Processing HI cube - II

A) We now have a cube V_los(x,y,z)

1. Compute V_min and V_max (extrema) of V_los matrix,
2. Create new array V_obs, where velocity values (V_los) range from V_min to V_max, in steps of 1 km/s,

B) We want an output image matrix, OUT(x,y,z), where x_i corresponds to V_obs(i)

1. Scan the V_los(x,y,z) matrix; say, V = V_los(x,y,z)
2. If V1 < V < V2, then OUT(v,y,z) += rho(x,y,z)
   
3. Repeat a & b for energy and pressure.

Processing HI cube - I

Computing the orientation of each cell w.r.t. the central pixel

We would like to keep the simulation cube at a distance d (element: X=0, YMAX/2, ZMAX/2 is at a distance d).

Now, we compute angle subtended by all cells, and compute differential rotation velocity as per Brand and Blitz (1991).



1) Read velocity cubes Vxx,Vyy,Vzz

a) Compute projects of components of V_rot (due to galactic rotation) along the los.
b) Compute projection of velocities Vxx, Vyy & Vzz along the line of sight (los)
c) V_los = V_rot + components from step a


Formulae

a)
tan(theta) = y / (d+x)
(D * D) = (d+x)^2 + (y*y)

R' = sqrt ( D^2 + R^2 + 2*R*D* cos(theta+L)

Compute V(R') using Brand & Blitz (1991)

R" = D sin(theta + L)
phi = 90 - (theta+L)
phi" = arccos(R"/R)

V_rot = V(R') * cos(90 - (phi+phi") ) = V(R') * cos(theta + L - phi)

b)
theta = arctan(y / (d+x) )
V"yy = Vyy cos(theta)
V"xx = Vxx sin(theta)

chi = arctan(z/ (d+x) )
V"zz = Vzz cos(chi)

c) v_los (x,y,z) = V"xx + V"yy + V"zz + V_rot

Fractals and image characterisation

Some links are in order

1. Fractal Dimension: Wikipedia
   
2. A course on Fractals in Yale U
3. A course on Fractal dimension from images: Munich U
4. Fractal Dimension explained
   

So, once you know about fractal dimensions, come to read the stuff on the right (Conti, 2001)


One can treat the image 3-D object. Compute the total number of occupied boxes in X-Y-I dimension box, as a function of size of the box. D = ln(number)/ ln(radius).

It is a little bit more complicated. Check the paper by Conci, a PPT talk can also be found.

How to distinguish between landscape and portrait pictures?

1. Perhaps we can search for a large number of pixels with same natural colors: green, blue and black (shadows). look if a large fraction of pixels contain the same 'Hue' and 'Saturation'.
2. Another try: Look at the Fourier spectra of images, and mark radii of 60%, 90%, 99%, 99.9% power. they should be distinct for landscape images and facial portraits or nearby objects.
   
3. Human objects have a lot more symmetry than the natural objects. In fact, there could be some fractal pattern seen over the different length scales of an image of a natural scenery. Try to capture 'fractal' properties of pixels.

speaking of the last one: one could look at fractal dimension of a picture pixel values. How? Perhaps in the next blog post...