Wavelet Transform Toolkit (WTT)

Wavelet Transform Toolkit (WTT) consists of a C++ header-only library for computing and defining multi-level lifted wavelet transforms on 3-D meshes. In addition to the library, the author has implemented a Qt- and OpenGL-based demo program for viewing the result of computing wavelet transforms on a 3-D mesh and demonstrating wavelet-based compression and denoising. Threaded rendering has been employed to provide a smooth user experience. Also, WTT consists of several command-line programs for simple use cases (e.g., computing wavelet transforms, wavelet denoising, and wavelet compression).

The author Shengyang Wei can be reached at the following email address:

• shengyangwei@protonmail.com
• Github: sywe1

Dependency

A complier with C++ 17 support is needed to compile WTT. The following versions of compilers and depended libraries have been verified to work with WTT:

• g++ (7.2+) or clang++ (5+)
• CGAL (4.2+)
• Boost (1.58+)

Since the demo is based on Qt and OpenGL, they are needed to build the demo program of WTT. The following versions of Qt and OpenGL have been verified to work with WTT:

• Qt (5.9+)
• OpenGL (3.3+)

In case the demo program is not needed, users could set the cmake option BUILD_DEMO to OFF (default: ON) to skip building the demo while running the following installation command. In this case, Qt and OpenGL are no longer need to be installed.

Installation

In what follows, let $TOP_DIR denote the top-level directory of WTT software distribution (i.e., the directory containing this README file); let $BUILD_DIR denote a new directory to be created for building the software; and let $INSTALL_DIR denote the directory in which to install WTT.

To install WTT with CMake, use the command sequence:

cmake -H$TOP_DIR -B$BUILD_DIR -DCMAKE_INSTALL_PREFIX=$INSTALL_DIR
cmake --build $BUILD_DIR --target install

Usage of the Demo Program

After a successful installation, the demo program can be found in $INSTALL_DIR/bin. To launch the program, users could run the following command:

./wtt_demo

The demo is designed to provide an instant view of computing the forward wavelet transform and inverse wavelet transform. Both Loop and Butterfly wavelet transforms are supported. Users could also try wavelet compression and denoising by performing a forward wavelet transform, modifying wavelet coefficients, and performing an inverse wavelet transform.

The wavelet transforms or wavelet applications can be performed by sequentially clicking the buttons, specifically the buttons in the bottom row. When the mouse hovers on a button, a helper text will be displayed to illustrate the action of the button. A detailed description of the buttons is given in what follows.

The bottom buttons are grouped into three columns:

1. The first column consists of two mesh-related buttons. The first one (a folder icon) is the loading mesh button. After clicking it, a dialog pops up for you to select a mesh in your local filesystem for the wavelet transform. The second one (a circular arrow) is the resetting button. Clicking it will reset the loaded mesh to its original state.

2. The second column consists of three wavelet-related buttons. These buttons will become valid after a mesh is loaded. The first button (a circle icon) is used to select a wavelet transform scheme. After clicking it, a dialog will pop up for selecting either Butterly or Loop. Once a scheme is selected, a letter will appear in the circle, indicating the current wavelet transform scheme. The second button (a left arrow) is the inverse wavelet transform button. Clicking it performs inverse wavelet transform on the mesh. The third button (a right arrow) is the forward wavelet transform button. Clicking it performs forward wavelet transform on the mesh. Both the forward and inverse transform buttons are invalid until a scheme is selected.

3. The third column consists of two wavelet coefficients modification buttons. The two buttons are invalid until there are available wavelet coefficients. Specifically, the two buttons will become valid only if a forward wavelet transform is computed. Clicking the first button (compression button) filters the wavelet coefficients by their magnitude. A dialog prompts on click for the user to set a percentage to the filter. The wavelet coefficients with larger magnitude within the given percentage are preserved, and the others are dropped. Clicking the second button (denoising button) filters the wavelet coefficients by levels. A dialog prompts on click for the user to set a level to the filter. The wavelet coefficients in and above the given level are dropped.

• To perform wavelet compression on a mesh, the user could click the following buttons in turn: load mesh button, forward transform button, compression button, inverse transform button

• To perform wavelet denoising on a mesh, the user could click the following buttons in turn: load mesh button, forward transform button, denoising button, inverse transform button

The buttons on the left are designed for view control. Descriptions of the buttons from top to bottom are given in turn as below:

1. Reset camera to the original state.
2. Toggle edge display.
3. Set smooth shading to OpenGL shader.
4. Set flat shading to OpenGL shader.
5. Take a screenshot of the current scene.

Usage of Command-line Programs

After a successful installation, three programs can be found in directory $INSTALL_DIR/bin: wtt_fwt, wtt_iwt, and wtt_filter. Programs wtt_fwt and wtt_iwt are used to compute the forward and inverse wavelet transform on a triangle mesh, respectively. Program wtt_filter combines the forward and inverse transform and filters the intermediately produced wavelet coefficients. Users could set the filtering schemes via command-line options to perform wavelet denoising and compression on a triangle mesh. For the three programs, either the Loop or Butterfly scheme can be selected via command-line options. Recently, the supported file format for a 3-D mesh is OFF.

Some example usages are listed below:

• To compute the 2-level Loop forward wavelet transform on mesh vase-8.off, users could run the following command:

wtt_fwt -m Loop -l 2 -i vase-8.off -o vase-fwt.off -c vase-fwt.coefs

Mesh vase-8.off could be found in $INSTALL_DIR/data directory.

• To recover the original vase.off by 2-level Loop inverse wavelet transform, users could run the following command:

wtt_iwt -m Loop -l 2 -i vase-fwt.off -c vase-fwt.coefs -o vase-recover.off

• To perform 3-level Butterfly wavelet compression on mesh vase-8.off, users could run the following command:

wtt_filter -m Butterfly -l 3 -i vase-8.off -o vase-reconstructed.off -c 5

The above command compresses the wavelet coefficients to 5%. That is, only the 5% wavelet coefficients are used to construct the output mesh.

Usage of Library API

The API is provided for defining and computing a custom wavelet transform. Users could incorporate custom operations into the API to define a lifted wavelet transform. If PTQ is used in the wavelet transform, some built-in functions of the WTT could be used to accelerate the development. The code example below with line-by-line comments illustrate the steps of defining a custom wavelet transform.

• defining a lifted wavelet transform

In case the Loop and Butterfly wavelet transforms are of interest, the WTT library provides built-in functions that can be called directly for computing those wavelet transforms. The examples below illustrate the usage of the two built-in functions for the Loop and Butterfly wavelet transform.

• computing loop wavelet transform
• computing butterfly wavelet transform