# Interactive Volume Illustration Using Intensity Filtering.

**ABSTRACT** We propose a simple and interactive technique for volume illustration by using the difference between the original intensity values and a low-pass filtered copy. This difference, known as unsharped mask, provides us with a spatial importance map that captures salient and separability information about regions in the volume. We integrate this map in the visualization pipeline and use it to modulate the color and the opacity assigned by the transfer function to produce different illustrative effects. We also apply stipple rendering modulating the density of the dots with the spatial importance map. The core of our approach is the computation of a 3D Gaussian filter, which is equivalent to three consecutive 1D filters. This separability feature allows us to obtain interactive rates with a CUDA implementation. We show results of our approach for different data sets.

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**ABSTRACT:**The aim of salient feature detection is to find distinctive local events in images. Salient features are generally determined from the local differential structure of images. They focus on the shape-saliency of the local neighborhood. The majority of these detectors are luminance-based, which has the disadvantage that the distinctiveness of the local color information is completely ignored in determining salient image features. To fully exploit the possibilities of salient point detection in color images, color distinctiveness should be taken into account in addition to shape distinctiveness. In this paper, color distinctiveness is explicitly incorporated into the design of saliency detection. The algorithm, called color saliency boosting, is based on an analysis of the statistics of color image derivatives. Color saliency boosting is designed as a generic method easily adaptable to existing feature detectors. Results show that substantial improvements in information content are acquired by targeting color salient features.IEEE Transactions on Pattern Analysis and Machine Intelligence 02/2006; 28(1):150-156. · 4.80 Impact Factor - SourceAvailable from: utah.edu
##### Article: Display of surfaces from volume data

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**ABSTRACT:**The application of volume-rendering techniques to the display of surfaces from sampled scalar functions of three spatial dimensions is discussed. It is not necessary to fit geometric primitives to the sampled data; images are formed by directly shading each sample and projecting it onto the picture plane. Surface-shading calculations are performed at every voxel with local gradient vectors serving as surface normals. In a separate step, surface classification operators are applied to compute a partial opacity of every voxel. Operators that detect isovalue contour surfaces and region boundary surfaces are examined. The technique is simple and fast, yet displays surfaces exhibiting smooth silhouettes and few other aliasing artifacts. The use of selective blurring and supersampling to further improve image quality is described. Examples from molecular graphics and medical imaging are given.< >IEEE Computer Graphics and Applications 06/1988; · 1.23 Impact Factor - SourceAvailable from: psu.eduEurographics A. Chalmers, T. -m. Rhyne, Balzs Csbfalvi, Lukas Mroz, Helwig Hauser, Andreas Knig, Eduard Grller[Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we present a fast visualization technique for volumetric data, which is based on a recent nonphotorealistic05/2001;

Page 1

Computational Aesthetics in Graphics, Visualization, and Imaging (2010)

O. Deussen and P. Jepp (Editors)

Interactive volume illustration using intensity filtering

Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert

Graphics and Imaging Laboratory, Universitat de Girona, Spain

Abstract

We propose a simple and interactive technique for volume illustration by using the difference between the original

intensity values and a low-pass filtered copy. This difference, known as unsharped mask, provides us with a spatial

importance map that captures salient and separability information about regions in the volume. We integrate

this map in the visualization pipeline and use it to modulate the color and the opacity assigned by the transfer

function to produce different illustrative effects. We also apply stipple rendering modulating the density of the dots

with the spatial importance map. The core of our approach is the computation of a 3D Gaussian filter, which is

equivalent to three consecutive 1D filters. This separability feature allows us to obtain interactive rates with a

CUDA implementation. We show results of our approach for different data sets.

Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Transfer functions—

Volume Rendering

1. Introduction

A main step in direct volume rendering is the definition of

the transfer function. This assigns optical properties such

as color and opacity to the original values of the data to

visualize the internal parts of the volume. In the case of

one-dimensional transfer functions, there is a direct map-

ping between optical values and voxel scalar values. On the

other hand, multidimensional transfer functions take more

information into account, such as first and second deriva-

tives [KKH02]. This additional gradient information allows

a better separation between materials and thus better visu-

alizations. The need for a good detection of boundaries be-

comes crucial for the quality of the rendering. Knowledge

of boundaries facilitates the understanding of the volume

data set by focusing on the most pertinent subset of data,

i.e., which can be considered as the most salient parts of

data [IK01].

Although it has already been used by different au-

thors [KV06], the concept of saliency in a volume model,

different to an image or a 3D polygonal scene, is not yet

a well defined concept. Saliency should facilitate learning

by focusing on the most pertinent subset of available sen-

sory data. On the other hand, saliency of a voxel (or region)

should arise from contrast between thisvoxel (or region) and

its neighborhood. Thus, it should include recognition of the

boundaries of the inner parts of the volume data, as well as

finding local deviations. When examining a 3D polygonal

model, we just have one isosurface, we do not have to single

it out, we just want to single out the particular oddities or

irregularities of this surface. In the case of volume data, we

first have to single out the components, i.e., the boundaries

that make up its structure. On the other hand, the observation

of the volume data model comes always via a transfer func-

tion, thus modulating an original, neutral transfer function

with this extended saliency will allow us to learn about the

data. A quantity very simple to compute that fills the above

requirements of generalized saliency is an unsharped mask.

This is the difference between low-pass filtered data and the

original one.

Different feature enhancement strategies based on un-

sharp masking have been proposed. Cignoni et al. [CST05]

performed unsharp masking to the normal field over the 3D

surfaces, to enhance the perception of discontinuous geo-

metric features. Luft et al. [LCD06] enhanced depth per-

ception by unsharp masking the depth buffer. The difference

between the filtered image and the original one was called

spatial importance map. Ritschel et al. [RSI∗08] coherently

enhanced the scene by unsharp masking the outgoing radi-

ance field over the mesh surface. Tao el al. [TLB∗09] use the

difference between the radiance volume and the smooth ra-

diance volume to enhance local contrast of features. In this

paper, we propose a similar approach but instead of using

c ? The Eurographics Association 2010.

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

Figure 1: Main steps of the proposed approach.

radiance we propose to operate with the original intensity

values, having lower memory requirements. We use the spa-

tial importance map toobtain both anenhanced visualization

of the data, by modulating color and opacity, and illustrative

effects such as stippling.

The structure of the paper is as follows. In Section 2, we

review related work. In Section 3, we describe the proposed

approach. Then, in Section 4 we show the different effects

that can be obtained in the proposed approach. Finally, con-

clusions are presented in Section 5.

2. Related Work

Direct volume rendering techniques allow to explore the

structures embedded in the volume data set by varying the

opacities and colors assigned to them. For the rendering to

be effective it is required a transfer function that assigns

colors and opacities to the different materials. Although a

large number of strategies have been proposed for automatic

and semi-automatic generation of transfer functions, the def-

inition of a proper transfer function is still challeging. The

main limitation is the classification process required to de-

finethe density intervals corresponding tothe structures, i.e.,

the boundaries that separate the different materials.

Levoy proposed the use of the gradient magnitude to iden-

tify surfaces in volume data [Lev88]. Kindlmann and Durkin

used thefirst and second derivatives along thegradient direc-

tion to calculate a boundary emphasis to be included in the

opacity transfer function [KD98]. In addition to the design

of the opacity transfer function, general multi-dimensional

transfer functions were studied to better convey the bound-

aries and features in volume data [KWTM03, KKH02,

KPI∗03,LM04]. These methods create two-dimensional his-

tograms where each entry represents the number of voxels at

a given feature space pair at which the user in a trial-and-

error manner assigns color and opacity until the desired vi-

sualization is obtained. To avoid this trial-and-error process,

Maciejewski et al. proposed the addition of non-parametric

clustering within the transfer function feature space in or-

der to extract patterns and guide transfer function genera-

tion [MWCE09]. Recently, Correa et al. [CM09] presented

a method for classifying volume data based on the ambient

occlusion of voxels. They detected occlusion patterns that

reveal the spatial structure of materials or features of a vol-

ume and represented them in an occlusion spectrum. This

occlusion spectrum leads to better two-dimensional transfer

functions that can help classify complex data sets in terms of

the spatial relationships among features.

Illustrative techniques are suitable for emphasizing cer-

tain features or properties while omitting or greatly simpli-

fying other, less important details [RE01]. The most pop-

ular styles, such as stippling, hatching and silhouettes, are

from the pen-and-ink family [CMH∗01,LME∗02]. To incor-

porate illustrativeeffects ina volume renderer, Kindlmann et

al. [KWTM03] utilized curvature-based transfer functions.

Hauser et al. [HMBG01] proposed thetwo-level volume ren-

dering concepts which allows focus+context visualization

of volume data. Different rendering styles, such as direct

volume rendering and maximum intensity projection, are

used to emphasize objects of interest while still displaying

the remaining data as context. Viola et al. [VKG04] intro-

duced importance-driven volume rendering, where features

within the volumetric data are classified according to object

importance. Bruckner et al. [BGKG06] presented context-

preserving volume rendering, where the opacity of a sam-

ple is modulated by a function of shading intensity, gradient

magnitude, distance to the eye point, and previously accu-

mulated opacity.

Different computational models have been proposed to

interpret the selective visual attention. The biologically-

inspired model of bottom-up attention of Itti et al. [IK01]

permits us to understand our ability to interpret complex

scenes in real time. The selection of a subset of available

sensory information is controlled by a saliency map which

is a topographic representation of the instantaneous saliency

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

of the visual scene and shows what humans find interesting

in visual scenes.

Inspired in Itti’s work, Lee et al. [LVJ05] introduced

the concept of mesh saliency, a measure of regional im-

portance for 3D meshes, computed using a center-surround

mechanism that is able to identify regions that are differ-

ent from their surrounding context. Feixas et al. [FSG09]

defined a view-based saliency of a polygon as the aver-

age information-theoretic dissimilarity between this poly-

gon and its neighbors. In the volume rendering field, Kim

et al. [KV06] presented a visual-saliency-based operator to

enhance human perception of the volume data by guiding

viewer’s attention to selected regions. In different works

on saliency, it has been shown that attention is attracted

by changes in luminance, color, curvature, texture, shape,

etc. [TIR05]. That is, salient features are generally deter-

mined from the local differential structure of images and

different operators such as color or luminance gradient have

been used [vdWGB06]. In González et al. [GSF08], from

an information theory perspective, ambient occlusion has

been defined as the occlusion information associated with

each polygon of the model. In Ruiz et al. [RBV∗08] voxel

saliency isdefined asthe magnitude of the gradient of obscu-

rances estimated by using the 4D linear regression method.

Considering that obscurance represents occlusion informa-

tion associated with a voxel, its variation with respect to its

surround can indeed be perceptually salient, i.e., it can be

considered as a salient feature of the volume.

3. Proposed Approach

Detection of the structures is an important step towards the

interpretation of volume data. In general, each structure is

represented by an interval of densities. The identification of

these intervals can be obtained from the identification of the

boundaries that separate from each other. Spatial importance

maps can be used to identify these boundaries. The idea of

our method is to exploit this fact to provide a simple strategy

for exploring volume data models and also obtain different

illustrative effects that enhance the perceptual quality and

interpretation of the images taking only the original intensity

values.

The main steps that compose the proposed approach are

represented in Figure 1. First, in a preprocessing step, we

compute the spatial importance map by filtering the input

model and subtracting the obtained result from the original

model. Then, the spatial importance map is integrated in the

visualization pipeline and used to modulate the color and/or

the opacities returned from the illumination process in order

to produce different illustrative effects. A detailed descrip-

tionof thesesteps and mainimplementation detailsaregiven

below.

Figure 2: From top to bottom, spatial importance maps ob-

tained for CT body (256 × 256 × 415), CT head (512 × 512

× 297), and salmon (336 × 173 × 511). The images of the

first and second columns have been obtained with a radius

of 5 and 10 for the Gaussian filter, respectively.

3.1. Spatial Importance Map

The first step of our approach consists in the computation

of the spatial importance map, that can be considered the

core of the method. This map is the extension to 3D of the

spatial importance function ∆D proposed by Luft [LCD06].

In contrast to Tao et al. [TLB∗09], who used radiance, we

use intensity values. The advantages of our approach are that

it does not depend on the transfer function and lighting, and

thus can be done as a preprocessing step, and that it requires

less memory.

Given a volume model V : N3→ Z where Z represents

the scalar values of the voxels, we compute the spatial im-

portance map ∆D by

∆D = G∗V −V,

(1)

where G∗V is a Gaussian blur of the volume. A Gaussian

c ? The Eurographics Association 2010.

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

Volume

CT body

R

1

5

10

1

5

10

1

5

10

1D filter (ms)Subtract (ms) Total (ms)

335.05

438.13

560.23

928.41

1221.18

1570.10

376.37

490.04

617.24

20.85

52.96

93.59

57.90

155.61

272.77

22.66

59.03

104.93

18.03

CT head51.90

Salmon 19.66

Table 1: Times in milliseconds (ms) to compute the spatial

importance map for the CT body (256 × 256 × 415), the

CT head (512 × 512 × 297), and the salmon (336 × 173

× 511) with different radii (R) of the Gaussian kernel. The

1D filter column reports the time to do a 1D convolution

with the kernel (this process has to be done once for each

axis). The Subtract column reports the time required to do

the subtraction. The Total column includes the time to do the

3 convolutions, the subtraction, and all the other additional

operations like memory allocations and transfers.

blur is the convolution of an image with the Gaussian func-

tion

1

√2πσe−x2

where x is the distance from the origin and σ is the standard

deviation of the Gaussian distribution. The above function is

for the 1D case, for 2D it is the product of two Gaussians

and in 3D the product of three Gaussians, one per direction.

The effect of a Gaussian blur is the reduction of the high-

frequency elements of the image, so it is a low-pass filter.

G(x) =

2σ2,

(2)

In Figure 2, we illustrate the spatial importance maps ob-

tained for different models, a CT body (256 × 256 × 415),

a CT head (512 × 512 × 297), and a salmon (336 × 173

× 511) and different radii of the Gaussian kernel. The maps

are colored using the thermal scale represented at the bot-

tom, where warm colors correspond to positive importance

values and cool colors to negative ones. Observe that the

voxels that are near density boundaries have values differ-

ent from zero, because in the blurred volume the boundaries

are smoothed and have values lower than the originals at one

side, and higher at the other side. So, positive difference val-

ues indicate voxels near a boundary with a higher density

material since this makes that those voxels have higher in-

tensity in the filtered volume. In a similar way, negative dif-

ference values correspond to voxels near a boundary with a

lower density material because in the filtered volume their

intensities are lowered. Note that both positive and negative

values are important.

3.2. Implementation

The spatial importance map is the result of subtracting the

original model from the filtered model. Therefore, the main

step is the computation of the filtered volume model. To im-

plement the Gaussian blur we take advantage of the separa-

bility property of the 3D Gaussian function. That is, the 3D

Gaussian function can be separated into the product of three

1D functions. From a practical point of view, this means that

convolving thevolumewitha3DGaussianfunction isequiv-

alent to convolving the volume with a 1D Gaussian function

along one axis, then convolving the result again with a 1D

Gaussian function along another axis, and finally convolv-

ing this last result with a 1D Gaussian function along the

other axis. This results in a computationally cheaper imple-

mentation.

Moreover, we have to take into account another feature

of the Gaussian function in the implementation. The Gaus-

sian function extends infinitely at both sides, so we would

have to take into account the full image to compute the fil-

tered version of each voxel. In practice, though, values fur-

ther than 3σ are small enough to be negligible, so we can

clamp the function at that distance. In our implementation,

we have only one parameter regulable by the user, which

is the radius of the Gaussian kernel measured in pixels (see

Figure 2). Then, we define σ to be one third of the radius, so

that all the values inside the radius are significant. The val-

ues in the kernel are sampled from the Gaussian function at

the center of each voxel, and then we normalize them so that

they sum 1.

The method hasbeen implemented withCUDAto achieve

real-time performance. We take advantage of the fact that

both the filtering and the difference are parallelizable for

each voxel. The steps of the CUDA implementation are the

following:

1. Preparevolumedata converting ittofloating point values.

2. Copy volume data to a 3D CUDA array and bind a 3D

texture to it. This texture returns the real values (not

scaled), and is accessed with non-normalized texture co-

ordinates with clamp address mode and with nearest

neighbour interpolation, so that it works like an array.

3. Allocate space in global memory to store the result of the

filtering.

4. Compute the Gaussian kernel according to the radius and

copy it to global memory.

5. Filter the array data in the X axis.

6. Copy the result of the previous filtering to the volume 3D

array so it is the source in the next step.

7. Filter the array data in the Y axis.

8. Copy the result of the previous filtering to the volume 3D

array so it is the source in the next step.

9. Filter the array data in the Z axis.

10. Copy the original volume data again to the 3D array.

11. Subtract theoriginal volume fromthefilteredvolume (the

last result).

12. Copy the final result to host memory.

13. Clean up all allocated memory in the graphics card.

In Table 1, we collect the time required to compute the

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

(a) λ = −10

Figure 3: Color modulation driven by spatial importance map of the CT body with ambient lighting.

(b) λ = 0 (original)(c) λ = 10 (d) λ = 20

(a) λ = −5

Figure 4: Color modulation driven by absolute spatial importance map of the CT body with local lighting.

(b) λ = 0 (original) (c) λ = 5 (d) λ = 10

spatial importance map for the CT body, the CT head, and

the salmon considering different radii of the Gaussian ker-

nel. The 1D filter column reports the time to do a 1D convo-

lution with the kernel (this process has to be done once for

each axis). The Subtract column reports the time required

to do the subtraction. The Total column includes the time

to do the 3 convolutions, the subtraction, and all the other

additional operations like memory allocations and transfers

previously described.

3.3. Modulation and Illustration

As it is illustrated in Figure 1, once the spatial importance

map has been obtained it is integrated at the end of the visu-

alization pipeline to obtain different effects. The modulation

process considers the map and also the colors and/or opaci-

ties assigned by the illumination module to the volume. The

set of effects that can be obtained depends on the considered

parameters. Wecan use theraw importance values or convert

them to absolute values. In addition, we can consider apply-

ing the modulation to the color assigned to the voxel or to

the opacity. Moreover, we can use it to regulate the density

of the dots in a stipple rendering. In the next section, we give

a detailed description of the most representative effects.

4. Applications

To describe the different effects that can be obtained with

the proposed approach, we grouped them into three different

sections. First, we consider the modulation of the illumina-

tion model (effects on the colors), then the modulation of

the transfer function (effects on the opacities), and at last the

modulation of dot density in stippling. In all the following

examples, the radius of the Gaussian filter is 10.

4.1. Color modulation

Aswehaveshown inSection3.1,thespatialimportance map

containsinformationabout theboundaries distributedinpos-

itive and negative values, which can be interpreted as both

sides of boundaries. To emphasize them, importance values

can be used to modulate the color and contrast of the volume

dataset. We propose different strategies that differ in how we

consider the values of the map for the modulation. Being I

the color of a voxel, the first strategy for adding the spatial

importance value ∆D is by considering the raw values. In

this case, we apply

I′= I+∆D·λ,

(3)

where λ is a factor used to modulate the effect.

The second effect we obtain is by taking absolute impor-

tance values instead of the raw ones. In this case, we obtain

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

(a) original (b) kl= 0.5 (c) kl= 1(d) kl= 2 (e) kl= 5

Figure 5: Different opacity modulation effects with different parameters applied to the CT head model. (a) Original model, and

(b-e) with tl= 1, th= 1, kh= 1 and modifying the klparameter.

the final color with

I′= I+|∆D|·λ.

(4)

All these effects can be applied both to the ambient light-

ing or thelocal illumination. InFigure 3, we show the effects

obtained using original importance values and ambient light-

ing on the CT body. From left to right, the λ values are −10,

0, 10, and 20. In Figure 4, we show the effects on the same

model with local lighting and absolute importance values.

From left to right, the λ values are −5, 0, 5, and 10. Observe

that with raw values and a positive λ we obtain a darker im-

age, due to the fact that most values in the map are negative;

on the other hand, a negative λ produces a brighter image.

With absolute values, the darkening and brightening effects

are reversed because all the values are positive.

(a) original (b) kl= 1(c) kl= 2

Figure 6: Different opacity modulation effects using a de-

fault transfer function applied to the CT head model. (a)

Original model, and (b-c) with tl= 1, th= 1, kh= 1 and

modifying the klparameter.

4.2. Opacity Modulation

Now we describe how to modulate the opacity. In this case,

the idea is to use the information of the spatial importance

map to increase or decrease the opacity in order to empha-

size the most salient parts.

Being A(z) the opacity of the voxel z, we compute the new

opacity A′(z) by

A′(z) =

A(z)kl|∆D(z)|,

A(z)kh|∆D(z)|,

A(z),

if |∆D(z)| < tl,

if |∆D(z)| > th,

otherwise,

(5)

where tland thare the low and high thresholds respectively,

kland khare factors to regulate the effect of the modulation,

and |∆D(z)| is the absolute spatial importance value of the

voxel znormalized inthe range[0,1].Weuse absolute values

because we are interested in detecting the boundaries, and

both positive and negative values give this information.

In Figure 5, we illustrate the opacity modulation effects

applied to the CT head. Column (a) corresponds to the orig-

inal model without any modulation. Columns (b-e) are ob-

tained with tl= 1, th= 1, kh= 1 and klset to 0.5, 1, 2,

5. From Equation 5 we can see that khhas no influence on

the rendering since th= 1. Furthermore, since tl= 1, nearly

all voxels are multiplied by the spatial importance and the

weighting factor kl. As klincreases, more detailed informa-

tion about inner structures is captured.

Figure 6 shows that the same previous effects can be ap-

plied to the original model considering a default transfer

function that is obtained by linearly mapping intensities to

opacities and gray values. Note that the proposed approach

can be used for first explorations of a volume dataset since

no a priori knowledge is required.

4.3. Stippling

Stippling is an illustration technique in which the image is

drawn using dots. This technique has been simulated algo-

rithmically by several authors. Deussen et al. [DHvOS00]

applied half-toning techniques to arrive at an initial stipple

distribution and then interactively applied relaxation based

on centroidal Voronoi diagrams. Secord [Sec02] used a fast

probabilistic method in which stipples are automatically

packed more densely in dark regions and more sparsely in

lighter regions. Schlechtweg et al. [SGS05] created a multi-

agent system to position the stipples. Sousa et al. [SFWS03]

approximate stippling by using short, serrated ink strokes

modeled directly over the mesh’s edge.

In our approach, we propose to regulate the density of the

dots according tothe normalized absolute spatial importance

map |∆D|. We have two user-defined parameters: a threshold

t above which everything is white, and a factor f that regu-

lates the density scale. In addition, there is a random value

r(s) generated for each sample s in the ray casting. The color

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Marc Ruiz, Imma Boada, Miquel Feixas, and Mateu Sbert / Interactive volume illustration using intensity filtering

(a) t = 0.1, f = 5 (b) t = 0.1, f = 10(c) t = 0.1, f = 15 (d) t = 0.1, f = 20

Figure 7: Stipple rendering of the CT head modulated by the spatial importance map with different parameters.

(a) t = 0.03, f = 10(b) t = 0.03, f = 20(c) t = 0.1, f = 10 (d) t = 0.1, f = 20

Figure 8: Stipple rendering of the CT body modulated by the spatial importance map with different parameters.

of each sample C(s) is defined as

?

white,

black,

if |∆D(s)| ≥ t or f ·|∆D(s)| ≥ r(s),

if |∆D(s)| < t and f ·|∆D(s)| < r(s).

(6)

In Figures 7 and 8, this stippling effect has been used to

render the CT head and the CT body, respectively, consider-

ing different parameters. This effect can also be applied in

combination with the opacity modulation, as shown in Fig-

ure 9.

5. Conclusions

We have presented a new approach for obtaining illustrative

volume renderings. The method computes a spatial impor-

tance map that captures information about the most salient

parts of the model. This map is integrated in the visualiza-

tion pipeline allowing to modulate color and opacity values.

Such modulations have been used to obtain differenct ef-

fects that enhance volume data interpretation giving visual

clues about structures contained in the volume. In addition,

we have used the spatial importance map to modulate the

density of the dots in a stipple rendering.

In our future work, we will explore the use of other low-

pass filters, such as the trilateral filter, and evaluate how they

behave compared to the Gaussian filter.

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