Quantitative Study on a Multiscale Approach for OCT Retinal Layer

Segmentation

A. Gonz

alez, C. Ortigueira, M. Ortega and M. G. Penedo

Department of Computer Science, University of A Coru

na, A Coru

na 15071, Spain

Keywords:

OCT Retinal Images, Layer, Segmentation, Graph, Multiscale, Pyramidal.

Abstract:

OCT technique for retinal imaging is establishing itself as a relevant modality among ophthalmologists due

to its capacity to show more information than classical modalities. Nowadays, most image processing-based

applications are emerging to extract that information automatically. As previous step of any automatic method

to extract features from these images, the segmentation of the retinal layers has to be done. Graph-based me-

thods provide good results for this problem, although their efﬁciency is an important limitation. In this work,

a multiscale or pyramidal-based approach is studied in order to solve this problem. Different conﬁgurations

are proposed to determine the optimal method. It is remarkable that this approach means an improvement not

only in computation time, but also in segmentation results.

1 INTRODUCTION

Optical Coherence Tomography (OCT) images from

the retina are used by experts to diagnose diseases,

since their capture consists in a contact-less, non-

invasive method that gives a cross sectional image

of the retina in a real time fashion(Puzyeyeva et al.,

2011). OCT provides information of the morphology

in the retina in an effective way and it is useful to ex-

plain disease pathogenesis and heralding disease pro-

gression. In the recent years OCT has progressed, be-

ing the Spectral-domain (SD) OCT the current tech-

nique that ophthalmology experts use in their clinical

practice because of its extremely high sensitivity and

image-acquisition speed.

Several diseases can be diagnosed analyzing the

OCT retinal images, some of them associated to hu-

man eye, such as glaucoma(Bowd et al., 2000), ma-

cular degeneration (Keane et al., 2012) and diabetic

retinopathy(S

anchez-Tocino et al., 2002); but also di-

seases like multiple sclerosis(Albrecht et al., 2012),

whose presence is strongly correlated with high-speed

retinal thinning. In fact, several pathologies affect to

the retinal layer morphology, so its appropriate seg-

mentation is essential as a previous step in any diag-

nosing process.

The problem of the retinal layers segmentation has

been studied using different approaches. One of the

most effectives methods is that proposed in (Haeker

et al., 2007), where the segmentation task is trans-

formed into that of ﬁnding the minimum-closed-set

in a geometric graph. Even though dynamic pro-

gramming is proposed in (Chiu et al., 2010), the main

problem in these approaches is the time required for

graph computation. The fast graph-based method pre-

sented in (Garvin et al., 2009) introduces the idea of a

multiscale algorithm, showing that the idea of a pyra-

midal approach, used in several ﬁelds, seems effective

in this kind of problems.

At the present time, several graph-based ap-

proaches to this task can only work off-line, making

them not useful for the ophthalmologists in their

everyday clinical practice. For the faster and more

effective techniques, there is not any quantitative

study of the improvements in performance than can

be achieved in this problem. Therefore, establishing

where the efﬁciency can be improved in this task is

essential and this is what this work aims for, also

showing that it is useful not only to reduce the pro-

cessing time, but also to avoid segmentation mistakes.

The aim of this paper is, therefore, presenting an

multiscale approach for the layer segmentation algo-

rithm based on the min-graph-cut. For that purpose, a

pyramidal structure is built based on the original OCT

image, and after studying the optimal parameters to

design it, a study of time and memory efﬁciency is

presented. Different ways to tackle this approach are

evaluated too. The layers that have been included in

this work are the top boundaries of the Internal Li-

miting Membrane (ILM) and bottom boundary of the

715

González A., Ortigueira C., Ortega M. and G. Penedo M..

Quantitative Study on a Multiscale Approach for OCT Retinal Layer Segmentation.

DOI: 10.5220/0004925107150723

In Proceedings of the 6th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2014), pages 715-723

ISBN: 978-989-758-015-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Retinal Pigment Epithelium (RPE). In the text that

follows, these layers will be referenced as layers 1

and 6. These layers have been chosen because they

are the ﬁrst to be segmented in several automatic me-

thods applied on the retinal images, because they are

which delimit the main part of the retina. In addi-

tion, they present different characteristics: the ﬁrst

one is evidently visible in the images, while the se-

cond one presents more difﬁculties, given that the se-

paration between the RPE and the choroid is not al-

ways clear, besides the ruptures or discontinuities that

can be found on the RPE. The approach presented in

this work can be adapted to segment the rest of the

layers of the retina.

This paper is organized as follows: In section 2, a

review of the graph-based segmentation is presented

and section 3 introduces the multiscale (or pyrami-

dal) approach. In section 4 experimental results are

shown, with a deep study in the conﬁguration which

optimizes the levels in the pyramidal approach and,

ﬁnally, section 5 offers conclusions and future work.

2 GRAPH-BASED LAYER

SEGMENTATION

Graph-based approach transforms the problem of seg-

mentation into that of ﬁnding the minimum closed

set in a geometric graph. This graph satisﬁes some

smoothness and interaction constraints. The idea is

mapping each pixel in the image to a node in the

graph. The graph search is guided by some cost

functions extracted from the image in order to ﬁnd

its minimum cut. The cost value is assigned to

each node, provided by the cost functions designed

previously and applied to the image. Therefore, nodes

that determine the minimum cut in the graph will co-

rrespond to pixels in the image that are interesting to

be found; in this case, those corresponding to the layer

that is being searched.

As a synthesis of this methodology, Figure 1

shows the phases required to tackle the segmentation

of generic a layer: Firstly, a preprocessing to enhance

and prepare the image (original images are bounded

by black square that must be automatically excluded);

after that, the segmentation itself, based on the graph

searching exposed before and ﬁnally, the representa-

tion of the layer over the image.

Applying cost functions

Graph building

Min-cuts searching

Figure 1: Main phases of the graph-based methodology.

It is necessary to consider that sometimes, the in-

formation that can be extracted from the image is not

enough, so adding information from adjacent ima-

ges in an OCT sequence could improve the perfor-

mance of the method. This is possible because the

graph can be designed to perform a 2-D or 3-D geo-

metric searching. Thus, in the 3-D approach, a layer

is segmented in an image considering not only va-

lues from cost functions applied to it, but also the

cost values from the adjacent images in the OCT se-

quence. This capability is useful in the case that the

layer presents discontinuities or low deﬁnition in the

image. Although the 3-D model seems to be the best

approach in the case of sequences of OCT images (al-

ways considering an appropriate number of images

per sequence), the main problem is the time required

for computation in the graph search. The pyramidal

structure can be also built in these situations in order

to reduce it.

Regarding the phases in the methodology, the

multiscale approach involves modiﬁcations in the seg-

mentation stage. As it was exposed, information ex-

tracted by the cost functions is used to guide the

graph searching. Therefore, these functions must be

suitably designed to reﬂect relevant information, in

this case, edges location and intensity distribution in

the image. In this work, not only cost functions from

(Haeker et al., 2007) and (Gonz

alez et al., 2013) are

included, but also additional terms that are needed in

some levels of the pyramid, as Section 3.2 presents.

Synthetically, the cost functions considered are the

following:

Edge-based functions, obtained using Sobel op-

erator with a previous Gaussian ﬁltering and a non-

maximum suppression, to extract dark-to-light ( f

edge

)

and bright-to-dark ( f

edge

) transitions. Gradient dis-

tance f

is also considered, taking a distance f

value between adjacent pixels. Terms f

and f

select

the ﬁrst and last edge in the image, respectively, using

thresholds t

and t

, whose deﬁnition is extended in

this work, to consider limits t

min

and t

max

. Term f

erase very close edges in the same column with diffe-

rent direction, while f

erase those with the same one.

A new term f

is added in this paper, penalizing the

ﬁrst edge on the image (useful for layer 6 detection).

Intensity-based functions: f

and f

encourage

pixels with bright areas above and below, respectively.

Term f

uses similar information to f

but encourag-

ing regions on the bottom part of the image. In order

to consider dark areas above instead of bright ones, f

is used.

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3 PYRAMIDAL APPROACH

As it was introduced before, the aim of this work

is presenting a deep study of a multiscale approach

for the graph-based segmentation algorithm, with the

purpose of reducing the computation requirements in

terms of time and memory. It is based on building

a pyramid for each OCT image, where its levels are

smaller versions of the original image. The main idea

is that the layer segmented in lower resolution ima-

ges is used in the original one to reduce the area of

searching of the graph-based algorithm. Improvement

is mainly given by the fact that, for smaller images,

smaller graphs are generated to apply the minimum

cut algorithm and as the problem in a single-scale has

not a linear complexity, linear changes in its dimen-

sions (image size, and therefore, graph size) provide

even bigger changes in performance.

In this context, the pyramid is a hierarchical struc-

ture consisting of the images resulting of applying

certain functions on the original one, whose dimen-

sions are reduced with each transformation. The ori-

ginal (and larger) image is the base of the pyramid,

and the successive levels are the resulting images of

these transformations. Thus, pyramidal basis con-

forms the level i = 0, whereas the peak corresponds

to the level i = h − 1, with h the pyramid height.

The construction of this pyramidal structure is the

ﬁrst step in this method and it can be considered as an

ascent over the pyramid. Once the original image size

has been reduced, according to certain scale factor sc,

and the different levels of the pyramid have been built,

it is possible to descend it. In this descending pro-

cess, the layer detected in the level above is used in

the current level to bound the area of searching, so

the graph-based method is applied in a smaller image.

Both ascending and descending processes involved in

the pyramidal approach are reﬂected in Figure 2.

Downsampling

Bounding area

of searching

and segmentation

S = * sc

Figure 2: Schema for pyramidal algorithm. At each level i,

image size S

is obtained applying the scale factor sc to its

dimensions in level i − 1.

3.1 The Pyramidal Ascent

The loss of information caused by the resolution re-

duction must be considered in the ascending process,

because at the time that pyramidal height increases, it

is more accused. Therefore, it determines the pyra-

midal height, since the location of the layers becomes

more difﬁcult as the structure is ascent. Even though

a precise segmentation in the middle levels is not

needed, information in the image should be enough

to obtain an appropriate detection.

In order to minimize the loss of information, the

transformation applied to the images to generate the

upper level includes not only a sub-sampling, but

also a previous low-pass ﬁltering, making possible

that each pixel in the reduced image is inﬂuenced

by the information of its neighbors. Difference be-

tween results obtained with this process and only sub-

sampling are presented in Figure 3.

Subsampling

Low-pass ltering

Subsampling

Figure 3: Image obtained during an ascent step using only

a sub sampling process and that with a previous low-pass

ﬁltering. Zoom has been applied to make the difference

more appreciable.

3.2 The Pyramidal Descent

Regarding the descending stage, two basic tasks are

needed in each level of the pyramid: ﬁrstly, the area

of searching is delimited in the current image using

the segmentation obtained in the level immediately

above (the image is cut and a mask is built based

on that, considering ﬂexibility thresholds t

sup

and

in f

), allowing to exclude irrelevant areas in the OCT

image. Then, the graph-based method is applied to

segment the layer in this level. As the area of interest

has been reduced, the number of nodes in the graph

is now lower and, therefore, computing time too. The

process is reﬂected in Figure 4.

Extrapolation

Bounding area

Figure 4: Bounding the area of searching: Layer 1 detected

in the image immediately above is extrapolated to the image

in the current level and the area of searching is bound.

Once the area of searching is determined and the

cost functions have been applied, the graph-based al-

gorithm is used to detect the layer of interest. This

entire process is repeated from the peak of the pyra-

mid (where the area of searching is the whole image,

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with reduced dimensions) to its base, where the ﬁnal

layer is detected in the original OCT image.

When using a 3-D model, the process is analo-

gous: pyramid is built with 3-D OCT images, and

the layer is detected in all of them during the descent

stage. In the base of the structure, only the layer seg-

mented in the central image of the group is preserved,

since it has the contribution of its adjacent images.

4 RESULTS AND DISCUSSION

Different experiments have been designed in order to

ﬁnd the best pyramidal structures for the segmenta-

tion of ﬁrst and sixth layers and compare its results

with those obtain with the original graph-based seg-

mentation method. The data set used in the experi-

ments is composed by 18 OCT sequences, including

both healthy and diabetic retinopathy patients. Each

sequence consists of 128 images, which makes a total

of 2304 images.

These images were captured using Cirrus HD-

OCT, with Spectral Domain Technology (Zeiss), at

a resolution of 334x334 pixels. All the results have

been obtained using an Intel Core TM 2 Duo proces-

sor (2,4 GHz) and a RAM of 2 GB.

Three experiments have been designed for each

layer separately, since their detection is independent.

The ﬁrst one has the purpose of studying the pyrami-

dal height, in order to determine the number of levels

that achieves a successful segmentation with mini-

mum cost. In the second experiment, the feasibility

of a descending method without intermediate levels

is studied, avoiding the segmentation in certain levels

of the structure with the aim of optimizing even more

the pyramidal process. Finally, in the last experiment,

results of the best pyramids obtained previously are

compared with those provided by the original seg-

mentation method.

Given that the aim of this work is optimizing the

efﬁciency of the graph-based segmentation method,

maintaining the accuracy in the segmentation results

is essential. With that purpose, experiments 1 and

2 are done in two steps: ﬁrstly the feasible pyrami-

dal heights are studied, in order to consider pyramids

with enough number of levels (but not excessive) to

achieve appropriate segmentation results. After that,

efﬁciency is studied for those structures. Thus, at each

experiment, both effectiveness (successful segmenta-

tion) and efﬁciency (in terms of consumed time and

memory) are considered.

It is necessary to take into account that, in these

experiments, layer 1 is segmented using a 2-D graph,

since its location is evident in the images, and the in-

formation from adjacent images is not needed. Re-

garding layer 6, a 3-D graph is needed, due to the dis-

continuities in this layer, in addition to the fact that the

borderline between RPE and Choroids is not well de-

ﬁned in the images. The 3-D graph for layer 6 is built

with overlapping groups of 3 consecutive images.

Parameters involved in the methodology have

been extracted empirically. The factor scale sc used

in this work is set to 0.5, so dimensions for the image

located in the level i of the pyramid are the half of the

image immediately below (level i − 1).

4.1 Experiment 1: Determining the

Optimal Pyramid Height

In this set of experiments, pyramids of different height

are evaluated, in order to determine the number of le-

vels that allows to obtain a successful segmentation

of each layer with minimum computational cost. This

task is done in two steps: ﬁrstly, a coarse study of the

heights than be considered to built pyramids for both

layers is done. After that, time and memory required

by the pyramid-based approach using these heights to

detect layers 1 and 6 is deeply studied.

Regarding layer 1, preliminary experiments show

that segmentation does not present mistakes for pyra-

mids of up to 4 levels, whereas layer 6 can not be cor-

rectly segmented with structures higher than 3 levels.

Once that the maximum number of levels for each

pyramid is known, performance is studied to select

the most appropriate structure. Table 1 shows results

obtained, while Figure 5 reﬂects them graphically.

Table 1: Time and memory consumed in the segmentation

task using pyramids of different heights, both expressed

as mean (standard deviation). Best time results have been

highlighted.

h = 2 h = 3 h = 4

Layer 1

Time (s) 58.44 (12.88) 30.22 (6.03) 29.67 (5.57)

Memory (MB) 103.22 (1.56) 103.83 (1.86) 104.00 (1.88)

Layer 6

Time (s) 1216.94 (557.36) 562.17 (93.10) –

Memory (MB) 115.11 (4.79) 123.22 (4.87) –

4.1.1 Discussion

First aspect to be observed is that the consumed me-

mory does not change signiﬁcantly using different le-

vels in the pyramid, so it is not a decisive factor in the

selection of the best structure. However, it is observed

that layer 6 requires more memory than the layer 1.

Obviously, this is because of the 3-D model used to

detect that layer.

The number of levels has more evident repercus-

sions in the computation time. As Figure 5 (a) ex-

poses, time required to detect layer 1 decreases con-

siderably when h = 3 , whereas the small difference

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2 3 4

Time(s)

2 3 4

100

110

120

130

140

150

Memory (MB)

(a)

2 3

500

1000

1500

Time (s)

2 3

100

110

120

130

140

150

Memory (MB)

(b)

Figure 5: Time and memory consumed using pyramids of

different heights to segment layer 1 (a) and 6 (b).

in performance with h = 3 and h = 4 indicates that

this extra level does not provide relevant informa-

tion to bound the area of searching in the lower le-

vels. This is due to the fact that some margins are

needed in the processes of cutting and mask extrac-

tion. Therefore, although segmentation with higher

pyramids may be possible, their contribution to re-

duce computation time is not relevant.

Time consumed to detect layer 6, shown in Figure

5(b), also experiments an evident decreasing when

the number of levels increases. In addition, it is ob-

served that improvement using h = 3 regarding h = 2

is higher than the obtained for layer 1. This is caused

by the 3-D model used to detect layer 6, which is more

sensitive to the different sizes of the image (and con-

sequently, the associated graph) than a 2-D model. In

a intuitive way, the number of arcs between nodes is

higher in the 3-D model, making the searching harder.

Therefore, when they are reduced, computation time

changes in a more accused way.

With regards to the standard deviation in the pre-

sented measures, it is remarkable that the variability

is mainly caused by the operations performed in the

preprocessing stage of the methodology. In this ﬁrst

phase, the dimensions of the input OCT image are op-

timized, removing the dark top and bottom, which do

not provide useful information. The different shape

of the retinal structure in the OCT images of the va-

lidation set causes a variation in the size of the in-

put image for the segmentation stage, which thereby

require different execution times. Results, however,

show that standard deviation does not affect in a sig-

niﬁcant way to the efﬁciency, compared to the other

factors do.

4.2 Experiment 2: Optimizing the

Pyramidal Descent

Previous experiments have determined the optimal

height for the pyramidal structure for both layers 1

and 6. Thus, after optimizing the process of ascen-

ding the pyramid, an improvement in the descent can

be suggested, studying if the levels between the peak

of the pyramid and its base are needed or instead,

the application of the algorithm in all of them can be

avoided, as depicted in Figure 6. This method will

be referenced as direct descent, because it intends to

extrapolate directly the layer segmented in the peak

of the pyramid to the image in its base, instead of ex-

ploring all the levels to bound the area of searching at

each one. Thus, the min-cut searching is only applied

in these two levels.

Bounding area

of seaching

and segmentation

Downsampling

Figure 6: Schema for the pyramidal-based algorithm, in-

cluding the direct descent method.

This experiment is developed following an analo-

gous scheme to the previous one: ﬁrstly, the optimal

height for the pyramids is studied and then, the perfor-

mance for each possible structure is evaluated. Pre-

liminary results show that an appropriate segmenta-

tion of layer 1 with structures with height h more than

3 is not possible, so results for the feasible structures

are presented in Table 2 and Figure 7. Computation

times required in this experiment are also compared

with those obtained in the previous one (Figure 8),

because determining if the direct descent is possible

is not enough, but also if it provides an improvement

with regards to the best performance obtained in the

previous set of experiments.

Table 2: Time and memory consumed in the segmentation

task using the direct descent, both expressed as mean (stan-

dard deviation). Best time results have been highlighted.

h = 2 h = 3

Layer 1

Time (s) 58.44 (12.88) 26.78 (5.00)

Memory (MB) 103.22 (1.56) 104.22 (1.66)

Layer 6

Time (s) 1216.94 (557.36) 2988.17 (336.62)

Memory (MB) 115.11 (4.79) 129.89 (3.74)

4.2.1 Discussion

In contraposition to results obtained in the previous

experiment, in this case, a suitable segmentation of

layer 1 can not be obtained using structures higher

that h = 3. This is due to the detection mistakes

present in the top of the pyramid caused by the loss of

information inherent to the downsampling. In the ori-

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2 3

Time (s)

2 3

100

120

140

Memory (MB)

(a)

2 3

1000

2000

3000

Time (s)

2 3

100

120

140

Memory (MB)

(b)

Figure 7: Time and memory consumed using the direct de-

scent method to segment layer 1 (a) and 6 (b).

2 3 4

26.78 s

Time (s)

Layer 1

2 3

1000

2000

3000

562.17 s

Time (s)

Layer 6

Experiment I

Experiment II

Figure 8: Comparison in time between both experiments to

segment layer 1 and layer 6.

ginal descending method, these deﬁciencies are cor-

rected gradually at each level, so the area of searching

in the base is the appropriate. In the direct descent

proposed in this experiment, these small errors at the

peak of the structure are transferred directly to its

base, and also magniﬁed due to the larger scale of ex-

trapolation.

Results show that, for layer 1, consumed memory

is approximately stable, whereas for layer 6 slightly

increases, mainly due to the larger areas of searching

required by this layer, given the difﬁculties to de-

termine its precise location. However, it is not a

critical factor in the selection of one or another me-

thod. Regarding execution time, it is observed that,

while using the direct descend method involves an

improvement to segment layer 1, it does not to layer

6. Once again, this is related to the larger areas of

searching used to detect this layer. Thus, it is possible

to afﬁrm that the middle levels in the pyramidal struc-

ture are not essential for layer 1, but they are needed

for layer 6.

Having analyzed the performance of the pyrami-

dal structures with the direct descent approach, a

comparison between these results and those obtained

Experiment 1 is necessary. Since consumed memory

remains fairly stable, execution time comparison (Fi-

gure 8) determines the best structure and the method

used to descend it for each layer.

As it was explained before, the information avail-

able in the peak of the pyramid with h = 3 is enough

to avoid using the intermediate levels in the segmen-

tation of layer 1. On the other hand, detecting layer

6 with the direct descent method is not proﬁtable in

terms of performance, because of the complex loca-

tion of this layer. Not considering the information of

the intermediate levels to correct the deﬁciencies of

the segmentation in the peak of the structure involves

using a larger area of searching in the basis. There-

fore, computation time increases, specially using a

3-D model. Thus, unlike layer 1, the best approach

to detect layer 6 consist in applying the algorithm in

all the levels of the structure, as it was presented in

Experiment 1.

4.3 Experiment 3: Comparison with the

Single-scale Approach

Experiments exposed previously have provided the

best conﬁgurations for the pyramidal approach pro-

posed to detect layers 1 and 6. Now, a comparison

between original single-scale approach and the new

pyramidal multiscale one is presented, considering

not only terms of performance but also effectiveness

(accuracy in the segmentation obtained).

Table 3 shows performance results obtained for

both options (results presented for the pyramid-based

method are those obtained with the best structures an-

alyzed the previous experiments). With regards to the

segmentation accuracy, most test show that both ap-

proaches provide similar results (some samples ob-

tained with each method are presented in Figure 9).

The most interesting fact is that multiscale approach

solves some mistakes made by the single-scale me-

thod, as Figure 10 shows, although this will be com-

mented in detail in the discussion.

Table 3: Consumed time and memory comparison between

the simple-scale method and the pyramidal-approach. Re-

sults are expressed as: mean (standard deviation). Percent

of improvement in time has been highlighted.

Original Pyramidal

Improvement(%)

Method Approach

Layer 1

Time (s) 1795.28 (873.55) 26.78 (5.00) 98.51

Memory (MB) 148.61 (11.71) 104.22 (1.66) 29.87

Layer 6

Time (s) 24499.39 (13259.34) 562.17 (93.10) 97.71

Memory (MB) 162.78 (6.31) 123.22 (4.87) 24.30

4.3.1 Discussion

Figure 9 shows that the quality obtained with the

single-scale method is maintained with the proposed

multiscale approach. Despite the similarity between

both segmentations, there are situations in which the

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(a) (b)

Figure 9: Segmentation samples obtained for layer 1, in

green, and 6, in red: (a) single-scale method; (b) pyramidal

approach.

(a) (b)

Figure 10: Segmentation results obtained for layer 1 and

6: (a) single-scale method; (b) pyramidal approach. Yellow

arrows indicate the mistakes using the single-scale method,

which are avoided using the pyramidal structure.

pyramid-based method provides better results. Thus,

it is possible to afﬁrm that the loss of information

inherent to the pyramidal process and the downsam-

pling, as well as the bounded area of searching ob-

tained, are really relevant. In particular, these terms

allow correcting some mistakes caused by the infor-

mation present in the original image. This is spe-

cially remarkable in the case of layer 6, given that the

choroid, located below it and with similar properties,

can involve wrong segmentation in some parts of the

image. As samples in Figure 10 show, these errors are

not made using the pyramidal approach.

On the other hand, comparison between both so-

lutions in terms of performance presented in Table 3

show that, as it was mentioned before, the most sig-

niﬁcant factor to take into account is the computation

time. It is remarkable that a relevant leap in time is

done (even in magnitude order, considering terms of

hours in the single-scale problem to minutes and se-

conds in the multiscale approach).

Results show the high computation time required

by the single-scale method, which make it nonviable,

specially for layer 6 detection (mean time required

over six hours). Proposed optimization, with con-

ﬁgurations for pyramidal structures exposed in the

previous experiments, achieves a signiﬁcant improve-

ment in time for each layer over the 97%. Addi-

tionally, although consumed memory is not excessive

in any of the approaches, pyramid-based solution re-

duces it in more than a 20% in each layer. For layer

1, segmentation using three-level pyramidal structure

and the direct descend from the peak to the base is

67 times faster than the original procedure, as Table

3 presents. However, the improvement is lower for

layer 6, whose proposed approach is 43 times lower

than the original. This difference is mainly caused by

the higher difﬁculty in the location of this layer, as

well as the use of 3-D model, as it was introduced in

the previous experiments.

Pyramid-based approach also involves an im-

provement in the variability of the consumed time.

For instance, results in Table 3 show that segmenta-

tion of layer 1 with the original method can vary in

function of the patient until a 48% of the mean time

(approximately 14 minutes), whereas the pyramidal

method presents a dispersion of 18.6% with respect

to the mean value (5 seconds). Regarding layer 6, re-

duction is analogous.

This improvement in the standard deviation is

mainly provided by the bounding area process (Sec-

tion 3.2), which has a direct repercussion in the graph

size generated in the detection. In this step, cutting

process affects mainly to the number of rows in the

image located on the pyramidal peak (lower levels

use a mask to bound even more the area of interest).

In addition, segmentation process in the peak of the

pyramid barely affects in the global time required to

detect a layer. Therefore, as variability between pa-

tients is caused by the cutting in the descent stage and

it affects specially to the image on the highest level

in the pyramid (whose segmentation time is short), it

seems obvious that the inﬂuence in the total time will

be also small. In contraposition to that, in the origi-

nal methodology the difference in size between two

images has a more relevant repercussion, because the

number of nodes (and therefore, the number of arcs)

erased in the cutting is much higher than that done in

the peak of a pyramid. Therefore, changes in terms

of dispersion are which should be expected and, as it

was determined in Experiment 1, this difference is not

a signiﬁcant factor to take into account.

As a synthesis of the results obtained in this expe-

riment, it is shown that the pyramid-based approach

provides better results than the single-scale method in

terms of computation time, at the time that maintains,

and also improves, segmentation obtained with this

QuantitativeStudyonaMultiscaleApproachforOCTRetinalLayerSegmentation

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Table 4: Parameters used to segment layer 1. They correspond to the best conﬁguration obtained after the experiments

(three-level pyramid, with the direct descent method).

Level (i)

Parameter

edge

min

max

sup

in f

2 f

edge

+ f

1000 2000 1000 1000 - 1000 20 5 0 2 - -

0 f

edge

+ f

1000 2000 1000 - 1000 - 20 10 2 10 15 10

Table 5: Parameters used to segment layer 6. They correspond to the best conﬁguration obtained after the experiments

(three-level pyramid, with the original descent method).

Level (i)

Parameter

edge

sup

in f

2 f

edge

+ f

1000 2000 1000 - - 1000 20 1 - 5 - -

1 f

edge

+ f

2000 2000 2000 1500 1000 1000 20 1 1 5 15 5

0 f

edge

+ f

2000 2000 1500 1000 1000 - 20 1 1 - 7 7

method.

5 CONCLUSIONS AND FUTURE

WORK

This paper presents a study of a multiscale approach

for a graph-based method to segment retinal layers in

OCT images. This approach is evaluated on two reti-

nal layers, considering terms of computing time and

memory. Three experiments have been designed to

evaluate the different conﬁgurations that can be taken

into account in this problem, in order to achieve the

most successful results. Values for parameters in the

graph-based method are presented in Tables 4 and 5,

corresponding to the best conﬁguration obtained in

the experiments. Quantitative measures show that this

approach improves considerably the performance of

the original method. They also determines the me-

thod that should be applied in each layer during the

pyramidal descent. Accuracy has been evaluated too,

because segmentation results obtained by the single-

scale method must be maintained. This approach

achieves not only the same results, but also improve

them, obtaining successful segmentation in situations

where the single-scale method makes mistakes.

ACKNOWLEDGEMENTS

This paper has been partly funded by the Ministe-

rio de Ciencia e Innovaci

on under TIN2011-25476

project of the Spanish Government (A. Gonzalez ac-

knowledges the support of Secretar

ıa de Estado under

FPI Grant Program).

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