Computing Local Thickness of 3D Structures with ImageJ

Abstract

The local thickness described by Hildebrand and Rüesgsegger can characterize a 3D binary image of a complex structure such as a bone, a cell, or a paper fiber [1]. Such images are available from, for example, micro-computed tomography [2]. Let 3 R W be the structure. The local thickness at point W p is the diameter of the largest sphere that contains p and is completely inside the structure.The problem is to transform the 3D binary image into the 3D local thickness image.Several steps to are given in [1]. The first is a Euclidean distance transformation (EDT) The distance map at W q , ( ) q D map , is the distance from q to the nearest background point. The sphere of radius ( ) q D map centered at q is completely inside the structure. If p is within this sphere, then the local thickness at p, ( ) p τ , is at least ( ) q D map . Points q are scanned to find ( ) p τ by maximizing this bound. A further simplification is to first remove many of the points whose spheres of radius ( ) q D map are completely contained within the corresponding spheres of other points. Removing all of the redundant points would produce the distance ridge (DR) which is related to the skeleton and the medial axis [1, 4].A 3D local thickness procedure has been implemented in Java as a plugin for ImageJ [5]. The EDT uses the fast algorithm given by Saito and Toriwaki [6]. The DR computation is a simplified form of a template scheme [7]. Care was taken to optimize the use computational resources. No temporary 3D buffers are required. A related implementation in C was given previously by Coeurjolly [8]

BoneJ: Free and extensible bone image analysis in ImageJ

“…Erodes an image to its medial axis, preparing it for skeleton analysis [27] Structure Model Index Calculates the structure model index (SMI) [14] Thickness Measures trabecular thickness (Tb.Th) and spacing (Tb.Sp) [10,28] Volume Fraction Measures volume fraction of bone (BV/TV) [15] For Whole Bones…”

Biodegradation of porous calcium phosphate scaffolds in an ectopic bone formation model studied by X-ray computed microtomograph

“…Once the different phases were segmented, volumes of the phases itself (bone volume and scaffold volume) were easily calculated counting the voxels in the specified segmented data range. Morphometric parameters, such as new bone and scaffold thicknesses, were evaluated according to (Dougherty and Kunzelmann, 2007), where the mean thickness and its distribution were calculated in a direct way and independently of an assumed structural model. Briefly, the computation of the thickness value was defined as the average of the local thickness at each voxel representing a given phase (new bone and scaffold).…”

A Simple Method to Measure Key Parameters of Soil-root Structure Using Medical X-ray Tomography Scanning Technique

“…Even the plug in Local thickness (Dougherty & Kunzelmann, 2007) gave the mean thickness of the main root. The 3D coordinates X, Y, and Z of the geometrical centre for each root were identified.…”

“…With images of the binaries, the main root thickness could be defined as the diameter of the most fitting sphere with centre P (x, y, z) onto the root structure. The plug in local thickness (Dougherty & Kunzelmann, 2007) gave the mean thickness of the main root and the thickness map is displayed at each point P of the root.The 3D coordinates X, Y, and Z of the geometrical centre for each root were identified. A thinning algorithm was applied to reduce iteratively the diameter of root until only a skeleton remained and available as a plug-in, 3D skeletonize, in ImageJ.…”