Lecture overview. Visualisatie BMT. Transparency. Transparency. Transparency. Transparency. Transparency Volume rendering Assignment

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1 Visualisatie BMT Lecture overview Assignment Arjan Kok 1 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 Compositing R = A s R s + (1 A s ) R b G = A s G s + (1 A s ) G b B = A s B s + (1 A s ) B b A = A s + (1 A s ) A b RGBA R s G s B s A s Important Render object in correct order: from back to front R b G b B b A b 3 4 Wrong rendering order: BRG (0.8, 0, 0, 0.5) (0, 0.8, 0, 0.5) (0, 0, 0.8, 0.5) (0.8, 0, 0, 0.5) (0, 0.8, 0, 0.5) (0, 0, 0.8, 0.5) (0.4, 0., 0.1, 0.875) (0, 0.4, 0., 0.75) (0, 0, 0.4, 0.5) (0, 0, 0, 0) (0.4, 0.0, 0., 0. 75) (0.3, 0., 0.175, 0.875) (0, 0, 0.4, 0.5) (0, 0, 0, 0) (0, 0, 0, 0) (0, 0.4, 0, 0.5) (0., 0.4, 0, 0.75) (0.1, 0., 0.4, 0.875) C s = (0.4, 0, 0., 0.75) 5 C b = (0, 0.8, 0, 0.5) 6 1

2 Visualization of volumetric data Scalar values in a regular 3D grid Applications Biomedical imaging CT or MRI scanners Ultrasound studies Meteorology Weather prediction Astrophysics 7 8 Volume Generation of intermediate geometric representation (points, lines, polygons) e.g. Marching Cubes Volume rendering direct volume visualization Surface renderer Volume renderer Surface rendering Shows surfaces at discrete values (isovalues) Shows continuous fields in 3D Enables to see through the data Data is seen more directly; less likely to miss details 9 10 Volume rendering Volume rendering methods Image-order Object-order Projection types (ray functions) Maximum intensity projection Average projection Distance projection projection (compositing) 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) image plane 11 volume 1

3 During tracing ray we must sample the volume Sample the volume at uniform intervals Evaluate at intervals t along ray Use a discrete representation of the line Evaluate at each encountered voxel Uniform sampling algorithm t = t1 initialize v while (t < t) { x = x0 + a*t y = y0 + b*t z = z0 + c*t v = EvaluateFunction(v, t) t = t + t Interpolation function Object-order volume rendering Object space (= data set) is traversed For each voxel Determine projection position Process data (using voxel and image information) image plane 17 volume 18 3

4 Object-order volume rendering Volume rendering Volume rendering methods Image-order Object-order Projection types (ray functions) Maximum intensity projection Average projection Distance projection projections (compositing) 19 0 Maximum intensity projection Image pixel is set to maximum sample value along ray Simple(st) Provides intuitive understanding of data No depth cues Average projection Image pixel is set to average value along ray Simple Provides less intuitive understanding of data No depth cues 1 Distance projection Projections Image pixel is set to distance of closest voxel with value larger than requested distance (thresholding) Simple Depth cues Iso-surface projection 3 4 4

5 projections Goal of visualization Classification of objects Selection of objects projections Basic model: Each point in the volume transmits and emits light Volume classification can be done by transfer functions t Opacity and emission along ray: Opacity: (t) Emission: (t) 5 6 projections projection I bg Back-to-front Alpha-compositing Back to front Front to back I pixel ρ( t ) = I(t ) = and α( t 0 ) = Ibg I (t ) = α(t ) ρ(t ) + (1 a(t ))I(t ) I 1 (t ) = α(t ) ρ(t ) + (1 a(t ))I(t ) I = I 0 for i = 1.. N do I = i i + (1- i ) I I = 0 T = 1 for i = N.. 1 do I = I + i i T T = (1- i ) T I = I + T I 0 I(tn ) = α(tn ) ρ(t n ) + (1 a(tn ))I(t n 1) N samples: N Ipixel = α(ti ) ρ(ti ) (1 α(t j)) i= 0 N j= i Transfer function Transfer function - opacity Transfer functions Assign opacity (), and emission () to points Opacity () Scalar value How do we assign opacity () to points? Scalar value Gradient magnitude How do we assign emission () to points? Scalar value Illumination 9 Gradient magnitude Large gradients indicate change of material f (x + x, y,z) f (x x, y,z) x f (x, y + y,z) f (x, y y,z) G(x, y,z) = y f (x, y,z + z) f (x, y,z z) z 30 5

6 Transfer function - emission Emission () Scalar value to color (I or RGB) Illumination Include lighting effects Emission () depends on illumination L g(x, y,z) N = g(x, y,z) n ( k (N L ) + k (V R ) ρ = ka Ia + Ii d i s i) i 31 3 Illumination Intermixing volume rendering and surface rendering Get the best from both techniques in the same picture (bone) Surface rendering (skin) Clipping Assignment Rendering not to generate image Rendering to generate structured point datasets 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

7 Assignment Use uniform sampling Step size t equal to distance between nodes No interpolation needed; use node values (If accuracy not sufficient: use 0.5 t) t Example max projection x-min // generate scalar field to store results.. for (int j = 0; j < dims[1]; j++) { for (int k = 0; k < dims[]; k++) { // y-direction // 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 Assignment Questions 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: D(i + 1, j,k) D(i 1, j,k) D(i, j+ 1,k) D(i, j 1,k) G(i, j,k) = D(i, j,k + 1) D(i, j,k 1)