Visualisatie BMT Volume visualization Arjan Kok a.j.f.kok@tue.nl - - PowerPoint PPT Presentation

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Visualisatie

BMT

Volume visualization Arjan Kok a.j.f.kok@tue.nl

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Lecture overview

• Transparency
• Volume rendering
• Assignment

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Transparency

• Makes it possible to see inside or behind objects
• Complement of transparency is opacity
• Opacity defined by alpha value with range [0,1]
• Alpha = 1:

Completely opaque

• Alpha = 0:

Completely transparent

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Transparency

• Compositing
• R = As Rs + (1 – As) Rb
• G = As Gs + (1 – As) Gb
• B = As Bs + (1 – As) Bb
• A = As + (1 – As) Ab
• Where s refers to the surface of the object,

while subscript b refers to what is behind the obj

• 1-As is called the transmissivity, the amount of light that is

transmitted through the actor

• Important
• Render object in correct order: from back to front

RGBA RbGbBbAb RsGsBsAs

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Transparency

(0.8, 0, 0, 0.5) (0, 0.8, 0, 0.5) (0, 0, 0.8, 0.5)

(0, 0, 0, 0) (0, 0, 0.4, 0.5) (0, 0.4, 0.2, 0.75) (0.4, 0.2, 0.1, 0.875) (0.1, 0.2, 0.4, 0.875) (0.2, 0.4, 0, 0.75) (0, 0.4, 0, 0.5) (0, 0, 0, 0)

We have to sort the obj from back to front and then render them in that order !!

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Transparency

• Wrong rendering order: BRG

(0.8, 0, 0, 0.5) (0, 0.8, 0, 0.5) (0, 0, 0.8, 0.5)

(0, 0, 0.4, 0.5) (0, 0, 0, 0) (0.3, 0.2, 0.175, 0.875) (0.4, 0.0, 0.2, 0. 75)

Cs = (0.4, 0, 0.2, 0.75) Cb = (0, 0.8, 0, 0.5)

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Surface Graphics

• Traditionally, graphics objects are modeled with surface

primitives (surface graphics).

• Continuous in object space

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Difficulty with Surface Graphics

• Volumetric object handling
• gases, fire, smoke, clouds (amorphous data)
• sampled data sets (MRI, CT, scientific)
• Peeling, cutting, sculpting
• any operation that exposes

the interior

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Volume Graphics

• Defines objects on a 3D raster, or discrete grid in object

space

• Raster grids: structured or unstructured
• Data sets: sampled, computed, or voxelized
• Peeling,cutting … are easy with a volume model

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Volume Graphics & Surface Graphics

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Volume Graphics Applications (simulation data set)

• Scientific data set visualization

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More Volume Graphics Applications (artistic data set)

• Amorphous entity visualization
• smoke, steam, fire

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Volume visualization

• Surface rendering
• Shows surfaces at

discrete values (iso- values)

• Volume rendering
• Shows continuous

fields in 3D

• Enables to see through

the data

• Data is seen more

directly; less likely to miss details

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Volume rendering

Volume rendering methods

• Image-order (“ray casting or ray tracing”)
• Object-order
• Projection types (ray functions)
• Maximum intensity projection
• Average projection
• Distance projection (compute the distance along the ray

at which a scalar value at or above val is first encountered)

• Transparency projection (alpha compositing)

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Ray Traversal Schemes

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Image-order volume rendering

• Ray casting
• Image space is traversed
• For each pixel one or more rays are fired into the volume
• Process the data along the ray (using a projection function)

volume image plane

Base plane

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Image-order volume rendering

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Image-order volume rendering

• During tracing ray we must sample the volume
• Sample the volume at uniform intervals
• Evaluate at intervals Δt along ray
• Use a discrete representation of the line
• Evaluate at each encountered voxel

a,b,c, - the normalized ray direction vector

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Image-order volume rendering

• Uniform sampling algorithm

t = t1 // distance where the ray enter the volume initialize v while (t < t2) { // distance where the ray exits the volume x = x0 + a*t y = y0 + b*t z = z0 + c*t v = EvaluateFunction(v, t) t = t + Δt }

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Image-order volume rendering

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Image-order volume rendering

• Interpolation function

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Object-order volume rendering

• Object space (= data set) is traversed
• For each voxel
• Determine projection position on the view pane
• Process data (using voxel and image information)

volume image plane

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Object-order volume rendering

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Volume rendering

Volume rendering methods

• Image-order
• Object-order
• Projection types (ray functions)
• Maximum intensity projection
• Average projection
• Distance projection
• Transparency projections (compositing)

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Maximum intensity projection

• Image pixel is set to

maximum sample value along ray

• Simple(st)
• Provides intuitive

understanding of data

• No depth cues

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Average projection

• Image pixel is set to

average value along ray

• Simple
• Provides less intuitive

understanding of data

• No depth cues

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Distance projection

• Image pixel is set to

distance of closest voxel with value larger than requested distance (thresholding)

• Simple
• Depth cues
• Iso-surface projection

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Projections

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Transparency projections

• Goal of visualization
• Classification of objects
• Selection of objects
• Volume classification can be done by transfer functions

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Drebin, et. al.

Original CT Data Fat Tissue Bone Density Color and Opacity Strength Gradient NX NY NZ Shaded Transformed Final Image

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Transparency projections

• Basic model: (we want to understand structure !!)
• Each point in the volume transmits and emits light
• Opacity and emission along ray:
• Opacity:

α(t)

• Emission:

ρ(t)

t

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Transparency projections

• Back-to-front
• Alpha-compositing
• and

bg

I ) t ( I ) t ( = = ρ

Ipixel Ibg

) t ( I )) t ( a 1 ( ) t ( ) t ( ) t ( I

1 n n n n n −

− + ρ α =

1 ) t ( 0 = α

) t ( I )) t ( a 1 ( ) t ( ) t ( ) t ( I

1 2 2 2 2

− + ρ α = ∏ α − ρ ∑α =

+ = = N 1 i j j i N i i pixel

)) t ( 1 ( ) t ( ) t ( I

N samples:

) t ( I )) t ( a 1 ( ) t ( ) t ( ) t ( I

1 1 1 1

− + ρ α =

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Transparency projection

• Back to front

I = I0 for i = 1 .. N do I = ρi αi + (1- αi) I

• Front to back

I = 0 T = 1 for i = N .. 1 do I = I + ρi αi T T = (1- αi) T I = I + T I0

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Transfer function

• Transfer functions
• Assign opacity (α), and emission (ρ) to points
• How do we assign opacity (α) to points?
• Scalar value
• Gradient magnitude
• How do we assign emission (ρ) to points?
• Scalar value
• Illumination

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Transfer function - opacity

• Opacity (α)
• Scalar value
• Gradient magnitude
• Large gradients indicate change of material

                ∆ ∆ − − ∆ + ∆ ∆ − − ∆ + ∆ ∆ − − ∆ + = z 2 ) z z , y , x ( f ) z z , y , x ( f y 2 ) z , y y , x ( f ) z , y y , x ( f x 2 ) z , y , x x ( f ) z , y , x x ( f ) z , y , x ( G

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Transfer function - emission

• Emission (ρ)
• Scalar value to color (I or RGB)

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Illumination

• Include lighting effects
• Emission (ρ) depends on illumination

        = ) z , y , x ( g ) z , y , x ( g N L

( ) ∑ ⋅ + ⋅ + = ρ

i n i s i d i a a

) R V ( k ) L N ( k I I k

V is the direction of the specular reflection

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Illumination

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Volume visualization

• Intermixing volume rendering and surface rendering
• Get the best from both techniques in the same picture
• Volume rendering

(bone)

• Surface rendering

(skin)

• Clipping

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Assignment

• Volume rendering
• Rendering not to generate image
• Rendering to generate structured point datasets

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Assignment

• Create 6 images (structured point datasets)
• For each side of dataset

(xmin, xmax, ymin, ymax, zmin, zmax)

• Do same volume rendering projections on each side
• Use parallel projection

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Assignment

• Use uniform sampling
• Step size Δt equal to distance between nodes
• No interpolation needed; use node values
• (If accuracy not sufficient: use 0.5 Δt)

Δt

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Example max projection x-min

// generate scalar field to store results .. for (int j = 0; j < dims[1]; j++) { // y-direction for (int k = 0; k < dims[2]; k++) { // z-direction double max = 0.0; for (int i = 0; i < dims[0]; i++) { // projection (ray) max = Math.max(max, scalars.getScalar(i, j, k)); } // store max value in scalar field .. } }

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Assignment

• Experiment with the projection types
• Experiment with transfer functions
• Use of scalars and gradients to compute opacity
• Use different colors for different objects
• Experiment with illumination, clipping, ..
• Reminder:

                − − + − − + − − + = 2 ) 1 k , j , i ( D ) 1 k , j , i ( D 2 ) k , 1 j , i ( D ) k , 1 j , i ( D 2 ) k , j , 1 i ( D ) k , j , 1 i ( D ) k , j , i ( G

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Questions