IMAGES

Using Digital Images in FracLac

Introduction

Images must be openable by ImageJ (e.g., jpg, tiff, png, gif), already in or convertible to grayscale or binary format, and amenable to pattern extraction.

If you can convert your images to a format ImageJ opens, the types of patterns you can use FracLac to objectively quantify include:



Preprocessing - Image Preparation

Sometimes images are ready for analysis immediately—for binary fractal contours or other control images, often the only information in an image is the pattern of interest itself.

But in other cases, pattern extraction may involve considerable preprocessing using ImageJ or other image processing software to threshold, subtract background, dilate, trace or find edges automatically or manually, etc.

The technique to prepare an image for analysis ultimately depends on the feature deemed of interest, the type of analysis, and the type of image (e.g., grayscale or binary, contour or texture, etc.).



Extracting Patterns to Analyze with FracLac

Patterns Extracted from Retinal Vessels Image

<html>Colour image of my retina along with 3 patterns<br/> extracted from it: binarized (the starting point, <br/> which is a filled silhouette), skeletonized, and outlined.

Colour image of retina along with 3 patterns extracted from it: binarized (the starting point, which is a filled silhouette), skeletonized, and outlined.

First decide which features are important and how you want to study them. The questions being asked determine how images will be prepared. The group of images above shows an original picture of retinal vessels, and 3 alternatives for analyzing the image: a binarized pattern (the starting point, which is a filled silhouette), a skeletonized pattern, and an outlined pattern.

The silhouette and contour patterns highlight branching in the retinal vessels in terms of changing length and diameter. To make them, the image was converted to binary and further to a one pixel wide contour using thresholding and ImageJ » Process » Binary » Make Binary » Outline.

The skeletonized pattern highlights vessel branching in terms of length but not diameter. It was made by skeletonizing the binarized image using ImageJ » Process » Binary » Skeletonize).



Often the same object may have more than one feature amenable to fractal analysis. In general, binarizing (thresholding to black and white), outlining, etc. are often appropriate if 1) the feature being studied is a contour (a cellular outline, fractal contour, or a control figure such as a circle) and 2) the method being used is a regular box counting scan.

However, preprocessing all images using the same set of steps is not always appropriate - such as for the images of biological cells shown here. As illustrated in the separate image of the nucleus, for instance, a method might remove detail that is noise to one investigation but critical to another.

The image was acquired using a light microscope with digital camera attached. It illustrates a stained neuron prepared for fractal analysis in two ways, highlighting different features of the same cell that would be studied in different ways.

Patterns Extracted from an Image of a Neuron

<html>One image of a neuron with <br/> several patterns extracted from it.
  1. The original image (bottom, left)
  2. That image grayscaled
  3. The nucleus cropped and extracted for a grayscale texture analysis (left of centre)
  4. The grayscaled image thresholded and outlined to a single pixel wide contour of the entire cell separate from the background, suitable for a binary box counting analysis (top, right).


ROIs

FracLac will analyze whole images and selections (ROIs) on images. Once an image is prepared, relevant ROIs can be selected and analyzed.

For grayscale images, the area outside of the selection will be filled with a filler colour that is ignored by grayscale processing. Grayscale images can be converted to RGB and irrelevant areas filled with non-gray values to tell FracLac to ignore those portions, or ROIs can be selected and FracLac will auto fill them.

You can also preload a set of ROIs, or scan using subscans or the ParticleAnalyzer.



Should I use Control Images?

Whenever possible, use control images. Although theoretical fractal dimensions do not depend on scale, digital images do. The patterns they represent are imperfect and limited by computer screen resolution and a myriad of other factors. Thus, testing images of known fractal dimension and lacunarity can provide a benchmark for your analyses.

To do this, you can make simple contours and shapes (i.e., lines, circles, etc.) easily in most digital imaging software including ImageJ (e.g., in ImageJ, create a new image, select a square or round ROI on the blank image, then select ImageJ » Edit » Draw).

Canonical Fractals: You can generate theoretical fractal images of known fractal dimension using software that lets the user specify line width, level of detail, size, etc. (e.g., see the Koch fractal and 32-segment quadric fractal).

The list below has addresses for fractal generating plugins designed for use with FracLac for ImageJ freely available from the NIH website, and a free standalone program:

Branched Cell With Known Scaling Parameters

<html>Image generated with MicroMod and <br/>analyzed using the Sub Scanner.

Microglial cell model simulated with known scaling features in MicroMod.



Although many images shown here are illustrated in colour, they can be generated in grayscale or binary formats. Generate control images in the format (binary or grayscale) they are going to be analyzed in to minimize loss and distortion of information during preprocessing.



Tips:

For binary scans, use control images of comparable size to the ones to be analyzed, showing rectangles, squares, circles, triangles, etc., as well as known fractals and multifractals.

Benchmark testing using a standard scan in FracLac has generally been 1-5% from theoretical for standard binary images ranging from 100 to 900 pixels in diameter.

There are practical upper and lower limits on size. Larger images tend to be closer to theoretical, and the smallest and most detailed generally deviate most from theoretical.



Digitization and Artefacts

Digitization is another practical issue to consider. Simple contours have a theoretical fractal dimension of 1.0, and filled planes of 2.0. However, a computer screen represents images using a grid of pixels which limits how precisely a pattern can be represented. Thus, even the simplest patterns, such as circles and lines are approximated in digital images, and as a result, calculated values of the Dʙ do not always match theoretical for even the simplest images.

The image below illustrates how this manifests when a circle is analyzed, especially when it is considered in distinct parts. At different sizes, an image of a circle appears round, but as seen in the scaled up image , curves and diagonal lines in digital images are approximated. When a circle is scanned using box counting, the overall Dʙ is generally around 1.02. This is attributable to variation over the pattern owing to the limitations of digital imaging. In particular, each part of the image is constructed from a grid with a 1 pixel limit of resolution, rather than being truly rounded. If considered separately, different pieces of the pattern can be shown to vary from theoretical depending on where the piece is taken from within the image (see figure below).

Local Variation in a Simple Contour Owing to Digitization

<html>Variation in the D<sub>F</sub> over a simple one pixel wide<br/> circular line revealed by sub area scanning

Variation in the DF over a simple one pixel wide circular line is revealed by sub area scanning.

Setting the Scaling

Furthermore, owing to the limitations of digital processing and the methods used in FracLac, the dimension for even a "perfect" filled rectangle, free of digital artifacts as are found in circles, can deviate from the theoretical of 1.00 or, alternatively, be that value, depending on the settings used for the analysis.

The series of box sizes can be especially important for determining fractal dimensions when scaling relationships are known ahead of time, as is generally the case with some of the control images that would be used in an analysis.

As an example, using the default settings, FracLac will generally yield results close to theoretical for many fractals of known dimension, but if set up with a priori knowledge of the scaling in a pattern, the results can be very, very close. Indeed, FracLac will calculate a perfect 1.00 for a line drawing of a square if it is told the scaling rule ahead of time, but the result for the same image will be different using the default settings. To set FracLac up to use a priori knowledge of the scaling in a square line drawing, set it to sample the image using a series scaled by 1/2, with the maximum box size set to 1/2 the image size at a full integer value and the minimum also set to a full integer value scaled down from that size. Alternatively, use a custom list that scales the same way (e.g., for a 400 pixel wide square, use boxes of 200, 100, 50, and 25 pixels).



HOME