Principal component analysis of the color spectra from natural scenes Long Nguyen ECE-499 Advisor: Prof. Shane Cotter.

Slides:

Advertisements

Similar presentations

Face Recognition Sumitha Balasuriya.

Advertisements

Covariance Matrix Applications

PCA Tomography and its application to nearby galactic nuclei João Steiner IAG - Universidade de São Paulo +R. B. Menezes, T. V. Ricci +F. Ferrari (UNIPAMPA)

Tensors and Component Analysis Musawir Ali. Tensor: Generalization of an n-dimensional array Vector: order-1 tensor Matrix: order-2 tensor Order-3 tensor.

1er. Escuela Red ProTIC - Tandil, de Abril, 2006 Principal component analysis (PCA) is a technique that is useful for the compression and classification.

Principal Component Analysis CMPUT 466/551 Nilanjan Ray.

Principal Component Analysis

An introduction to Principal Component Analysis (PCA)

Principal Component Analysis

Symmetric Matrices and Quadratic Forms

Factor Analysis Research Methods and Statistics. Learning Outcomes At the end of this lecture and with additional reading you will be able to Describe.

Principal Component Analysis IML Outline Max the variance of the output coordinates Optimal reconstruction Generating data Limitations of PCA.

CHAPTER 19 Correspondence Analysis From: McCune, B. & J. B. Grace Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon.

Face Recognition Using Eigenfaces

CSE 300: Software Reliability Engineering Topics covered: Software metrics and software reliability.

Principal Components Analysis (PCA) 273A Intro Machine Learning.

Principal Component Analysis. Consider a collection of points.

Techniques for studying correlation and covariance structure

Summarized by Soo-Jin Kim

Principle Component Analysis Presented by: Sabbir Ahmed Roll: FH-227.

Linear Least Squares Approximation. 2 Definition (point set case) Given a point set x 1, x 2, …, x n  R d, linear least squares fitting amounts to find.

Chapter 2 Dimensionality Reduction. Linear Methods

Hyperspectral Imaging Alex Chen 1, Meiching Fong 1, Zhong Hu 1, Andrea Bertozzi 1, Jean-Michel Morel 2 1 Department of Mathematics, UCLA 2 ENS Cachan,

Feature extraction 1.Introduction 2.T-test 3.Signal Noise Ratio (SNR) 4.Linear Correlation Coefficient (LCC) 5.Principle component analysis (PCA) 6.Linear.

BACKGROUND LEARNING AND LETTER DETECTION USING TEXTURE WITH PRINCIPAL COMPONENT ANALYSIS (PCA) CIS 601 PROJECT SUMIT BASU FALL 2004.

Review of Statistics and Linear Algebra Mean: Variance:

1 Recognition by Appearance Appearance-based recognition is a competing paradigm to features and alignment. No features are extracted! Images are represented.

Principal Component Analysis Bamshad Mobasher DePaul University Bamshad Mobasher DePaul University.

Techniques for studying correlation and covariance structure Principal Components Analysis (PCA) Factor Analysis.

Chapter 7 Multivariate techniques with text Parallel embedded system design lab 이청용.

CSE 185 Introduction to Computer Vision Face Recognition.

CSSE463: Image Recognition Day 27 This week This week Today: Applications of PCA Today: Applications of PCA Sunday night: project plans and prelim work.

Principal Component Analysis Machine Learning. Last Time Expectation Maximization in Graphical Models – Baum Welch.

EE4-62 MLCV Lecture Face Recognition – Subspace/Manifold Learning Tae-Kyun Kim 1 EE4-62 MLCV.

A NOVEL METHOD FOR COLOR FACE RECOGNITION USING KNN CLASSIFIER

Principle Component Analysis and its use in MA clustering Lecture 12.

Principal Component Analysis (PCA)

Principal Component Analysis Zelin Jia Shengbin Lin 10/20/2015.

Feature Selection and Extraction Michael J. Watts

CSSE463: Image Recognition Day 10 Lab 3 due Weds Lab 3 due Weds Today: Today: finish circularity finish circularity region orientation: principal axes.

ECE 8443 – Pattern Recognition ECE 8527 – Introduction to Machine Learning and Pattern Recognition LECTURE 10: PRINCIPAL COMPONENTS ANALYSIS Objectives:

Presented by: Muhammad Wasif Laeeq (BSIT07-1) Muhammad Aatif Aneeq (BSIT07-15) Shah Rukh (BSIT07-22) Mudasir Abbas (BSIT07-34) Ahmad Mushtaq (BSIT07-45)

CSSE463: Image Recognition Day 10 Lab 3 due Weds, 11:59pm Lab 3 due Weds, 11:59pm Take-home quiz due Friday, 4:00 pm Take-home quiz due Friday, 4:00 pm.

Principal Components Analysis ( PCA)

Multivariate statistical methods. Multivariate methods multivariate dataset – group of n objects, m variables (as a rule n>m, if possible). confirmation.

Principal Component Analysis (PCA)

CSSE463: Image Recognition Day 27

Principal Component Analysis

Dimensionality Reduction

9.3 Filtered delay embeddings

Principal Component Analysis (PCA)

Principal Components Analysis

Principal Component Analysis

Principal Component Analysis (PCA)

Lecture 14 PCA, pPCA, ICA.

Techniques for studying correlation and covariance structure

PCA is “an orthogonal linear transformation that transfers the data to a new coordinate system such that the greatest variance by any projection of the.

Presented by Nagesh Adluru

Recitation: SVD and dimensionality reduction

X.1 Principal component analysis

Symmetric Matrices and Quadratic Forms

Principal Components What matters most?.

Linear Algebra Lecture 32.

Spectral Transformation

Feature Selection Methods

Principal Component Analysis

Marios Mattheakis and Pavlos Protopapas

Dimensionality Reduction Part 1 of 2

Outline Variance Matrix of Stochastic Variables and Orthogonal Transforms Principle Component Analysis Generalized Eigenvalue Decomposition.

Presentation transcript:

Principal component analysis of the color spectra from natural scenes Long Nguyen ECE-499 Advisor: Prof. Shane Cotter

Goal We wish to determine if there is some small number of underlying components (basis functions) which can be linearly combined to produce the wide variety of spectral data observed in nature

Equipments Portable laptop Spectrophotometer Matlab

Collection of Spectral data Summer in Jackson Gardens

Collection of Spectral data Jackson Gardens: 120 samples of natural color spectrums.

Collection of Spectral data Jackson Gardens: 120 samples of natural color spectrums. 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway)

Collection of Spectral data Jackson Gardens: 120 samples of natural color spectrums. 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway) Leaves:

Collection of Spectral data Jackson Gardens: 120 samples of natural color spectrums. 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway) Leaves: 60 samples of maple leaves

Fig. 1 Open up sky color spectrum of a sunny day

Calibration Aim beam of light with known intensity at the sensor

Calibration Aim beam of light with known intensity at the sensor Convert all garden measurements into radiance (  mol/m 2 /s/sr/nm)

Mathematical Analysis Principal Component Analysis (PCA)

Mathematical Analysis Principal Component Analysis (PCA) PCA is a technique used to reduce multidimensional data sets to lower dimensions for data compression.

Mathematical Analysis Principal Component Analysis (PCA) PCA is a technique used to reduce multidimensional data sets to lower dimensions for data compression. PCA extracts components which are orthogonal to one another. The first component accounts for the greatest variance observed in the data, the second component accounts for variance in an orthogonal direction, and so on until the data is completely accounted for.

PCA Data Covariance Matrix Eigenvalues & Eigenvectors

Eigen values 11 Significant Eigen values

Eigen values 11 Significant Eigen values

11 Eigenvectors from biggest to smallest Eigen values

11 Eigen Vectors continue….

3 eigenvectors represent 98% of the data

Future Work Relate eigenvectors to real spectra Analyze the leaves data Independent Component Analysis (ICA)

Acknowledgements Prof. Shane Cotter Prof. Fleishman