Sensor fusion and nonlinear filtering - Lars Hammarstrand

About professor Lars Hammarstrand

Associate Professor at Chalmers University of Technology, Göteborg, Sweden

LinkedIn:
https://www.linkedin.com/in/lhammarstrand/



YouTube channel:
https://youtube.com/playlist?list=PLTD_k0sZVYFqjFDkJV8GE2EwfxNK59fJY

1.3 Distributions

https://www.youtube.com/watch?v=X7ePpI4qgTQ&list=PLTD_k0sZVYFqjFDkJV8GE2EwfxNK59fJY&index=5&t=126s

Conditional Distributions

Conditional Distributions are indispensable in Sensor Fusion, Filtering, and Bayesian estimation in general.

Conditional distribution - product rule

Let x and z be two random variables with the "joint probability" pdf p(x,z)

z is some constant value

The function
p (x | z)
read as "conditional density" of x, given z,
is defined:

p(x, z) = p(z | x) p(x)

where 

p(x)

 is read as a "modular distribution" of x

and if 

p(x) =/= 0

read as: possible values of x for which probability density is non-zero,

when can write

p( z | x ) =  p(x, z) / p(x)

read as: 

The conditional density of x given z 

is the ratio of the joint probability of x and z

divided by modular distribution of x. 

This can be re-written as:

p(z | x = x') = p(x', z) / p(x')

where:

x' is some constant

p(x') is also some constant

and that is proportional \alpha to the joint probability (x', z).

we fixed one dimension x' which is a function of z.

Interpretation: Conditional density p( z | x) describes the distribution of z given that x is known. 

Example:

Sara decided how many pieces of candy she can have every day

by tossing a coin and rolling the dice.

40% coin

60% dice

Coin: 

- heads 1 candy

- tails 0 candy

Pr {z = i | Sara tosses coin} =
{ 

    0.5 if i = 0,1 

    0  otherwise

Pr {z = i | Sara throws dice} = 

{

    1/6 if i = 1,2,..., 6

    0  otherwise

Marginal distributions

TBC

sensor_fusion

https://youtu.be/6qV3YjFppuc

How is the Bird-Eye-View used in autonomous driving?

Andrej Karpathy talks about the Bird-Eye-View image-stitching and transformation and then Deep Neural Training

https://youtu.be/2iq6CnMcL6g

pose

Body pose recognition has applications in:

• image compression when only the position of the subject is needed
• social signaling
• ADAS driver monitoring system (DMS)

The human body pose consists of:

• body detection in the image
• body segmentation from the image
• mapping the 2D image to the 3D model
• tracking the pose over time (movie)

photo credit: posetrack.net

REFERENCES

• https://posetrack.net/workshops/iccv2017/
• http://vision.imar.ro/human3.6m/challenge_open.php
• https://competitions.codalab.org/competitions/19650
• https://github.com/facebookresearch/DensePose/blob/master/detectron/datasets/densepose_cocoeval.py
• 
  

pose

Body pose recognition has applications in:

• image compression when only the position of the subject is needed
• social signaling
• ADAS driver monitoring system (DMS)

The human body pose consists of:

• body detection in the image
• body segmentation from the image
• mapping the 2D image to the 3D model
• tracking the pose over time (movie)

photo credit: posetrack.net

REFERENCES

• https://posetrack.net/workshops/iccv2017/
• http://vision.imar.ro/human3.6m/challenge_open.php
• https://competitions.codalab.org/competitions/19650
• https://github.com/facebookresearch/DensePose/blob/master/detectron/datasets/densepose_cocoeval.py
• 
  

Point Cloud Library (PCL) on Mac OS

Install PCL using BREW.

PCL is a Point Cloud Library for C++

$ xcode-select --install

xcode-select: error: command line tools are already installed, use "Software Update" to install updates



After updating Mac OS, please re-install the brew:

$ /usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"

$ brew update

Already up-to-date.

$ brew tap homebrew/science
Error: homebrew/science was deprecated. This tap is now empty as all its formulae were migrated.

$ brew tap brewsci/science

Cloning into '/usr/local/Homebrew/Library/Taps/brewsci/homebrew-science'...

DANGER (no need to do it if you re-insalled the brew):

$ sudo install -d -o $(whoami) -g admin /usr/local/Frameworks

$ brew reinstall pcl

🍺  /usr/local/Cellar/pcl/1.9.1_4: 1,173 files, 147.4MB

$ brew upgrade pcl

Error: pcl 1.9.1_4 already installed


Compile the Lidar Simulator (Udacity nd313)

cd /Volumes/DATA/_Drive/_REPOS/SFND_Lidar_Obstacle_Detection/build/

build $ rm ../CMakeCache.txt

build $ cmake ../CMakeLists.txt
-- The C compiler identification is AppleClang 10.0.1.10010046
-- The CXX compiler identification is AppleClang 10.0.1.10010046
-- Check for working C compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc
-- Check for working C compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -- works
-- Detecting C compiler ABI info
-- Detecting C compiler ABI info - done
-- Detecting C compile features
-- Detecting C compile features - done
-- Check for working CXX compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++
-- Check for working CXX compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -- works
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Detecting CXX compile features
-- Detecting CXX compile features - done
-- Checking for module 'eigen3'
--   No package 'eigen3' found
-- Found Eigen: /usr/local/include/eigen3 
-- Eigen found (include: /usr/local/include/eigen3, version: 3.3.7)
-- Looking for pthread.h
-- Looking for pthread.h - found
-- Looking for pthread_create
-- Looking for pthread_create - found
-- Found Threads: TRUE 
-- Boost version: 1.70.0
-- Found the following Boost libraries:
--   system
--   filesystem
--   thread
--   date_time
--   iostreams
--   serialization
--   chrono
--   atomic
--   regex
-- Checking for module 'flann'
--   No package 'flann' found
-- Found FLANN: /usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib 
-- FLANN found (include: /usr/local/Cellar/flann/1.9.1_7/include, lib: optimized;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib;debug;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib)
-- Checking for module 'flann'
--   No package 'flann' found
-- FLANN found (include: /usr/local/Cellar/flann/1.9.1_7/include, lib: optimized;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib;debug;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib)
** WARNING ** io features related to pcap will be disabled
** WARNING ** io features related to png will be disabled
-- Found libusb-1.0: /usr/local/include 
** WARNING ** io features related to libusb-1.0 will be disabled
-- Found Qhull: optimized;/usr/local/lib/libqhull_p.dylib;debug;/usr/local/lib/libqhull_p.dylib 
-- QHULL found (include: /usr/local/include, lib: optimized;/usr/local/lib/libqhull_p.dylib;debug;/usr/local/lib/libqhull_p.dylib)
-- Found OpenGL: /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.14.sdk/System/Library/Frameworks/OpenGL.framework 
-- Found PkgConfig: /opt/local/bin/pkg-config (found version "0.29.2")
-- Checking for module 'glew'
--   No package 'glew' found
CMake Error at /usr/local/share/pcl-1.9/PCLConfig.cmake:58 (message):
  simulation is required but glew was not found
Call Stack (most recent call first):
  /usr/local/share/pcl-1.9/PCLConfig.cmake:361 (pcl_report_not_found)
  /usr/local/share/pcl-1.9/PCLConfig.cmake:545 (find_external_library)
  CMakeLists.txt:10 (find_package)


-- Configuring incomplete, errors occurred!
See also "/Volumes/DATA/_Drive/_REPOS/SFND313_Lidar_Obstacle_Detection/CMakeFiles/CMakeOutput.log".
See also "/Volumes/DATA/_Drive/_REPOS/SFND313_Lidar_Obstacle_Detection/CMakeFiles/CMakeError.log".

$ brew install glew

Updating Homebrew...
==> Auto-updated Homebrew!
Updated 1 tap (homebrew/core).
No changes to formulae.

Warning: glew 2.1.0 is already installed and up-to-date
To reinstall 2.1.0, run `brew reinstall glew`
(turi) uki  16:17 build $

References

• http://www.pointclouds.org/documentation/tutorials/installing_homebrew.php
• https://gist.github.com/irazasyed/7732946
• 
  

Point Cloud Library (PCL) on Mac OS

Install PCL using BREW.

PCL is a Point Cloud Library for C++

$ xcode-select --install

xcode-select: error: command line tools are already installed, use "Software Update" to install updates



After updating Mac OS, please re-install the brew:

$ /usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"

$ brew update

Already up-to-date.

$ brew tap homebrew/science
Error: homebrew/science was deprecated. This tap is now empty as all its formulae were migrated.

$ brew tap brewsci/science

Cloning into '/usr/local/Homebrew/Library/Taps/brewsci/homebrew-science'...

DANGER (no need to do it if you re-insalled the brew):

$ sudo install -d -o $(whoami) -g admin /usr/local/Frameworks

$ brew reinstall pcl

🍺  /usr/local/Cellar/pcl/1.9.1_4: 1,173 files, 147.4MB

$ brew upgrade pcl

Error: pcl 1.9.1_4 already installed


Compile the Lidar Simulator (Udacity nd313)

cd /Volumes/DATA/_Drive/_REPOS/SFND_Lidar_Obstacle_Detection/build/

build $ rm ../CMakeCache.txt

build $ cmake ../CMakeLists.txt
-- The C compiler identification is AppleClang 10.0.1.10010046
-- The CXX compiler identification is AppleClang 10.0.1.10010046
-- Check for working C compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc
-- Check for working C compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/cc -- works
-- Detecting C compiler ABI info
-- Detecting C compiler ABI info - done
-- Detecting C compile features
-- Detecting C compile features - done
-- Check for working CXX compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++
-- Check for working CXX compiler: /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/bin/c++ -- works
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Detecting CXX compile features
-- Detecting CXX compile features - done
-- Checking for module 'eigen3'
--   No package 'eigen3' found
-- Found Eigen: /usr/local/include/eigen3 
-- Eigen found (include: /usr/local/include/eigen3, version: 3.3.7)
-- Looking for pthread.h
-- Looking for pthread.h - found
-- Looking for pthread_create
-- Looking for pthread_create - found
-- Found Threads: TRUE 
-- Boost version: 1.70.0
-- Found the following Boost libraries:
--   system
--   filesystem
--   thread
--   date_time
--   iostreams
--   serialization
--   chrono
--   atomic
--   regex
-- Checking for module 'flann'
--   No package 'flann' found
-- Found FLANN: /usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib 
-- FLANN found (include: /usr/local/Cellar/flann/1.9.1_7/include, lib: optimized;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib;debug;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib)
-- Checking for module 'flann'
--   No package 'flann' found
-- FLANN found (include: /usr/local/Cellar/flann/1.9.1_7/include, lib: optimized;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib;debug;/usr/local/Cellar/flann/1.9.1_7/lib/libflann_cpp.dylib)
** WARNING ** io features related to pcap will be disabled
** WARNING ** io features related to png will be disabled
-- Found libusb-1.0: /usr/local/include 
** WARNING ** io features related to libusb-1.0 will be disabled
-- Found Qhull: optimized;/usr/local/lib/libqhull_p.dylib;debug;/usr/local/lib/libqhull_p.dylib 
-- QHULL found (include: /usr/local/include, lib: optimized;/usr/local/lib/libqhull_p.dylib;debug;/usr/local/lib/libqhull_p.dylib)
-- Found OpenGL: /Applications/Xcode.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.14.sdk/System/Library/Frameworks/OpenGL.framework 
-- Found PkgConfig: /opt/local/bin/pkg-config (found version "0.29.2")
-- Checking for module 'glew'
--   No package 'glew' found
CMake Error at /usr/local/share/pcl-1.9/PCLConfig.cmake:58 (message):
  simulation is required but glew was not found
Call Stack (most recent call first):
  /usr/local/share/pcl-1.9/PCLConfig.cmake:361 (pcl_report_not_found)
  /usr/local/share/pcl-1.9/PCLConfig.cmake:545 (find_external_library)
  CMakeLists.txt:10 (find_package)


-- Configuring incomplete, errors occurred!
See also "/Volumes/DATA/_Drive/_REPOS/SFND313_Lidar_Obstacle_Detection/CMakeFiles/CMakeOutput.log".
See also "/Volumes/DATA/_Drive/_REPOS/SFND313_Lidar_Obstacle_Detection/CMakeFiles/CMakeError.log".

$ brew install glew

Updating Homebrew...
==> Auto-updated Homebrew!
Updated 1 tap (homebrew/core).
No changes to formulae.

Warning: glew 2.1.0 is already installed and up-to-date
To reinstall 2.1.0, run `brew reinstall glew`
(turi) uki  16:17 build $

References

• http://www.pointclouds.org/documentation/tutorials/installing_homebrew.php
• https://gist.github.com/irazasyed/7732946
•