Gabor filter

A bandpass filter consisting of a Gaussian filter modified by a complex sinusoid. Gabor filters are useful for extracting multi-directional and multi-scale texture information.

g_σ,λ,γ,θ[k] = e−^{(X_θ2+γY_θ2)/2σ2 +j2πX_θ/λ}     [1]

where
σ - Standard deviation of the Gaussian envelope
λ - Wavelength of the sinusoidal factor
γ - Spatial aspect ratio, specifying the ellipticity of the support of the Gabor function
θ - Orientation of elliptic Gaussian axes at the orientation. We define θ to turn clockwise in the axial plane. X,Y - Image directions (X goes from left to right with increasing grid index values, Y goes from top to bottom with increasing grid index values)

and X_θ, Y_θ define the elliptic Gaussian axes at orientation θ via the 2D rotation matrix [cosθ sinθ; sinθ −cosθ].

Filter parameters

• Required

Sigma_mm : Gaussian smoothing width in mm
VoxelSize_mm: Voxel dimensions [dx, dy, dz] in mm (Note: Not required if using JSON settings file)
SpatialAspectRatio: Elongation of Gaussian mask
Orientation: Orientation in degrees (may be a vector)
Wavlength_mm: Wavelength of sinusoid

• Optional

Radius_mm.: Filter radius (default: OrientationAggregation.: "average", "max", or "std". Used to aggregate responses over a range of input orientations. ImagePlane.: "Axial" (default), "Sagittal" or "Coronal". Specify list of planes to approximate 3D computation. PlaneAggregation: "average", "max", or "std". Used to aggregate responses over input image planes.

• 3D implementation
  To approximate 3D filtering, a 2D Gabor filter is applied to each orthogonal plane, followed by averaging response maps across the planes.

Usage

Filters can be applied by manually creating a dictionary of parameters or passing them via JSON-format configuration files.

• Dictionaries are created using the syntax:

paramS.<parameter_name>.val = <value>;

where parameter_name is one of the supported filter parameters listed above and value, one of the associated arguments.

• Sample filter configuration
  The following settings can be used to (1) apply Gabor filters at a number of orientations and return their average. This examples shows a filter with σ= 5mm, λ=2mm, γ=1.5, θ=π/8, π/4,...,2π radians, applied after cropping around the specified structure and padding by 10 voxel widths, and (2) calculate first-order statistics from the filtered image.

{

"structures": ["ROI"],

"imageType": {
  		  "Gabor": {
			    	"Sigma_mm": 5,
				"Wavlength_mm": 2,
                                "SpatialAspectRatio": 1.5,
                                "Orientation":[22.5,45,67.5,90,112.5,135,157.5,180,202.5,225,247.5,270,292.5,315,337.5,360],
                                "OrientationAggregation": "average",
                                "ImagePlane": "Axial"
			   }
	    },

"settings": {		   

                   "padding": {
                                "cropToMaskBounds": "yes",
                                "method": "mirror",  
                                "size": [10,10,0]
                              },

                   "firstOrder": { 
				     "offsetForEnergy": 0,
                                     "binNumhEntropy":64
                                 }
                              
	    }

}

• Modification for 3D implementation
  To approximate 3D filtering, a 2D Gabor filters is applied to each orthogonal plane, followed by averaging response maps across the planes.

"imageType": {
  		  "Gabor": {
			    	"Sigma_mm": 5,
				"Wavlength_mm": 2,
                                "SpatialAspectRatio": 1.5,
                                "Orientation":[22.5,45,67.5,90,112.5,135,157.5,180,202.5,225,247.5,270,292.5,315,337.5,360],
                                "ImagePlane": ["Axial","Sagittal","Coronal"],
                                "PlaneAggregation": "average"
			   }
	    }

Configurations are parsed and converted to parameter dictionaries using

paramFile = 'Path/to/config_file.json'
paramS = getRadiomicsParamTemplate(paramFile);

Generating filtered images

global planC
strNum = 1;
scanNum = [];  % leave empty when passing structNum to automatically identify associated scan index
planC = generateTextureMapFromPlanC(planC,scanNum,strNum,paramS)

Extracting radiomic features

global planC
scanNum  = 1;
strNum = 2; 
featureS = calcGlobalRadiomicsFeatures(scanNum, structNum, paramS, planC);

References

1. IBSI reference manual