Table of Contents generated with DocToc

• Julia
• LLST
• PHLCT
• Troubleshooting

Project

This project is from Professor Saito's paper, fully converted from Matlab to Julia. The implementation is almost identical with Matlab except some minor feature differences or lack of features like matlab meshgrid is not in Julia so similar feature is customly built. Similarly, matlab repmat is equivalent to Julia repeat.

Julia

This project is running in Julia version 1.85 and fully tested in mac os and windows with version 1.8-1.86 and developed in VS Code with Julia extension version 1.47.2.

/
  /matlab                       matlab files
  /katsu                        Professor Yamatani's version
  /polyharmonictrigtransforms:  package toml
  /public:                      etc
  /src:                         julia source files
  /tests:                       julia test files
    /data:                      image of barbara converted to data

The above is the file structure.

Read more about Julia, Julia Plot and Matlab.

PolyHarmonicTrigTransforms

include(".PolyHarmonicTrigTransforms.jl")
using .PolyHarmonicTrigTransforms

julia> dst
dst (generic function with 2 methods)

julia> llst
llst (generic function with 2 methods)

julia> solvelaplace
solvelaplace (generic function with 1 method)

LLST

This Julia project focuses on LST (Local Sine Transformation) from Professor Saito's paper

LLST - Laplace LST

To test llstapprox2, it requires 3 inputs: data, leveled list, range.

In a high level, llstapprox2.jl calls llst.jl and calculates the coefficients into grids and llstapprox2.jl determines the boundaries/borders/corners/interior data to remove/process via split_llst_coefs and at the end of llstapprox2.jl, combines the boundaries/borders/corners/interior data into a grid through merge_llst_coefs then calculates the PSNR of the processed data and raw data.

A sample test with 127x127 dataset:

n=127
x = LinRange(-1,1,n) 
y = LinRange(-1,1,n) 
Gaussian = zeros((length(x), length(y)))

for i in 1:n
    for j in 1:n
        t = exp(-(x[i] + 1/3)^2 - (y[j] + 1/3)^2)
        Gaussian[i, j] = t
    end
end


# test for J = 1
levlist1 = [1 1 1 1]
krange1 = [1:n^2;]

psnr = llstapprox2(Gaussian, levlist1, krange1)

To test LLST with the same data from the above:

llst_data = llst(Gaussian, levlist1)

Reference: Professor Saito's paper page 13 Figure 3(a).

PHLCT

The PHLCT (PolyHarmonic Local Cosine Transformation) from Professor Saito's paper Chapter 6.2.2. (This PHLCT was compared with the version from Professor Katsu Yamatani: phlct2d and iphct2d)

PHLCT - PolyHarmonic LCT

To test PHLCT, it requires 2 inputs: data and the size of block.

In a high level, PHLCT has 3 methods: phlct_forward, phlct_backward, and phlct_restore. The phlct_forward is calculating the DCT coefficients of u = in - v where v denotes the PolyHarmonic function.

The phlct_backward reconstructs the data from DCT coefficients and PolyHarmonic function and returns the data close to the original data.

To run PHLCT, run phlct_forward then phlct_backward it should return the original input. For Professor Yamatani's version, run phlct2d then iphlct2d.

The phlct_restore attempts to restore the data back to the original data from truncation by referencing the quantization table to each blocks.

To test PHLCT:

n = 8
bfo128 = [...] #input data
forward = phlct_forward(bfo128, n)
backward = phlct_backward(forward, n)

#Professor Yamatani's version
phlct = phlct2d(bfo128, n)
iphlct = iphlct2d(phlct, n)

Reference: Professor Saito's paper page 30 Chapter 6.2.2.

Image Testing

To test images, first take your chosen image and convert it into a square image (i.e. size n x n where n is the new size of the image after using tools to square it).

Then, use the above sample set of 5 x 5 dataset with the following changes:

n = 5
x = LinRange(-1, 1, n)
y = LinRange(-1, 1, n)
Gaussian = zeros((length(x), length(y)))
		
function GaussianFromImage(image_path)
    img = load(image_path)
    width, height = size(img)
    Gaussian = zeros(Float64, (width, height))
	
    for i in 1:width
        for j in 1:height
          pixel_value = Gray(img[i, j])
          t = exp(-((1 - i/3)^2 + (1 - j/3)^2))
          Gaussian[i, j] = t
        end
    end
    return Gaussian
end
	
image_path = "(insert your image path)"
Gaussian = GaussianFromImage(image_path)
img = load(image_path)
width, height = size(img)

Troubleshooting

1. Package is missing.

To install a package:

In Julia CLI:

julia> import Pkg; Pkg.add("MAT")

or In a Package Manager ]

julia> ]

(@v1.8) pkg> add "MAT"

Example plain HTML site using GitLab Pages.

Learn more about GitLab Pages at https://pages.gitlab.io and the official documentation https://docs.gitlab.com/ce/user/project/pages/.

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