**Technical Report **

** Institute of Biomedical Engineering, National ** **Taiwan University **

**ACCOMP— Augmented Cell Competition Algorithm ** **for Delineating Boundaries of Objects of Interested **

**for Sonography **

**IBME-TR-20061101**

Chung-Ming Chen^{1}, Jie-Zhi Cheng^{1}, Yi-Hong Chou^{2}

1 Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan

2 Department of Radiology, Taipei Veterans General Hospital and National Yang Ming University, Taipei, Taiwan

November 1, 2006

**ACCOMP─ Augmented Cell Competition Algorithm for **
**Delineating Boundaries of Objects of Interested in Sonography **

Chung-Ming Chen^{1}, Jie-Zhi Cheng^{1}, Yi-Hong Chou^{2}

1 Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan

2 Department of Radiology, Taipei Veterans General Hospital and National Yang Ming University, Taipei, Taiwan

{chung, jzcheng}@ntu.edu.tw

**Abstract. A new novel boundary delineation algorithm for sonography is **
proposed in this paper. Standing on the cell structure, the proposing
algorithm firstly parses the Region Of Interest (ROI) into several
Prominent Components (PCs) which can be parts of desired target, tissue
structure, artifact, and so on. Following that, a graph search scheme is
applied upon the PCs structure to find out arbitrary meaningful boundaries
by mimicking the visual perception experience. It can be shown that this
algorithm is capable of capturing highly winding contours and
withstanding the irregular interior echo pattern of the target. This
algorithm has been validated on 294 breast sonograms which comprise of
160 carcinomas and 134 fibroadenomas. Three assessments have been
exercised and the results suggest that the derived boundaries from the
proposed algorithm are comparable to the manual delineations and the
proposed algorithm is robust to the variation of ROI for each image.

**Keywords: Cell competition, boundary delineation, edge grouping, graph **
models, watershed.

**1 Introduction **

Morphological features about the object of interest can deliver valuable information in clinical US examination. They have been widely applied to many clinical applications to understand heart dynamics [1] [2], derive the volume of kidney and prostate [3] [4], manifest the benignancy or malignancy of breast lesion [5] [6], locate the biopsy needle [7], evaluate the ovarian follicle ovulation [8] [9], assess the

coronary artery disease [10] [11], render the 3D panoramic view, etc. In order to substitute the tedious manual delineation and provide more objectively quantitative and qualitative analysis, numerous image segmentation techniques were contrived to obtain the morphological information about the object of interested, says boundary, for US images either automatically or semi-automatically. In the literature, the segmentation methods for US images can be roughly categorized as parametric deformable models [12] [13], level set methods [14], the approaches modeling on shape [15] [16], texture [17] or both [18-20], edge-linking methods [21], region-based methods [9] [22] [23], classification [8], graph-based approaches [24], and thresholding [25]. By and large, an effective image segmentation method for sonogram must be capable of dealing with the complex inherences of sonography, i.e., speckle noise, artifact, shadowing effect and so on. The model-based approach is one of the most effective methods via taking training scheme against the complex inherences. This kind of approach often characterizes the features of object of interested as prior information from training data and seeks the result on test data under guidance of prior information especially when the image evidence can’t provide deterministic solution. Although promising result the model-based approach often achieves, it might be inapplicable when the features of object of interested can not be easily characterized. For instance, there is almost no regular pattern about the shape and texture of breast lesion in ultrasound. For the other methods in the literature, the performance may be easily limited to image quality or specific application domain if the prior knowledge about the object of interested is not incorporated. This is because most methods are implemented in pixel-by-pixel fashion, which may be easily disturbed by speckle noises. As a result, a structural operating unit which can tolerate noise more is demanded for better segmentation result if prior knowledge is not taken or can not be effectively extracted.

Distinct from the pixel-based methods in the literature, a structural operating unit derived from watershed transformation, cell, is served as the replacement of pixel for demarcating the target boundary in this context. The cell is the catchment basin inundated by two pass watershed transformation [23] and appears as a homogenous area in grey level intensity. The Region of Interested (ROI) hence is parsed into cell structure by cells. The driving advantage of establishing the cell structure may consist in that not only the perceivable edge evidences the cell structure can efficiently

uphold but also sufficiently preserve the subtle-but-significant ones. In addition, the cell structure is able to exploit the mechanism of quantum jump for boundary searching by taking the septa edge segment between two adjacent cells as basic searching unit. The mechanism of quantum jump can possibly alleviate the chance of being trapped into undesired situations, from which the conventional deformable models usually suffer.

Grounding on the cell structure, this paper proposes a novel algorithm, denoted as Augmented Cell Competition (ACCOMP) algorithm, for demarcating boundary of the object of interested. The ACCOMP algorithm combines the watershed-related technique with the encoding of a subset of Gestalt principles and is realized in two main steps: 1) parsing the ROI into Prominent Components (PCs) and 2) edge grouping based on the PC structure subjecting to a subset of Gestalt principles. The fist step tries to reduce the over-segmentation and preserve significant edge fragments simultaneously and is practiced by the cell competition algorithm [23]. The second step manages to group the preserved edge fragments by mimicking visual perception experience and is realized by a graph search scheme. To make the description conveniently, the second step of the ACCOMP algorithm is denoted as cell-based graph-searching (CBGS) algorithm throughout this paper. In this study, the ACCOMP algorithm is validated on capturing the lesion boundaries in breast sonograms which is quite challenging for not only the complex inherences of ultrasound images but the complicated morphological and textural expression of breast lesions. It will be demonstrated that the ACCOMP algorithm is capable of dealing with the targets of irregular shapes and complex echo patterns and the results are comparable to manual delineation. The most part of this context will be focused on the CBGS algorithm. The details of the cell competition algorithm may be found in [23].

**2 Material and Methods **

In the first step, the PCs and the concomitant PC structure which contains the geometrical information about the PCs are sought by the cell competition algorithm [23]. The sought PCs exhibit as large and relatively homogeneous regions circumscribed with discernible boundaries and could be sub-structures of tissue or the target, artifacts, etc. The second step is purposed to group the septa edge fragments

between two adjacent PCs, called cell edges, into meaningful closed contours and
produce five candidates for user selection. To obtain meaningful contours, a subset of
Gestalt principles is adopted to imitate the empirically visual perception. The Gestalt
laws incorporated in this context are those commonly utilized in the computer vision
*literature: proximity, continuity, closure and similarity. Proximity requires that the *
closer pair of two cell edges should have higher priority to be grouped together.

*Continuity calls for that features, such as the bilateral vicinity along the contour and *
*the contour profile, should be globally as smooth as possible. Closure demands that *
*the contour has to be a cycle. Similarity needs that the two consecutive cell edges on *
the contour path hold similar pattern in bilateral vicinity.

As demonstrated in [26] that the Gestalt properties can be formulated more
conveniently in terms of pre-extracted edge fragments than pixels and realized in the
framework of graph, the PC structure in this context is converted into an undirected
graph, denoted as c-graph, by taking cell edges as graph nodes and the connections
among cell edges as graph links. The nature of c-graph can intrinsically justify the law
*of proximity for that the closer two cell edges on one path the more proximal these *
two will be. To obtain the desired contours, a Constrained Depth First Search (CDFS)
scheme is applied to find out non-self-crossing cycles by exploring the bilateral
vicinity consistence along the contours. The bilateral consistence emphasizes that two
adjacent cell edges with similar relieves, that is the same slope inclination, are more
likely grouped together. The practicing of CDFS can not only assure the law of
*closure by pursuing of non-self-crossing cycles but satisfy the similarity law locally *
*for exploring the bilateral consistence along the contour path. The continuity law is *
encoded within some of the five selecting criteria for globally characterizing the
continuity of bilateral vicinity intensity and contour profile smoothness. Five selecting
criteria are used to select five best candidates among the pool of found cycles
focusing on the contour salience, bilateral smoothness, boundary profile smoothness.

As it can be observed that the bilateral vicinities around the boundary of the object of interested usually emerge as Dark Inside and Bright Outside (DIBO) in several important ultrasound examinations, for examples, the heart ventricle, kidney, breast lesion, ovarian follicle and so on, an extra constraint for edge grouping is applied in the CDFS scheme to find the contours bearing the DIBO pattern. It can be easily modified when the object of interested holds the contrary appearance.

To generate the cell structure for the first step, the edge-strength map, which is
computed by Sobel operator, of ROI is tessellated by two-pass watershed
transformation. Right after the first pass inundates the gradient map under the
favorable immersion scheme [27], the second pass is enforced via toppling down the
inferior watersheds whose edge strengths are less than *T*_{2} =μ* _{e}*−βσ

*, where μ*

_{e}*and σ*

_{e}*e*are the mean and standard deviation of the edge strengths of the watersheds identified in the first pass and β is a positive constant. The larger the β is, the more inferior watersheds would remain. On the other hand, the smaller the β is, the more likely the desired object boundary may be missing because some parts of the object boundary may be weak edges. It has been shown in [23] that the cell competition algorithm is robust to the variation of β for 1≤β ≤1.5 and most cases in this context can be tested successfully with β =1.2. The derived catchment basins in the second pass, cells, organize the cell structure as the initial state of competition process. The cell competition algorithm activates the cells to compete each other for consorting the best allies to form PCs with two types of cell competition mechanism, where the first type enable the cell to chose its preferable ally and the second type allow the cell to be an independent ally from the original ally. The cost function controlling the evolving of the competition process is to characterize the interior homogeneity and boundary saliency of the all allies. The optimization of the competition process is sought by minimizing the cost function under the gradient descending scheme. As the competition process terminated, the consorted allies at the final state are taken as PCs which might be the substructures of a tissue, parts of object interested and artifacts.

**Fig. 1. (a) One example of simulated PCs structure and cell edges map. (b) The corresponding c-graph. **

**Fig. 2. The cell edge defined by **
*the two vertices, V**s** and V**e*. and its
*bilateral vicinity, B**L **and B**R***. **

**Fig. 3. (a) Demonstration of the cell edges of cliff type with **
discernible altitude difference in bilateral vicinities. (b)
**Demonstration of the cell edges of peak type. **

In the second step, the job of edge grouping is enforced by the CBGS algorithm
*which encodes a subset of the Gestalt principles: proximity, similarity, closure and *
*continuity. To facilitate the practice of Gestalt principles, the map of cell edges which *
define two neighboring PCs is converted into c-graph by taking the cell edges as
graph nodes and the connection among cell edges as graph links. Based on graph
*structure the proximity law can be naturally assured by graph-based algorithms, i.e., *
graph-cut, depth first search, etc. As an example, the converting can be consulted in
Fig. 1 where ‘*ce** _{i}*’ represents one cell edge and Fig. 1(a) suggests one PC structure
with 7 PCs and 13 cell edges, whereas Fig. 1(b) shows the corresponding c-graph of

*(a). The points intersected by cell edges in Fig. 1(a) are denoted as vertices.*

In addition to maintain the connectivity among the cell edges in the c-graph, the graph nodes are associated with the intensity profiles of the bilateral vicinities around the cell edges, the strengths of the cell edges and the two end vertices of the cell edges.

The bilateral vicinities are obtained by dilating the cell edges with a 7×7
structuring element as depicted in Fig. 2 where it can be noted that **B***_{L}* is taken as
left vicinity and

**B as right vicinity in relative to the vertex**

_{R}

**V of this cell edge.***The cell edge in Fig. 2 is also can be represented as the equivalent vector*

_{s}*V*

_{s}*V*

*by the two end vertices, from*

_{e}

**V to**

_{s}

**V , for suggesting that left and right vicinities are**

_{e}**B and ****L****B respectively or the **_{R}**V**_{e}**V***_{s}*, from

**V to**

_{e}

**V , for indicating the left as**

_{s}

**B and**

**R**

**B***as the right. Assuming that a cell edge*

_{L}*ce comprises of a set of*

_{i}*n*

*edge points, {*

_{i}*w*

^{i}*}, 1≤*

_{j}*j*≤

*n*

*, and the gradient response of edge point is ℘*

_{i}

^{i}*, the strength of the cell edge*

_{j}*ce ,*

*ℑ , can be defined as:*

_{i}

_{i}## ∑

=℘

=

ℑ ^{n}^{i}

*j*
*i*

*j*
*i*

*i* *n* 1

1 . (1)

The information of bilateral vicinities is necessary for identifying whether two
consecutive cell edges are similar and the strength is useful to evaluate the salience of
found closed boundary. For the association of two end vertices, it is essential to detect
whether a cycle is found and can assist the exploration of bilateral consistence. To
meet these requirements, the establishment of c-graph is realized by identifying all
vertices first. The identification process of all vertices is to find out all the edge points
having more than two neighboring edge points in eight-connectivity among all edge
points on the PC structure and push each vertex into an auxiliary queue. Following
that, the defining of each cell edge, *ce , is iterated by tracing on the undefined cell ** _{i}*
edges which is started from a vertex,

**V**

_{s}*, which is popped up from the auxiliary queue, and is ended up with another vertex*

^{i}

**V**

_{e}*. The defining process of all cell edges will be iterated until the auxiliary queue is empty. The goal of tracing on the cell edge*

^{i}*ce is to acquire the bilateral vicinities determined by the equivalent vector*

*i*

**V**

_{s}

^{i}

**V**

_{e}*and calculate the strength of the cell edge*

^{i}*ce . The two cell edges sharing the same*

*vertex are connected in the c-graph. The pseudo-codes of building the c-graph are summarized in Algorithm 1 where the input CEPoints is the set of the cell edge points with the number of M on the PC structure.*

_{i}Exploring the characteristics of bilateral vicinities around the contour of the object of interested had been shown effective for boundary delineation in sonography [15] [19]. However the extraction of the bilateral vicinity features usually require a learning scheme and hence possibly suffers when the features of object of interested are not easily characterized. Apart from directly modeling the bilateral vicinity appearance, this context exploits the bilateral consistence around the boundary of interested by grouping the similar cell edges. Two adjacent cell edges are similar when they hold consistence in slope inclination, which indicates a cell edge inclining toward left or right or appearing as a peak. Generally speaking, the cell edges can be classified into two types of relief, cliff and peak, which are illustrated respectively in Fig. 3(a) and (b). The cliff type features significant altitude difference in bilateral vicinities while the peak type has a substantial difference between the peak and the

vicinities. We note that the slope inclination of a cliff cell edge toward left or right is determined by the equivalent vector while the cell edges of peak show no slope inclination. As a result, the cell edges are classified by practicing two sample t-test upon the bilateral vicinities. If the null hypothesis of the t-test is rejected, the cell edge will be taken as cliff type; an acceptance of null hypothesis implies the cell edge is of peak.

**Algorithm 1. The establishment of c-graph is summarized. The CellEdge possesses two attributes, **
**EndVertex and Profiles, for recording the demanded information and CellEdgeList collects all **
**graph nodes defined. The function NeighborCount returns the number of edge points among the eight **
**neighboring pixels. DetectNeighborCEPoints finds out those edge points of one vertex in eight **
**neighbors while NumberNeighborCEPoints records the number of those edge points. The function **
**FindAnotherCEPointsNotVisisted is to find out another edge point which has not been visited yet **
**among the eight neighboring pixels. The Connect function builds a link between the two designated **
**CellEdge graph nodes. **

C-GRAPH-BUILD(CEPoints)
**{ Queue Vertices; **

** Struct CellEdge{ **

EndVertex[2];

** Profiles;} **

** for i = 1 to M **

** if (NeighborCount(CEPoints[i]) > 2) **
Vertices.Push(CEPoints[i]);

** while(Size(Vertices) != EMPTY){ **

V := Vertices.PopUp();

TraceStart := DetectNeighborCEPoints(V);

N := NumberNeighborCEPoints(V);

** for (j = 1 to N) **

** { P := TraceStart[j]; **

Mark P as Visited;

Define CellEdge[j];

CellEdge[j].EndVertex[1] := P;

CellEdge[j].Profiles.Add(P);

** do **

** { P := FindAnotherCEPointsNotVisited(P); **

Mark P as Visited;

** CellEdge[j].Profiles.Add(P);} **

** while (P is not a vertex); **

CellEdge[j].EndVertex[2] := P;

** for (k = 1 to j-1) **

** Connect(CellEdge[k],CellEdge[j]); **

CellEdgeList.Add(CellEdge[j]);

** }} **

** return CellEdgeList;} **

To group the consecutive similar cell edges as closed contours from the c-graph structure, it is intuitively to adopt Depth First Search (DFS) scheme. Since a closed contour is isomorphic to a cycle in the c-graph, DFS scheme is more convenient to exploring cycles than Breath First Search for that DFS can remember the whole path

traversed in the working stack. In this context, it is attempted to explore all possible
cycles holding the DIBO pattern in the c-graph. For that reason, the DFS scheme is
constrained with some criteria, which are for the assurance of bilateral consistence
and DIBO pattern, and is denoted as CDFS. The criterion for securing consistence in
bilateral vicinities is to rule out the pairs which consist of two cliff cell edges with
different slope inclination but the pairs comprising of one cliff cell edge and one peak
cell edge will be taken as admissible ones appearing on desired contour. The
combination of a cliff with a peak doesn’t show strong inconsistence in slope
inclination and may not be ruled out in the search scheme. Because the slope
inclination of a cliff cell edge is determined by the equivalent vector, the inclination
consistence of two cell edges can be checked by cascading the common vertex shared
by the two cell edges into two sequential equivalent vectors. Fig. 4(a) demonstrates
the pairs of slope inclination consistence and inconsistence with four cliffs and one
peak which are marked with bold lines and the corresponding equivalent vectors are
shown in dotted grey arrow. The single arrows indicate the slope inclination of cliffs
by directing the dark-lateral vicinity while double arrow suggests the corresponding
cell edge is of peak type. The pair of sequential vectors, **V**_{1}**V***_{2}* cascading with

**V**_{2}

**V***, shows inclination inconsistence and is supposed to be ruled out in the CDFS scheme while the inclinations of the pairs of*

_{3}

**V**

_{1}

**V***with*

_{2}

**V**_{2}

**V***and*

_{4}

**V**

_{1}

**V***with*

_{2}

**V**_{2}

**V***are consistent. The pair of*

_{6}

**V**

_{1}

**V***with*

_{2}

**V**_{2}

**V***shows an example of the combination of one cliff with one peak. Concerning to find out the DIBO cycles, the awareness of which lateral vicinity should be inside/outside of the contour must be explicitly determined and applied within the search scheme. It can be observed that if one traverse on a DIBO contour clockwise, the dark lateral is always on the right hand side; if one traverse in the orientation of counterclockwise, the dark lateral is one the left hand side. With this observation, the awareness of inside/outside can be decided by traversing orientation, clockwise and counterclockwise. Assuming that a found cycle π is composed of a set of cell edges, {*

_{5}*ce ,*

*} 1≤*

_{i}*i*≤

*l*, with cascading order vertices set, {

*V*

*}, 1≤*

_{j}*j*≤

*l*, as illustrated in Fig. 4(b) where

*l*is set to 6 and the equivalent vectors are shown as dotted black arrows, each cell edge

*ce can be*

*represented as*

_{i}

**V**

_{i}

**V**

_{i}_{+}

*except the*

_{1}*ce which can be represented as*

_{l}

**V**

_{l}

**V***. The*

_{1}traversing orientation can be decided by accumulating the all turning angles, τ* _{k}*,

*l*

*k* ≤

1≤ , of two sequential equivalent vectors, which are the angles of the directional rotation between the two sequential vectors. The turning angle between the vectors

**1****i****i****V**

**V**_{+} and **V**_{i}_{+}_{1}**V**_{i}_{+}*_{2}* can be estimated as:

τ* _{i}* =sin

^{−}

^{1}(

*V*

_{i}*V*

_{i}_{+}

_{1}⋅

*V*

_{i}_{+}

_{1}

*V*

_{i}_{+}

_{2}/||

*V*

_{i}*V*

_{i}_{+}

_{1}||||

*V*

_{i}_{+}

_{1}

*V*

_{i}_{+}

_{2}||), (2)

where *V*_{i}*V*_{i}_{+}_{1}⋅*V*_{i}_{+}_{1}*V*_{i}_{+}_{2} is the inner product and the ||*V*_{i}*V*_{i}_{+}_{1}|| and ||*V*_{i}_{+}_{1}*V*_{i}_{+}_{2}|| are the
norms of the vectors **V**_{i}**V**_{i}_{+}*_{1}* and

**V**

_{i}_{+}

_{1}

**V**

_{i}_{+}

*respectively. The turning angles are presented as dotted grey arrows in Fig. 4(b). A positive total turning angle indicates that the cycle is traversed counterclockwise while a negative one represents a clockwise cycle. Consequently, if the traversing orientation is clockwise, the found cycle holds the DIBO pattern as the dark lateral vicinity is on the right hand side of the initial cell edge. On the contrary, a counterclockwise cycle appears as DIBO one should have the dark lateral vicinity on the left hand side of the initial cell edge. Those cycles not bearing the DIBO pattern are then discarded in the CDFS. The procedure of CDFS is summarized in Algorithm 2. Noticeably, the self-crossing cycles can be prevented by marking vertices in the stack from visited twice.*

_{2}The found DIBO cycles may consist of desired ones and numerous meaningless
cycles. As result of that, five criteria are devised to select the most admissible
delineations as possible. Assuming that a found cycle π comprises of the set of cell
edges {*ce , ** _{i}*} 1≤

*i*≤

*l*, with cascading order in CDFS, the five criteria are formulated as five cost functions along the boundaries isomorphic to found cycles and are listed and expressed as follows:

C1: Overall absolute difference of bilateral mean intensities:

## ∑

=−

= ^{l}

*i*

*i*
*R*
*i*

*l* *L*

*C*

1

| 1 |

1 μ μ ; (3)

*C2: Continuity of mean gradient: *

1

1 1

1

2 1( | | | |)

*l*

*i* *i* *l*

*i*

*C* *l*

−

= +

=

## ∑

ℑ − ℑ + ℑ − ℑ^{; }

^{(4) }

C3: Overall edge strength:

## ∑

=ℑ

= ^{l}

*i*

*l* *i*

*C*

1

3 1 ; (5)

*C4: Continuity of mean intensities: *

1

1 1 1 1

1

4 1[ (| | | |) | | | |]

*l*

*i* *i* *i* *i* *l* *l*

*L* *L* *R* *R* *L* *L* *R* *R*

*i*

*C* *l* ^{−} μ μ ^{+} μ μ ^{+} μ μ μ μ

=

=

## ∑

− + − + − + −^{; (6) }

C5: Sum of the continuity of mean intensities and the negative overall edge strength:

4 3

5 *C* *C*

*C* =α − . (7)

The cost functions C2, C4 and C5 are minimized, whereas C1 and C3 are maximized.

The μ_{L}* ^{i}* and μ

_{R}*are the intensity means of left and right vicinities of*

^{i}*ce and*

*α is the weighting of C3 against C4 in C5 and is set to 1 in this context. The five criteria are defined according to the empirical visual awareness and characterize globally the*

_{i}*contour salience and continuity in boundary profile and bilateral vicinities. The five*contours satisfying the five criteria best are then proposed to user for choosing.

(a) (b)

**Fig. 4. (a) Demonstration of consistence and inconsistence in slope inclination. (b) Illustration the **
relation between the equivalent vectors with turning angles.

**Algorithm 2. The pseudo-codes of CDFS. The InitialCE is the initial cell edge. The function Cliff **
**check the whether a cell edge is cliff and Peak return the peak cell edge as true. SlopeConsistent will **
return true if the two cell edge do not violate slope consistence.

**CDFS (InitialCE){ **

vertex Start, Terminal;

CellEdge CE, NCE;

Start := InitialCE.EndVertex[1];

Terminal := InitialCE.EndVertex[2];

** for (all neighboring cell edges, NCE, at Terminal) **
** { if (Cliff(NCE) & SlopeConsistent(NCE, InitialCE)) **

CDFSRecursive(NCE, Terminal, Start);

** else If (Peak(NCE)) **

CDFSRecursive(NCE, Terminal, Start);

** }} **

**CDFSRecursive(CE, Terminal, Start){ **

vertex nextTerminal;

CellEdge NCE;

nextTerminal := BindVector(CE, Terminal);

** if (nextTerminal == Start){ **

found Cycle;

** if (Cycle holds DIBO pattern) **
record Cycle;

** }else{ **

** for(all neighboring cell edges, NCE, at Terminal){ **

** if (Cliff(NCE) & SlopeConsistent(NCE, CE)) **
CDFSRecursive(NCE, nextTerminal, Start);

** else If (Peak(NCE)) **

** CDFSRecursive(NCE, nextTerminal, Start);} **

** }} **

BindVector(CE, Terminal)

**{ if(CE.EndVertex[1] == Terminal **
** return CE.EndVertex[2]; **

** else return CE.EndVertex[1]);} **

To attain admissible performance, a correct initial graph node (cell edge) is critical for the CDFS; more specifically the initial cell edge is supposed to be part of desired boundary of target. Heuristic guessing is one of the approaches to obtain the initial cell edge. In general, the more salient the cell edge is, the more likely the cell edge is the part of desired boundary. To guide the heuristic guessing, the region competition algorithm [28] which is participated only by two regions, interested and outer regions, is adopted to produce a rough outline of target as the reference of guessing. Although this rough outline is usually far from useful, it still can possibly capture some prominent segments of truly boundary and is incorporated in the heuristic guessing to select the initial cell edge which is not only obviously salient but also highly correlated with the rough outline.

**3 Results and Discussion **

The ACCOMP algorithm is tested upon 294 breast sonograms, including 160 malignant and 134 benign cases, for delineating lesion boundaries. There are considerable difficulties confronted in demarcating the lesion contour of breast

sonograms. For instance, the complex nature of sonograms including speckle noises, artifacts, etc, often disturbs the functionality of image process techniques. Also in some cases, the lesion boundary may be blurred by the abutting lipid tissue and can not be defined precisely. For malignant tumors, highly-winding shapes are usually developed and the interiors echo pattern commonly appears irregular. By and large, the complicated breast anatomy and lesion morphological and textural expression can exacerbate the difficulties of image segmentation.

To corroborate the performance of the proposed algorithm, four sets of boundaries derived from the ACCOMP algorithm with different ROIs are compared to five manual delineations by five graduate students supervised and approved of five physicians. Three assessments proposed in [12] are adopted to evaluate the performance of the ACCOMP algorithm. The first assessment is to check if the computer-to-observer distance is less than the maximum interobserver distance, both of which are calculated relative to the same manually delineated boundary. Table 1 summarizes the first assessment for the first set of computer-generated boundaries with respect the five set of manual delineation. In the Table 1, CO stands for the mean computer-to-observer distance for all 294 images. IO represents the mean maximum interobserver distance. The fourth column headed by “CO-IO” denotes the mean of differences between the computer-to-observer distances and the corresponding maximum interobserver distances. The 95% confidence interval of all values of

“CO-IO” is listed in fifth column. Note that the upper bound of the 95% intervals is less 0 for all observers in Table 1, which suggests that the mean of the first set of computer-to-observer distances attained by ACCOMP algorithm is smaller than the mean maximum interobserver distance for each observer at 5% significant level.

**Table 1. The mean computer-to-observer distances versus mean maximum interobserver distances for **
the first set of computer-generated boundaries achieved by the proposed ACCOMP algorithm. CO =
mean computer-to-observer distance, IO = mean maximum interobserver distance, and P = percentages
of cases within the interobserver range.

Observer CO IO CO-IO 95% CI P(%)

1 2.85 6.00 -3.16 (-3.67, -2.65) 92.86

2 3.79 5.80 -2.01 (-2.54, -1.49) 80.61

3 4.72 6.06 -1.35 (-1.81, -0.88) 76.53

4 4.96 6.30 -1.34 (-1.68, -0.99) 74.15

5 3.23 5.91 -2.68 (-3.26, -2.10) 83.67

The second assessment tests if there is a significant difference among the four sets of

computer-generated boundaries with respect to the averaged manual delineations.

Friedman test for related samples is used to test if there is a significant difference
among the four distances between the four set of computer-generated boundaries
*against the averaged manual delineations. The p value of the Friedman test is 0.753 *
which implies that the null hypothesis suggesting that the four sets of distances
between the four sets of computer-generated boundaries against the averaged manual
delineations are accepted. The third assessment is to check if the areas enclosed by
each set of computer-generated boundaries are closely related with those enclosed by
the corresponding averaged manual delineations. This assessment is evaluated by
computing the Pearson’s correlation of each set of areas enclosed by each set of
computer-generated boundaries and the set of areas enclosed by the set of averaged
manual delineations. The Pearson’s correlations for four sets of computer-generated
boundaries are 0.992, 0.988, 0.987 and 0.991. The high Pearson’s correlations suggest
that the lesions sizes derived by the ACCOMP algorithm are highly correlated with
the lesions defined by the averaged manual delineations.

To make the process of ACCOMP more comprehensible, Fig. 5 demonstrates every significant step in the ACCOMP algorithm for a malignant lesion. Fig. 5(a) and (b) reveal the first and second pass watershed transform respectively while Fig. 5(c) exhibits the PCs consorted by cell competition process and the map of cell edges. The rough outline derived from specialized region competition algorithm is depicted in (d) as the initial cell edge derived from heuristic guess is illustrated in Fig. 5(e) and enhanced by the white dotted circle. The origin image can also be observed in Fig.

5(e). The following Fig. 5(f), (g)-(j) demonstrate the best matched contours with respect to the five criteria, C1~C5.

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

**Fig. 5. Every significant step of ACCOMP **
algorithm. The MDFS produces 384 DIBO
contours in this case.

**Fig. 6. Four manual outlines. **

It can be observed that in Fig. 5 the proposed algorithm can delineate highly- winding boundary even with irregular echo pattern in interior. Also the five criteria sometimes introduce the same contour as illustrated in Fig. 5(f) and Fig. 5(h). The results in Fig. 5 are compared to four manual delineations. The significant inter-observer variation can be perceived in Fig 6. A low contrast malignant case with PC structure and the five suggested contours is demonstrated in Fig. 7 where (a) shows the PC structure, (b)~(f) exhibit the five contours, and the origin image is given in (g). Another typical benign case with boundary blurred by the abutting tissue is demonstrated in Fig. 8 where (a) shows the PC structure, (b)~(f) exhibit the five contours, and the origin image is given in (g). Fig. 9 gives a more difficult malignant case with speculated boundary and irregular echo pattern.

(a) (b) (c)

(d) (e) (f)

(g)

**Fig. 7. Low contrast malignant case. **

(a) (b) (c)

(d) (e) (f)

(g)

**Fig. 8. One benign case with boundary blurred by the abutting tissue. **

(a) (b) (c)

(d) (e) (f)

(f)

**Fig. 9. The malignant case with speculated boundary and irregular echo pattern. **

**4 Conclusions **

Grounding on the cell structure, the ACCOMP algorithm proposes the five most likely target boundaries to user for selection. The ACCOMP algorithm overcomes the drawbacks of traditional parametric deformable models and level set methods that can not effectively circumscribe highly winding boundary and those with irregular interior echo pattern. Promising results have been obtained on hundreds of breast sonograms.

The derived boundaries from the ACCOMP algorithm can be utilized to manifest the benignancy and malignancy by simplifying the human intervention in the research of breast computer aided diagnosis (CAD). The ACCOMP algorithm is also able to demarcate the targets with BIDO boundaries by slightly modifying the eliminate criterion for found cycles.

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