Dendrogram Generation with IDL

There are currently several codes to generate dendrograms – we are working on unifying these packages. For now, we will look at the original IDL code written by Erik Rosolowsky, available here

Make sure this is in your IDL path

Also download this file, which is used in this tutorial.

First, read in the image:

im = mrdfits('demo.fits')

The code expects a binary mask – an array that has the same shape as the image, where each entry is 1 if that pixel is to be included in the output, and 0 otherwise. For now, lets just use the entire image, and create a mask of all 1s:

mask = byte(im * 0) + 1B

There are a few other important parameters:

• friends. This is used to control when a pixel is considered a local maximum (i.e., a leaf in the dendrogram). A pixel must be brighter than all of its neighbors within “friends” pixels. If the input is a 3D cube, then friends only applies to the first 2 dimensions.
• specfriends. Just like friends, but applies to the third dimension for 3D cubes.
• delta. The height of each leaf must be at least “delta” above its first merger
• minpix. Every leaf must contain at least minpix pixels before its first merger.
• minpeak. Every leaf must have an intensity of at least minpeak

We will use these values for now:

friends = 3
delta = 1.0
minpix = 10
minpeak = 5.0

We create the dendrogram with the Topologize procedure:

topologize, im, mask, friends = friends, delta = delta, minpix = minpix, minpeak = minpeak, /fast, pointer = ptr

This puts the output of the into a pointer variable ptr. For convenience, lets dereference that and store in a normal variable:

dendro = *ptr

Viewing the Dendrogram

The cloud-viz package provides some ability to view dendrograms. Simply invoke with:

dendroviz, ptr

to play around. More coming soon.

Description of Dendrogram Structure Fields

Lets examine the contents of the pointer output from topologize. The original code represents the dendrogram in a slightly cumbersome way, but there are at least several programs which save you from having to understand too much of what’s going on here:

IDL> help, *ptr, /struct
** Structure <192e208>, 21 tags, length=3610048, data length=3610041, refs=1:
 MERGER          DOUBLE    Array[49, 49]
 CLUSTER_LABEL   INT       Array[150801]
 CLUSTER_LABEL_H LONG      Array[98]
 CLUSTER_LABEL_RI
                 LONG      Array[60217]
 LEVELS          DOUBLE    Array[96]
 CLUSTERS        LONG      Array[2, 48]
 HEIGHT          DOUBLE    Array[97]
 KERNELS         LONG      Array[49]
 ORDER           LONG      Array[49]
 NEWMERGER       DOUBLE    Array[49, 49]
 X               LONG      Array[150801]
 Y               LONG      Array[150801]
 V               LONG      Array[150801]
 T               FLOAT     Array[150801]
 SZ              LONG      Array[5]
 CUBEINDEX       LONG      Array[150801]
 SZDATA          LONG      Array[5]
 ALL_NEIGHBORS   BYTE         0
 XLOCATION       DOUBLE    Array[97]
 NPIX            LONG      Array[49, 49]
 FAST            INT              1

Here’s what some of these fields describe:

• kernels : These list the 1D indices (of the input image) of the location of 49 local maxima. Each of these kernels defines a leaf in the dendrogram
• clusters: Describes which two structures merge at each merger in the dendrogram. The number of mergers is always one less than the number of kernels. clusters[*, i] lists the ids of the two structures that merge to form structure i + n_kernel (the first n_kernel structures are the leaves.
• merger : The [i,j] entry lists the intensity below which kernel i and j are contained within a single contour
• x : A 1 dimensional list of x locations in the original data. (Not all pixels are included, if the input mask contains zeros. This is cumbersome, I know)
• y : Like x
• v : The velocity, if the input image was 3 dimensional
• t : The intensity at each (x,y,v) location
• cluster_label : the ID of the highest (most leafward) dendrogram structure that each (x,y,v) point belongs to.
• cubeindex : the 1d index of each (x,y,v) location in the original cube
• height: The height of each structure in the dendrogram, for plotting. The height of the leaves is the intensity of the local maximum. The height of all other structures is the intensity of the relevant contour merger
• xlocation : The xlocation of each structure, for plotting. At the moment, this carries no physical meaning.