Added 2D Gabor filter (#57)

* Added function to construct 2D Gabor kernel.

* Modified gabor function to include imaginary part of the filter.

* Added tests for gabor filter function.

* Modified gabor function and placed validate_gabor outside of gabor.

* Added warnings for cases when size_x or size_y is not positive.

* Added test cases for errors/exceptions.

src/ImageFiltering.jl

@@ -53,7 +53,7 @@ ArrayLike{T} = Union{ArrayType{T}, AnyIIR{T}}
 
 include("kernel.jl")
 using .Kernel
-using .Kernel: Laplacian, reflect, ando3, ando4, ando5, scharr, bickley, prewitt, sobel
+using .Kernel: Laplacian, reflect, ando3, ando4, ando5, scharr, bickley, prewitt, sobel, gabor
 
 NDimKernel{N,K} = Union{AbstractArray{K,N},ReshapedOneD{K,N},Laplacian{N}}
 

src/kernel.jl

@@ -11,6 +11,7 @@ dimensionality. The following kernels are supported:
   - `DoG` (Difference-of-Gaussian)
   - `LoG` (Laplacian-of-Gaussian)
   - `Laplacian`
+  - `gabor`
 
 See also: [`KernelFactors`](@ref).
 """
@@ -295,7 +296,7 @@ end
 """
     Laplacian((true,true,false,...))
     Laplacian(dims, N)
-    Lacplacian()
+    Laplacian()
 
 Laplacian kernel in `N` dimensions, taking derivatives along the
 directions marked as `true` in the supplied tuple. Alternatively, one
@@ -328,6 +329,67 @@ function Base.convert(::Type{AbstractArray}, L::Laplacian{N}) where N
 end
 _reshape(L::Laplacian{N}, ::Type{Val{N}}) where {N} = L
 
+
+"""
+    gabor(size_x,size_y,σ,θ,λ,γ,ψ) -> (k_real,k_complex)
+
+Returns a 2 Dimensional Complex Gabor kernel contained in a tuple where
+
+  - `size_x`, `size_y` denote the size of the kernel
+  - `σ` denotes the standard deviation of the Gaussian envelope
+  - `θ` represents the orientation of the normal to the parallel stripes of a Gabor function
+  - `λ` represents the wavelength of the sinusoidal factor
+  - `γ` is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function
+  - `ψ` is the phase offset
+
+#Citation
+N. Petkov and P. Kruizinga, “Computational models of visual neurons specialised in the detection of periodic and aperiodic oriented visual stimuli: bar and grating cells,” Biological Cybernetics, vol. 76, no. 2, pp. 83–96, Feb. 1997. doi.org/10.1007/s004220050323    
+"""
+function gabor(size_x::Integer, size_y::Integer, σ::Real, θ::Real, λ::Real, γ::Real, ψ::Real)
+
+    σx = σ
+    σy = σ/γ
+    nstds = 3
+    c = cos(θ)
+    s = sin(θ)
+
+    validate_gabor(σ,λ,γ)
+
+    if(size_x > 0)
+        xmax = floor(Int64,size_x/2)
+    else
+        warn("The input parameter size_x should be positive. Using size_x = 6 * σx + 1 (Default value)")
+        xmax = round(Int64,max(abs(nstds*σx*c),abs(nstds*σy*s),1))
+    end
+
+    if(size_y > 0)
+        ymax = floor(Int64,size_y/2)
+    else
+        warn("The input parameter size_y should be positive. Using size_y = 6 * σy + 1 (Default value)")
+        ymax = round(Int64,max(abs(nstds*σx*s),abs(nstds*σy*c),1))
+    end
+
+    xmin = -xmax
+    ymin = -ymax
+
+    x = [j for i in xmin:xmax,j in ymin:ymax]
+    y = [i for i in xmin:xmax,j in ymin:ymax]
+    xr = x*c + y*s
+    yr = -x*s + y*c
+
+    kernel_real = (exp.(-0.5*(((xr.*xr)/σx^2) + ((yr.*yr)/σy^2))).*cos.(2*(π/λ)*xr + ψ))
+    kernel_imag = (exp.(-0.5*(((xr.*xr)/σx^2) + ((yr.*yr)/σy^2))).*sin.(2*(π/λ)*xr + ψ))
+
+    kernel = (kernel_real,kernel_imag)
+    return kernel
+end
+
+function validate_gabor(σ::Real,λ::Real,γ::Real)
+    if !(σ>0 && λ>0 && γ>0)
+        throw(ArgumentError("The parameters σ, λ and γ must be positive numbers."))
+    end
+end
+
 """
     reflect(kernel) --> reflectedkernel
 

test/gabor.jl

@@ -0,0 +1,52 @@
+using ImageFiltering, Base.Test
+
+@testset "gabor" begin
+    σx = 8
+    σy = 12
+    size_x = 6*σx+1
+    size_y = 6*σy+1
+    γ = σx/σy
+    kernel = Kernel.gabor(0,0,σx,0,5,γ,0)
+    @test isequal(size(kernel[1]),(size_x,size_y))
+    kernel = Kernel.gabor(0,0,σx,π,5,γ,0)
+    @test isequal(size(kernel[1]),(size_x,size_y))
+
+    for x in 0:4, y in 0:4, z in 0:4, t in 0:4
+        σx = 2*x+1
+        σy = 2*y+1
+        λ = 2*z+1
+        γ = σx/σy
+        θ = 2*t+1
+        kernel1 = Kernel.gabor(9,9,σx,θ,λ,γ,0)
+        kernel2 = Kernel.gabor(9,9,σx,θ+π,λ,γ,0)
+        @test abs(sum(kernel1[1] - kernel2[1])) < 1e-2
+        @test abs(sum(kernel1[2] - kernel2[2])) < 1e-2
+    end
+
+    x = [j for i in 0:49,j in 0:49]
+    wavelengths = (3, 10)
+    images = [sin.(2*π*x/λ) for λ in wavelengths]
+    σx = 4
+    σy = 5
+    function match_score(image, λ)
+        gabor_real = imfilter(image,centered(Kernel.gabor(6*σx+1,6*σy+1,σx,0,λ,σx/σy,0)[1]),[border="replicate"])
+        gabor_imag = imfilter(image,centered(Kernel.gabor(6*σx+1,6*σy+1,σx,0,λ,σx/σy,0)[2]),[border="replicate"])
+        gabor_result = sqrt.((gabor_real.*gabor_real) + (gabor_imag.*gabor_imag))
+        return mean(gabor_result)
+    end
+    gabor_output = rand(Float64,2,2)
+    for i = 1:2
+        for j = 1:2
+            gabor_output[i,j] = match_score(images[i],wavelengths[j])
+        end
+    end
+    @test gabor_output[1,1] > gabor_output[1,2]
+    @test gabor_output[2,2] > gabor_output[1,2]
+    @test gabor_output[1,1] > gabor_output[2,1]
+    @test gabor_output[2,2] > gabor_output[2,1]
+
+    @test_throws ArgumentError Kernel.gabor(9,9,-2,0,5,0.1,0)
+    @test_throws ArgumentError Kernel.gabor(9,9,2,0,-5,0.1,0)
+    @test_throws ArgumentError Kernel.gabor(9,9,2,0,5,0,0)
+
+end

test/runtests.jl

@@ -14,5 +14,6 @@ include("specialty.jl")
 include("gradient.jl")
 include("mapwindow.jl")
 include("basic.jl")
+include("gabor.jl")
 
 nothing