HiPS utilizes the HEALPix framework and uses it for mapping a sphere (in this case, part of a sky) and compiles / transforms it into tiles and pixels. Of course, this is in context of astronomical data. HiPS emphasizes on usability thus it tries abstract the scientific details while preserving them. This can be further built upon for statistical analysis of large datasets. Thus, first a brief overview of HEALPix is given below before moving onto HiPS.
Introduction to HEALPix
HEALPix, an acronym of ‘Hierarchical Equal Area isoLatitude Pixelization of a sphere’, is a framework for discretizing high resolution data. The software is available in C, C++, Fortran90, IDL, Java, and Python. It extends a data structure (with a library), for each language. The main features provided by the software are:
- Pixel manipulation
- Spherical Harmonics Transforms
- Input / Output (supports FITS files)
In a nutshell, the pixelization procedure subdivides a spherical sphere in which each pixel is equidistant from the origin - meaning it covers the same surface area. This produces a HEALPix grid, whose interesting property is that pixels are distributed on lines of constant latitude. Due to this iso-latitude distribution of pixels the complexity for computing integrals over each harmonics is N1/2.
HEALPix provides a standard format on how to store data in FITS files. There are numerous software packages that can work with HEALPix data. For this project,
healpy will be used which is built on the HEALPix C++ package. But there are others, e.g. in Aladin Lite. The main functionality needed for this project is HEALPix pixel index to sky coordinate transformation (back and forth), and one or two methods to list HEALPix pixels in a given region of the sky (e.g.
Pixel numbering schemes
HEALPix provides two numbering schemes for pixels, namely the RING scheme and NESTED scheme.
- RING scheme In this scheme the pixels are counted down from north to south along each iso-latitude ring.
- NESTED scheme This scheme arranges the pixels into 12 tree structures with respect to their base-resolution pixels.
Introduction to HiPS
HiPS is the hierarchical tiling mechanism which allows one to access, visualize and browse seamlessly image, catalogue and cube data. The original HiPS paper can be found here.
The multi-resolution representation of original images provides the basis for visualizing data in a progressive way as the pixels that are required for a given view can be accessed through pre-computed HEALPix maps, and the nested pixel numbering scheme provides a simple hierarchical indexing system that encodes pixel inheritance across different orders.
HiPS scheme groups pixels into different tiles. The general relationship between tiles and pixels is that a tile with
n-tile pixels along each side forms a HEALPix mesh of order ktile. Tiles store map information from HEALPix. These tiles are presented as square arrays and it is possible to store them in different file formats. The files are organized into different directories. Here tiles are used as files and tile orders are used for grouping data in directories - all following a naming convention. For more information on the method on file storage, this document can be viewed, written by Pierre Fernique.
Using the header
hips_pixel_bitpix the HiPS pixels are stored in BITPIX code.
hips_pixel_bitpix refers to the data type used to store the FITS tile (a value of 8 means 8-bits integers, -32 means simple floating points, -64 double precision floating points).
This is usually the same value as the BITPIX value of the original images (described in keyword data_pixel_bitpix), but might be different, notably for HiPS built from heterogeneous origins.
The BITPIX value is always present in the HiPS FITS tiles.
As it is cumbersome to transfer each pixel (essentially a file), so HiPS scheme groups pixels into different tiles. The general relationship between the tiles and pixels is that a tile with n-tile pixels along each side forms a HEALPix mesh of order of k-tile. A HiPS tile is show below.
The way HiPS represents images is by resampling them onto a HEALPix grid at the maximum desired order, say kmax. Then it generates tile images for tile orders. When mosaicking / stitching images, the angular resolution is taken into account. There are various methods for filling the data region when stitching images and dealing with background difference. The kmax chosen earlier determines minimum pixel size which is near to the angular pixel size or the resolution of original data.
Next important thing is whether to emphasize on
display quality or
photometric accuracy, which depends on our use case. Image encoding can be done either in FITS, PNG, or JPG file format. For most cases it is enough to only generate FITS and PNG files. The lowest order pixel values correspond to a large area of the sky. The HiPS indexing structure takes care of mapping correct tiles onto a display.
HiPS generation for huge amounts of data such as the Hubble Space Telescope requires planning of system growth.
A HiPS catalogue contains the RA / DEC coordinates stored in a TSV file. The data is ASCII tab separated and is organized in various directories the same way as HiPS images.
Google Summer of Code project
The coding period is about to begin. My future blog posts will be based around this topic.