush/erase tool.

The labeling function for the markers is derived

associating a unique label for each connected

INTERACTIVE IMAGE SEGMENTATION WITH INTEGRATED USE OF THE MARKERS AND THE

HIERARCHICAL WATERSHED APPROACHES

191

component drawn (for this reason, the user does

not need to change the brush color when marking

each ROI). If markers for distinct ROIs need to be

placed adjacently, the user can use different col-

ors in order to make the markers receive different

labels. The brush and the erase tool are available

selecting only one icon, so the user can edit (draw

and erase) markers just using different mouse but-

tons.

4. Merging of adjacent regions with a welding

brush. This is more ﬂexible than the local merge

operation over the hierarchy, since it can weld re-

gions using edges that are not in an MST of the

RAG, as described in Section 3.2. To accomplish

this, a partition with the selected regions welded

is derived (associating the same label to them) and

this partition is utilized to compute markers or

to derive a hierarchy that contains it (depending

on the approach being used). This operation was

used to obtain the partition shown in Figure 5(c),

as it cannot be found in the original hierarchies

(from the uniform and synchronous ﬂoodings).

5. Use of the hierarchy in a selected region. This

enables the user to reﬁne a region obtained from

a previous use of the hierarchical watershed, or

from manually created/edited markers. For in-

stance, to obtain the primitive CBs of the land in

a satellite image like the one shown in Figure 6,

one could ﬁrst design markers by hand in order

to separate land from water, and then select the

ﬁnest partition after applying the hierarchy in the

land region. This is a more straightforward way

to achieve the desired partition, instead of ﬁrst ob-

taining the classical watershed partition for the en-

tire image and them merging all the regions that

are not located at land.

(a) Original image

with markers

(b) Intermediary

step

tion

Figure 6: Using the hierarchy restricted to a region:

(a) Original image. (b) Partition (with markers) separating

land from water. (c) Primitive CBs of the land region.

4.2 Additional Features

The implemented tool also includes additional fea-

tures:

• Segment automatically option, that executes the

algorithm at each edition of the markers (it can be

disabled to improve performance when designing

markers to segment large images, for instance);

• save the markers image for posterior reﬁnements;

• control over the output image (the user can choose

which images will be superimposed: original im-

age, gradient image, catchment basins, markers

and watershed lines).

• support for segmentation of color images using

the weighted gradient, as described in (Flores

et al., 2004). The user can use either the automat-

ically computed weights or arbitrary weights for

each gradient considered (the weighted gradient

consists in a weighted sum of gradients deﬁned

on each band of the image: hue, saturation and

brightness). The color information can be a key

factor in reducing the interaction effort to obtain a

desired partition, as can be observed in Figure 7.

(a) (b) (c) (d)

Figure 7: Color information reducing the interaction effort

(markers in red, watershed lines in black): (a)-(b) Simple

markers are enough to divide land from water using the

weighted gradient. (c)-(d) Complex markers are needed

when using the morphological gradient of the image ob-

tained without color information.

4.3 A Coarse to Fine Approach

Since markers obtained by computing the MSS on G

tend to be located at the borders of the ROIs, they

are not interesting for user edition. Thus, we choose

markers from the MSS computed on the RAG, inde-

pendently of the precision level of the graph being

utilized in the markers approach. With this choice,

the partition obtained by switching from the hierar-

chy to markers over a PAG may differ slightly from

the partition before the switching. Similarly, as noted

in Section 3.2, there may be differences in the inverse

mapping.

Since ﬁne reﬁnements done at a pixel level preci-

sion may be undone by a transition to the hierarchical

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

192

approach or to the region level precision, segmenta-

tion process should follow a coarse to ﬁne approach:

ﬁrst the user can work with both approaches to obtain

a partition as close as possible to the desired partition,

using only the RAG (which implies efﬁcient process-

ing time); then, using only markers (i.e., editing mark-

ers) over the PAG, he/she can reﬁne the partition at a

pixel level precision.

5 CONCLUSIONS

We investigated how to perform transitions between

the hierarchical and the watershed from markers ap-

proaches. In particular, we discussed the effects ob-

served when these transitions involve changes in the

precision level of the partitions (pixels or regions).

These transitions have been implemented in conjunc-

tion with several interaction possibilities from both

watershed approaches as an interactive segmentation

tool. The implemented tool allows one to take advan-

tage of the best features of each approach and it is ex-

pected that the interaction effort necessary to produce

a desired result may be reduced.

An interesting characteristic of the proposed ap-

proach is that it allows producing partitions with pre-

cisions at pixel or region levels. As a consequence,

the tool may be used for different segmentation pur-

poses.

We plan some use case studies, in order to eval-

uate and improve the usability of the developed tool.

This study should take into consideration not only the

available functionalities but also aspects related to the

interaction process. For example, in applications in

which a precise segmentation is important, the inter-

action effort necessary to draw the markers can still

be very intense. It would be interesting if the tool

could provide means to easily place markers, on both

sides of the borders of interest. As an another exam-

ple, support for color image segmentation is currently

rather limited. These aspects, together with others to

be found in the use case studies, will guide our future

investigations.

ACKNOWLEDGEMENTS

This work is supported by CNPq, Brazil.

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