Scale and Resolution in Image and Data Analysis

- For New Levels of Innovation and Performance

The reasons why you should consider multiresolution methods are all to do with squeezing performance out of your work. The theory of wavelet and multiscale analysis is well-represented by a growing wealth of literature. What is equally if not more challenging is to demonstrably show that these new methods offer substantial improvements in your work. Check out the results of studies using these novel methods. You are sure to find case-studies close to your problem, and your data. MR/1 is unique in its support of many of the topics sketched out below.

Here are some of the ways you can keep a step - or more - ahead of the competition.

• Noise modelling. Among noise models supported are: Gaussian, and Gaussian and low-count Poisson models, typical of CCD detectors; sparse and low-count Poisson, typical of X-ray images, of point pattern data, and of document-term incidence data; non-stationary additive noise; stationary and non-stationary multiplicative noise; robust treatment of undefined stationary noise; speckle removal; and a locally adaptive strategy for undefined noise.

  Such noise modelling is part and parcel of all multiscale methods. You will find such comprehensive noise modelling in no other software package. Application domains include medical imaging, high-peformance image processing in physics and astronomy, surface analysis in materials science, ...

• Visualization of scientific and engineering data. MR/1 goes straight to the essentials in multiresolution visualization. Included are linear and B-spline à trous wavelet transforms, wavelet transforms of Mallat, Feauveau and Haar, pyramidal and redundant wavelet transforms, and a range of non-wavelet multiresolution transforms - morphological median, morphological min-max, pyramidal Laplacian, and various other methods.

  You can perform exactly the desired processing on the different resolution scales. Application domains include fluid dynamics, faint feature detection and measurement, handling variable background and superimposed information, ...

  The multiscale support image can be easily obtained - a very powerful visualization aid.

  Filtering. Many filtering methods can be used with these multiscale transforms. These include: hard, soft and iterative thresholding; median, average and B-spline filtering; and many more.

  2D image and 1D signals are covered by these methods.

  Image restoration or deconvolution or deblurring. Common methods are often notoriously user-unfriendly and badly behaved - denoising is an excellent way to regularize the result.

• Blob analysis and counting, multiple resolution object detection and characterization. Multiple resolution image segmentation. Multiple resolution edge detection.

• Image registration - the best spatial fit between two images of approximately the same scene, with various deformation models, and support for up to 2nd order interpolation of the fit.

  Applications to Earth observation images, or other images taken with different detectors, with or without the same image resolution.

• Image compression. Various multiscale and wavelet options are available, together with all-important noise-modelling. Decompression includes options for selective reconstruction of the image, allowing use as a tool for progressive transmission via the Web.

• IDL, PV-Wave routines. Many routines are available for IDL (Research Systems Inc.) and PV-Wave (Visual Numerics Inc.), interfacing the above-mentioned analysis methods and transforms.

• Utility programs are available for the following:
  • Image simulation based on a given image. The image can have random shot and/or Gaussian noise added, and can be blurred with a given instrument response function.
  • Mathematical morphology operations - erode, dilate, opening, closing, with different shapes and sizes of structuring elements.
  • Image thinning: determine the morphological skeleton of a 2-level (black and white) image.
  • Fast Fourier transform (FFT) on real or complex data.
  • Image conversion between a range of formats. Rescaling to 8 bits per pixel is performed for formats (e.g. GIF) requiring this. A 32-bit precision FITS format is fully supported in all routines, as is a simple format to accommodate data in byte, short integer, integer, floating and double precision floating formats.

MR/1 consists of some 100,000 lines of C++, and 5000 lines in IDL. MR/1 is a unique software package, offering innovative solutions for challenging image and data analysis problems.