From multiple images to catalogs
|
|
- Christiana Griffin
- 5 years ago
- Views:
Transcription
1 Lecture 14 From multiple images to catalogs Image reconstruction Optimal co-addition Sampling-reconstruction-resampling Resolving faint galaxies Automated object detection Photometric catalogs
2 Deep CCD imaging Raw image C, additive systematics image B. De-biased flat-field image F. Form the data image D: Image calibration: D(x, y) = [C(x, y) B(x, y)] / F(x, y) Var(D) = [ σ 2 0 +<D > / Gain] F(x,y) could be super-flat. Co-addition of many images: Register flat-fielded shift-and-stare images Map each image onto a reference image. Warp if necessary, so all stars are reqistered to fractional pixels. Simple nearest-neighbor schemes create correlated noise. Sinc filter avoids this. Co-add by median averaging (but there are even better ways!)
3 Imaging and photometry Raw image C, additive systematics image B. De-biased flat-field image F. Form the data image D: Co-add by median filter: Noise model: D( x, y) Var( D) = mediand( x, = 2 D /Gain σ + < 0 > y) over N images / N Digital data: DN = digitized (Gain * Intensity) Find objects: Sort pixels by DN Set thresholds Decrease toward sky level. x
4 Imaging and photometry CCDs and CMOS imagers are pixelated i.e. they sample the image
5 Two methods of co-adding Simple median using fractional pixel interpolation weights Drizzle resampling onto higher resolution grid with sinc interpolation Rather than shifting and adding the original pixels with interpolation, drizzle shrinks each pixel into a smaller footprint (called a "drop") and then places them onto the finely sampled reconstruction grid (hence the name "drizzle").
6 resampling If you know the signal shape, you can determine the value at every location. In practice, we sample the underlying function. Pixels! First let's consider functions which are sampled. For many imaging applications, there is a physical process (e.g., seeing) which limits the amount of high spatial frequency information. If there is an upper frequency cutoff in the power spectrum of the objects being observed, it is possible to recover the full function from samples of it if the samples are sufficiently fine. The Nyquist sampling theorem says that if you have a band-limited function, you can recover the function if you sample at spatial frequencies over twice the frequency at which the power spectrum goes to zero. For example, if you say seeing wipes out scales less than 0.2 arcsec, you need to sample at 0.1 arcsec to recover the full function. If you can recover the function, then you can sample it at different locations. You can do this using the sampling theorem by something known as sinc interpolation. This works by recovering the original function; the process is done by filtering by a box function in transform space, which is equivalent to convolution with a sinc function in real space. However, even at ``critical'' sampling, the binned function is not equivalent to the sampled function. So in fact, sinc interpolation may not be accurate unless you are better than critically sampled. If you are undersampled, it fails miserably (aliasing). Near critical sampling, it can lead to non- flux conserving interpolation.
7 Ideal Reconstruction A band-limited function can be exactly reconstructed by convolution with the appropriate kernel.
8 Shannon says By hypothesis f has a Fourier transform, F bandlimited to 1/2T. Pixelate: Multiply by Comb function) with separation of T -1/(2T) 1/(2T) means convolve the Fourier transform with the Fourier Transform of Comb, but this is just another Comb function with separation of 1/T which just relplicates the Fourier Transform. 5T but that s equivalent to convolving in space with Fourier transform of boxcar, sinc(). So we just need to use sinc interpolation to get back original image. So mutiplying by a boxcar gets back original F
9 Possible kernels Exact area sampling Drizzle redistribution Boxcar smoothing with resampling Step pyramid kernel with different fraction of flux in each box Adjusting the size of the rectangle changes how the algorithm considers the flux in the pixel to be distributed.
10 A big driver in commercial applications is rendering of text.
11 Sampling Features Features in Lanczos resampling. NN LI Lcz2 Lcz3 Lcz4 Moire patterns in linearly interpolated resampled images
12 Automated photometry Search each line in an image for pixels above some threshold. Bayesian prior: convolve with PSF or expected object kernel Use a moving average updated sky as threshold Define objects as connected above-threshold convolved pixels in x,y Deblend overlapping objects For each resulting object, measure the integrated flux with a kernel, and measure various intensity moments Generate a list (catalog) of detected objects, and their photometry Example software: FOCAS, Sextractor, DoPhot
13 Define apertures Aperture photometry round / square / partial pixels allowed Sum counts in aperture: F ˆ = i D i Var( ˆ F ) = PROBLEM: sky Var(D i ) i Noise increases with aperture size So use small aperture to maximise S/N Calibrate bias using bright stars.
14 Better: PSF fitting PSF = point spread function = image of star. Use analytic model, e.g.: Gaussian: DoPHOT: P(x, y) = exp 1 x σ + y2 2 x σ y P(x, y) = 1 z β z β z 6 6 z = 1 2 x 2 σ + 2xy 2 x + y2 2 σ xy σ y β 4 = β 6 = 1 gives truncated series of Gaussian.
15 Optimal extraction of stellar flux If P(x,y) is known, scale this to fit the skysubtracted star image: Iterate ˆ F = i P i (D i sky) / σ i 2 2 P i2 / σ i i F σ 2 i = σ ˆ P i + sky Gain Var( ˆ F ) = i 1 P i2 /σ i 2
16 PSF fitting We want to reconstruct F but must also find MODEL PARAMETERS: Centroid:x 0, y 0 Shape parameters:σ x, σ y, σ xy, β 4, β 6, etc. How to find centroid: Rough: Refine: x 0 ~ 1 N i (D i sky)x i 0 = (D i sky)(x i x 0 )P(x i x 0 ) i x 0 x (x i -x 0 )P(x i -x 0 ) x
17 Shape parameters: second moments of intensity Same area under fitted curves: σ x2 ~ σ y 2 ~ σ xy ~ Orthogonality: (D xy sky) (x x 0 ) 2 x,y (D xy sky) (y y 0 ) 2 x,y Centroid and shape parameters are roughly orthogonal to area, so small errors won t affect photometry true only for totally isolated stars! (D xy sky) (x x 0 )(y y 0 ) x,y x 0 x x 0 x x 0 x
18 Better: use optimal filter 2 σ x 2 σ y ~ ~ x, y x, y ( D ( D xy xy sky ) G sky ) G xy xy ( x ( y x y 0 0 ) ) 2 2 σ xy Apodization : ~ ( D x, y sky ) G ( x Given a prior for the signal G, the second moments have highest S/N and are more immune to outlying flux from other objects or bright pixels xy xy x 0 )( y y 0 ) x 0 x If stellar photometry, G is PSF. If galaxy, G is estimate of galaxy profile.
19 Automated photometry of crowded fields e.g. DoPHOT, FOCAS, Sextractor Set threshold, find objects. Many objects, often overlapping Make object list. Store parameters F, x 0, y 0, σ x, σ y,... Classify objects based on size/shape parameters: star double star galaxy: bigger than PSF, not round blemish, cosmic: <PSF, saturated σ-clip thresholds set to divide categories Flag cosmic rays, saturated pixels; ignore flagged pixels σ 2 faint galaxies stars cosmics mag = -2.5 log F bright
20 Automated photometry -- continued Find mean PSF shape parameters by weighted averages over all objects classified as stars May be functions of position and/or brightness Scale PSF to measure star fluxes. Subtract all nearby objects before scaling. Perform aperture photometry if desired ITERATE!
21 Problems with crowded-field photometry Light pollution residual PSF structure near bright objects Crowding errors/incompleteness/misclassification use Monte carlo tests inject fake stars or other objects at random positions see what fraction are recovered correctly with what errors in flux Sky levels PSF wings and large numbers of faint stars merge to create bumpy pseudo-sky Solution: use local sky level, e.g. median of pixels in ring around object Fit polynomial or spline to local sky levels Boost error bars accordingly
22 Galaxy images Design and fit appropriate models e.g. Ellipse fitting (structure of elliptical galaxies) Aim: find ellipses that fit image contours at specified brightnesses Sample data around a trial ellipse Fit truncated sin/cos series: f (θ) = A + Bsinθ + C cosθ θ 0 2π + Dsin 2θ + E sin 2θ A: If mean contour level too high/low, expand/shrink ellipse B, C: If ellipse not centred, adjust x 0, y 0 D, E: If shape/orientation not correct, adjust ellipticity/position angle. Plot ellipse parameters vs size or contour level to quantify radial brightness profile, twists, shifts, etc
23 Galaxy photometry completeness Histogram of pixel values Consider N images with sky mean μ and rms noise σ Significance R = y 1/2
24 Galaxy photometry completeness Consider N images with sky mean μ and rms noise σ Χ 2 image Significance R = y 1/2
25 Subaru telescope Point spread function: 0.7 arcsec full width at half maximum
26 resolving galaxies A given galaxy at high redshift (more distant) should appear smaller. But two effects oppose this: cosmological angle-redshift relation, and greater star formation in the past (higher surface brightness). Here are lots of galaxy surface brightness vs radius (arcsec) in redshift bins from z = for apparent mag. At a surface brightness of 28 i mag/sq.arcsec (horizontal dashed line) most galaxies at z<3 are resolved in 0.6 arcsec FWHM seeing (vertical dashed line).
27 Comparing HST with Subaru ACS: 34 min (1 orbit) PSF: 0.1 arcsec (FWHM) 2 arcmin
28 Comparing HST with Subaru Suprime-Cam: 20 min PSF: 0.52 arcsec (FWHM)
29 1981AJ J
30 F4p22 public, N(mx), x=(tot, iso, ap), for B,V,R,z.
31 F4p22 public, N(mx), x=(tot, iso, ap), for B,V,R,z. Highlighted: FLAGS=0
32 Galaxy photometry completeness Number per square arcminute vs log flux DEEP LENS SURVEY Completeness suffers for galaxies at or below the sky noise on an individual image. If the goal is to reconstruct the galaxy counts N(mag) then Monte Carlo simulations can be used to extract that statistically. But if the goal is the photometry of individual galaxies (such as shape) then we can do better: use all the information we have.
33 3-band reconstruction Each pixel in reconstructed image based on probability of same object of resolution equal to the point spread function is present in all 3 bands. reconstruction Band 1 Band 2 Band 3
34
Single-epoch Measurement Algorithms Robert Lupton Applications Lead
Single-epoch Measurement Algorithms Robert Lupton Applications Lead 2013-09-19 CDP FINAL DESIGN REVIEW September 19-20, 2013 Name of Mee)ng Loca)on Date - Change in Slide Master 1 Outline Single-epoch
More informationSampling, Aliasing, & Mipmaps
Sampling, Aliasing, & Mipmaps Last Time? Monte-Carlo Integration Importance Sampling Ray Tracing vs. Path Tracing source hemisphere Sampling sensitive to choice of samples less sensitive to choice of samples
More informationSampling, Aliasing, & Mipmaps
Sampling, Aliasing, & Mipmaps Last Time? Monte-Carlo Integration Importance Sampling Ray Tracing vs. Path Tracing source hemisphere What is a Pixel? Sampling & Reconstruction Filters in Computer Graphics
More informationPrincipled point-source detection in collections of astronomical images
Principled point-source detection in collections of astronomical images Dustin Lang 1,,3, David W. Hogg 4,5, & Others ABSTRACT Given a collection of images taken of the same patch of sky, it is possible
More informationAliasing and Antialiasing. ITCS 4120/ Aliasing and Antialiasing
Aliasing and Antialiasing ITCS 4120/5120 1 Aliasing and Antialiasing What is Aliasing? Errors and Artifacts arising during rendering, due to the conversion from a continuously defined illumination field
More informationComputer Vision I. Announcements. Fourier Tansform. Efficient Implementation. Edge and Corner Detection. CSE252A Lecture 13.
Announcements Edge and Corner Detection HW3 assigned CSE252A Lecture 13 Efficient Implementation Both, the Box filter and the Gaussian filter are separable: First convolve each row of input image I with
More informationconvolution shift invariant linear system Fourier Transform Aliasing and sampling scale representation edge detection corner detection
COS 429: COMPUTER VISON Linear Filters and Edge Detection convolution shift invariant linear system Fourier Transform Aliasing and sampling scale representation edge detection corner detection Reading:
More informationAnno accademico 2006/2007. Davide Migliore
Robotica Anno accademico 6/7 Davide Migliore migliore@elet.polimi.it Today What is a feature? Some useful information The world of features: Detectors Edges detection Corners/Points detection Descriptors?!?!?
More informationWSDC Subsystem Peer Review
WSDC Subsystem Peer Review Multiband DETector () Ken Marsh (IPAC/Caltech) 1 Outline Relationship of to other WSDS pipeline modules Why multiband? Theoretical basis Procedure - Steps involved - Allowance
More informationImage Filtering, Warping and Sampling
Image Filtering, Warping and Sampling Connelly Barnes CS 4810 University of Virginia Acknowledgement: slides by Jason Lawrence, Misha Kazhdan, Allison Klein, Tom Funkhouser, Adam Finkelstein and David
More informationFourier analysis and sampling theory
Reading Required: Shirley, Ch. 9 Recommended: Fourier analysis and sampling theory Ron Bracewell, The Fourier Transform and Its Applications, McGraw-Hill. Don P. Mitchell and Arun N. Netravali, Reconstruction
More informationLecture 17 Reprise: dirty beam, dirty image. Sensitivity Wide-band imaging Weighting
Lecture 17 Reprise: dirty beam, dirty image. Sensitivity Wide-band imaging Weighting Uniform vs Natural Tapering De Villiers weighting Briggs-like schemes Reprise: dirty beam, dirty image. Fourier inversion
More informationComputer Graphics. Texture Filtering & Sampling Theory. Hendrik Lensch. Computer Graphics WS07/08 Texturing
Computer Graphics Texture Filtering & Sampling Theory Hendrik Lensch Overview Last time Texture Parameterization Procedural Shading Today Texturing Filtering 2D Texture Mapping Forward mapping Object surface
More informationSampling and Monte-Carlo Integration
Sampling and Monte-Carlo Integration Sampling and Monte-Carlo Integration Last Time Pixels are samples Sampling theorem Convolution & multiplication Aliasing: spectrum replication Ideal filter And its
More informationImaging and Deconvolution
Imaging and Deconvolution Urvashi Rau National Radio Astronomy Observatory, Socorro, NM, USA The van-cittert Zernike theorem Ei E V ij u, v = I l, m e sky j 2 i ul vm dldm 2D Fourier transform : Image
More informationLecture 2: 2D Fourier transforms and applications
Lecture 2: 2D Fourier transforms and applications B14 Image Analysis Michaelmas 2017 Dr. M. Fallon Fourier transforms and spatial frequencies in 2D Definition and meaning The Convolution Theorem Applications
More informationDetecting Sources in Chandra Data
Detecting Sources in Chandra Data Goal Identify statistically significant brightness enhancements, over local background, deriving from both unresolved (point) and resolved (extended) x-ray sources. Emphasize
More informationReading. 2. Fourier analysis and sampling theory. Required: Watt, Section 14.1 Recommended:
Reading Required: Watt, Section 14.1 Recommended: 2. Fourier analysis and sampling theory Ron Bracewell, The Fourier Transform and Its Applications, McGraw-Hill. Don P. Mitchell and Arun N. Netravali,
More informationA new algorithm for difference image analysis
Mon. Not. R. Astron. Soc. 386, L77 L81 (2008) doi:10.1111/j.1745-3933.2008.00464.x A new algorithm for difference image analysis D. M. Bramich Isaac Newton Group of Telescopes, Apartado de Correos 321,
More informationFMA901F: Machine Learning Lecture 3: Linear Models for Regression. Cristian Sminchisescu
FMA901F: Machine Learning Lecture 3: Linear Models for Regression Cristian Sminchisescu Machine Learning: Frequentist vs. Bayesian In the frequentist setting, we seek a fixed parameter (vector), with value(s)
More informationBroad field that includes low-level operations as well as complex high-level algorithms
Image processing About Broad field that includes low-level operations as well as complex high-level algorithms Low-level image processing Computer vision Computational photography Several procedures and
More informationSynthesis Imaging. Claire Chandler, Sanjay Bhatnagar NRAO/Socorro
Synthesis Imaging Claire Chandler, Sanjay Bhatnagar NRAO/Socorro Michelson Summer Workshop Caltech, July 24-28, 2006 Synthesis Imaging 2 Based on the van Cittert-Zernike theorem: The complex visibility
More informationSampling: Application to 2D Transformations
Sampling: Application to 2D Transformations University of the Philippines - Diliman August Diane Lingrand lingrand@polytech.unice.fr http://www.essi.fr/~lingrand Sampling Computer images are manipulated
More informationXRDUG Seminar III Edward Laitila 3/1/2009
XRDUG Seminar III Edward Laitila 3/1/2009 XRDUG Seminar III Computer Algorithms Used for XRD Data Smoothing, Background Correction, and Generating Peak Files: Some Features of Interest in X-ray Diffraction
More informationSpectral Extraction of Extended Sources Using Wavelet Interpolation
The 2005 HST Calibration Workshop Space Telescope Science Institute, 2005 A. M. Koekemoer, P. Goudfrooij, and L. L. Dressel, eds. Spectral Extraction of Extended Sources Using Wavelet Interpolation Paul
More informationScaled representations
Scaled representations Big bars (resp. spots, hands, etc.) and little bars are both interesting Stripes and hairs, say Inefficient to detect big bars with big filters And there is superfluous detail in
More informationAliasing. Can t draw smooth lines on discrete raster device get staircased lines ( jaggies ):
(Anti)Aliasing and Image Manipulation for (y = 0; y < Size; y++) { for (x = 0; x < Size; x++) { Image[x][y] = 7 + 8 * sin((sqr(x Size) + SQR(y Size)) / 3.0); } } // Size = Size / ; Aliasing Can t draw
More information( ) = First Bessel function, x = π Dθ
Observational Astronomy Image formation Complex Pupil Function (CPF): (3.3.1) CPF = P( r,ϕ )e ( ) ikw r,ϕ P( r,ϕ ) = Transmittance of the aperture (unobscured P = 1, obscured P = 0 ) k = π λ = Wave number
More informationSampling, Aliasing, & Mipmaps
Last Time? Sampling, Aliasing, & Mipmaps 2D Texture Mapping Perspective Correct Interpolation Common Texture Coordinate Projections Bump Mapping Displacement Mapping Environment Mapping Texture Maps for
More informationSampling and Reconstruction
Page 1 Sampling and Reconstruction The sampling and reconstruction process Real world: continuous Digital world: discrete Basic signal processing Fourier transforms The convolution theorem The sampling
More informationComputer Vision I. Announcement. Corners. Edges. Numerical Derivatives f(x) Edge and Corner Detection. CSE252A Lecture 11
Announcement Edge and Corner Detection Slides are posted HW due Friday CSE5A Lecture 11 Edges Corners Edge is Where Change Occurs: 1-D Change is measured by derivative in 1D Numerical Derivatives f(x)
More informationSoftware tools for ACS: Geometrical Issues and Overall Software Tool Development
Software tools for ACS: Geometrical Issues and Overall Software Tool Development W.B. Sparks, R. Jedrzejewski, M. Clampin, R.C. Bohlin. June 8, 2000 ABSTRACT We describe the issues relating to internal
More informationEdge and local feature detection - 2. Importance of edge detection in computer vision
Edge and local feature detection Gradient based edge detection Edge detection by function fitting Second derivative edge detectors Edge linking and the construction of the chain graph Edge and local feature
More informationUsing External SExtractor (v2.8.6) Catalogs from *_crclean.fits Images to Align ACS/WFC Images With Drizzlepac/Tweakreg
Using External SExtractor (v2.8.6) Catalogs from *_crclean.fits Images to Align ACS/WFC Images With Drizzlepac/Tweakreg Introduction* * *!!! This!example!describes!the!alignment!of!four!ACS/WFC!images!that!contain!a!!
More informationTABLE OF CONTENTS PRODUCT DESCRIPTION VISUALIZATION OPTIONS MEASUREMENT OPTIONS SINGLE MEASUREMENT / TIME SERIES BEAM STABILITY POINTING STABILITY
TABLE OF CONTENTS PRODUCT DESCRIPTION VISUALIZATION OPTIONS MEASUREMENT OPTIONS SINGLE MEASUREMENT / TIME SERIES BEAM STABILITY POINTING STABILITY BEAM QUALITY M 2 BEAM WIDTH METHODS SHORT VERSION OVERVIEW
More informationImage subtraction using a space-varying kernel
ASTRONOMY & ASTROPHYSICS JUNE I 2000, PAGE 363 SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 144, 363 370 (2000) Image subtraction using a space-varying kernel C. Alard 1,2 1 DASGAL, 61 avenue de l
More informationImaging and non-imaging analysis
1 Imaging and non-imaging analysis Greg Taylor University of New Mexico Spring 2017 Plan for the lecture-i 2 How do we go from the measurement of the coherence function (the Visibilities) to the images
More informationSampling and Reconstruction
Sampling and Reconstruction Sampling and Reconstruction Sampling and Spatial Resolution Spatial Aliasing Problem: Spatial aliasing is insufficient sampling of data along the space axis, which occurs because
More informationEE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 14 130307 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Stereo Dense Motion Estimation Translational
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationAdvanced Computer Graphics. Aliasing. Matthias Teschner. Computer Science Department University of Freiburg
Advanced Computer Graphics Aliasing Matthias Teschner Computer Science Department University of Freiburg Outline motivation Fourier analysis filtering sampling reconstruction / aliasing antialiasing University
More informationEdges, interpolation, templates. Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth)
Edges, interpolation, templates Nuno Vasconcelos ECE Department, UCSD (with thanks to David Forsyth) Edge detection edge detection has many applications in image processing an edge detector implements
More informationOutline. Sampling and Reconstruction. Sampling and Reconstruction. Foundations of Computer Graphics (Fall 2012)
Foundations of Computer Graphics (Fall 2012) CS 184, Lectures 19: Sampling and Reconstruction http://inst.eecs.berkeley.edu/~cs184 Outline Basic ideas of sampling, reconstruction, aliasing Signal processing
More informationCPSC 425: Computer Vision
CPSC 425: Computer Vision Image Credit: https://docs.adaptive-vision.com/4.7/studio/machine_vision_guide/templatematching.html Lecture 9: Template Matching (cont.) and Scaled Representations ( unless otherwise
More informationOutline. Foundations of Computer Graphics (Spring 2012)
Foundations of Computer Graphics (Spring 2012) CS 184, Lectures 19: Sampling and Reconstruction http://inst.eecs.berkeley.edu/~cs184 Basic ideas of sampling, reconstruction, aliasing Signal processing
More informationBasic Use of SExtractor Catalogs With TweakReg - I
Instrument Science Report ACS 2015-04 Basic Use of SExtractor Catalogs With TweakReg - I Ray A. Lucas and Bryan Hilbert May 27, 2015 ABSTRACT We describe using external SExtractor (v2.8.6) catalogs from
More informationSpectroscopy techniques II. Danny Steeghs
Spectroscopy techniques II Danny Steeghs Conducting long-slit spectroscopy Science goals must come first, what are the resolution and S/N requirements? Is there a restriction on exposure time? Decide on
More informationWSDC Subsystem Peer Review. Frame Co-addition
WSDC Subsystem Peer Review Frank Masci IPAC/Caltech 1 Outline 1. Atlas (co-add) Image deliverables and strategy 2. Co-add pipeline overview 3. Preprocessing steps: outlier detection strategy and plans
More informationHomework. Gaussian, Bishop 2.3 Non-parametric, Bishop 2.5 Linear regression Pod-cast lecture on-line. Next lectures:
Homework Gaussian, Bishop 2.3 Non-parametric, Bishop 2.5 Linear regression 3.0-3.2 Pod-cast lecture on-line Next lectures: I posted a rough plan. It is flexible though so please come with suggestions Bayes
More informationME/CS 132: Introduction to Vision-based Robot Navigation! Low-level Image Processing" Larry Matthies"
ME/CS 132: Introduction to Vision-based Robot Navigation! Low-level Image Processing" Larry Matthies" lhm@jpl.nasa.gov, 818-354-3722" Announcements" First homework grading is done! Second homework is due
More informationLecture 6: Edge Detection
#1 Lecture 6: Edge Detection Saad J Bedros sbedros@umn.edu Review From Last Lecture Options for Image Representation Introduced the concept of different representation or transformation Fourier Transform
More informationDigital Image Processing. Prof. P. K. Biswas. Department of Electronic & Electrical Communication Engineering
Digital Image Processing Prof. P. K. Biswas Department of Electronic & Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Image Enhancement Frequency Domain Processing
More informationImage Sampling and Quantisation
Image Sampling and Quantisation Introduction to Signal and Image Processing Prof. Dr. Philippe Cattin MIAC, University of Basel 1 of 46 22.02.2016 09:17 Contents Contents 1 Motivation 2 Sampling Introduction
More informationMultimedia Computing: Algorithms, Systems, and Applications: Edge Detection
Multimedia Computing: Algorithms, Systems, and Applications: Edge Detection By Dr. Yu Cao Department of Computer Science The University of Massachusetts Lowell Lowell, MA 01854, USA Part of the slides
More informationImage Sampling & Quantisation
Image Sampling & Quantisation Biomedical Image Analysis Prof. Dr. Philippe Cattin MIAC, University of Basel Contents 1 Motivation 2 Sampling Introduction and Motivation Sampling Example Quantisation Example
More informationesac PACS Spectrometer: forward model tool for science use
esac European Space Astronomy Centre (ESAC) P.O. Box, 78 28691 Villanueva de la Cañada, Madrid Spain PACS Spectrometer: forward model tool for science use Prepared by Elena Puga Reference HERSCHEL-HSC-TN-2131
More informationPoint-Based Rendering
Point-Based Rendering Kobbelt & Botsch, Computers & Graphics 2004 Surface Splatting (EWA: Elliptic Weighted Averaging) Main Idea Signal Processing Basics Resampling Gaussian Filters Reconstruction Kernels
More informationFIFI-LS: Basic Cube Analysis using SOSPEX
FIFI-LS: Basic Cube Analysis using SOSPEX Date: 1 Oct 2018 Revision: - CONTENTS 1 INTRODUCTION... 1 2 INGREDIENTS... 1 3 INSPECTING THE CUBE... 3 4 COMPARING TO A REFERENCE IMAGE... 5 5 REFERENCE VELOCITY
More informationImage processing. Reading. What is an image? Brian Curless CSE 457 Spring 2017
Reading Jain, Kasturi, Schunck, Machine Vision. McGraw-Hill, 1995. Sections 4.2-4.4, 4.5(intro), 4.5.5, 4.5.6, 5.1-5.4. [online handout] Image processing Brian Curless CSE 457 Spring 2017 1 2 What is an
More informationComputer Vision. Recap: Smoothing with a Gaussian. Recap: Effect of σ on derivatives. Computer Science Tripos Part II. Dr Christopher Town
Recap: Smoothing with a Gaussian Computer Vision Computer Science Tripos Part II Dr Christopher Town Recall: parameter σ is the scale / width / spread of the Gaussian kernel, and controls the amount of
More informationObject classification in photometric surveys using machine learning techniques
Object classification in photometric surveys using machine learning techniques Walter A. Santos Marcus Costa-Duarte, Alberto Molino, Laura Sampedro, Laerte Sodre et al. S-PLUS meeting - 11/ago/2016 - IAG/USP
More informationPACS Spectrometer Simulation and the Extended to Point Correction
PACS Spectrometer Simulation and the Extended to Point Correction Jeroen de Jong February 11, 2016 Abstract This technical note describes simulating a PACS observation with a model source and its application
More informationComputer Graphics. Sampling Theory & Anti-Aliasing. Philipp Slusallek
Computer Graphics Sampling Theory & Anti-Aliasing Philipp Slusallek Dirac Comb (1) Constant & δ-function flash Comb/Shah function 2 Dirac Comb (2) Constant & δ-function Duality f(x) = K F(ω) = K (ω) And
More informationBiomedical Image Analysis. Spatial Filtering
Biomedical Image Analysis Contents: Spatial Filtering The mechanics of Spatial Filtering Smoothing and sharpening filters BMIA 15 V. Roth & P. Cattin 1 The Mechanics of Spatial Filtering Spatial filter:
More informationFeature descriptors. Alain Pagani Prof. Didier Stricker. Computer Vision: Object and People Tracking
Feature descriptors Alain Pagani Prof. Didier Stricker Computer Vision: Object and People Tracking 1 Overview Previous lectures: Feature extraction Today: Gradiant/edge Points (Kanade-Tomasi + Harris)
More informationTheoretically Perfect Sensor
Sampling 1/60 Sampling The ray tracer samples the geometry, only gathering information from the parts of the world that interact with a finite number of rays In contrast, a scanline renderer can push all
More informationEdge Detection. Announcements. Edge detection. Origin of Edges. Mailing list: you should have received messages
Announcements Mailing list: csep576@cs.washington.edu you should have received messages Project 1 out today (due in two weeks) Carpools Edge Detection From Sandlot Science Today s reading Forsyth, chapters
More informationPACS. Considerations for PACS Mapping. Herschel. PACS Mapping Page 1. Babar Ali,David Frayer,Pierre Chanial
PACS Mapping Page 1 Considerations for PACS Mapping Babar Ali,David Frayer,Pierre Chanial PACS Mapping Page 2 Req. I Mapping considerations for PACS data reduction pipelines I - A. History Version Date
More informationContrast Optimization: A faster and better technique for optimizing on MTF ABSTRACT Keywords: INTRODUCTION THEORY
Contrast Optimization: A faster and better technique for optimizing on MTF Ken Moore, Erin Elliott, Mark Nicholson, Chris Normanshire, Shawn Gay, Jade Aiona Zemax, LLC ABSTRACT Our new Contrast Optimization
More informationContrast Optimization A new way to optimize performance Kenneth Moore, Technical Fellow
Contrast Optimization A new way to optimize performance Kenneth Moore, Technical Fellow What is Contrast Optimization? Contrast Optimization (CO) is a new technique for improving performance of imaging
More informationACS/WFC Crosstalk after Servicing Mission 4
Instrument Science Report ACS 2010-02 ACS/WFC Crosstalk after Servicing Mission 4 Anatoly Suchkov, Norman Grogin, Marco Sirianni, Ed Cheng, Augustyn Waczynski, & Marcus Loose March 10, 2010 ABSTRACT The
More informationSampling and Reconstruction. Most slides from Steve Marschner
Sampling and Reconstruction Most slides from Steve Marschner 15-463: Computational Photography Alexei Efros, CMU, Fall 2008 Sampling and Reconstruction Sampled representations How to store and compute
More informationBasics. Sampling and Reconstruction. Sampling and Reconstruction. Outline. (Spatial) Aliasing. Advanced Computer Graphics (Fall 2010)
Advanced Computer Graphics (Fall 2010) CS 283, Lecture 3: Sampling and Reconstruction Ravi Ramamoorthi http://inst.eecs.berkeley.edu/~cs283/fa10 Some slides courtesy Thomas Funkhouser and Pat Hanrahan
More informationERROR RECOGNITION and IMAGE ANALYSIS
PREAMBLE TO ERROR RECOGNITION and IMAGE ANALYSIS 2 Why are these two topics in the same lecture? ERROR RECOGNITION and IMAGE ANALYSIS Ed Fomalont Error recognition is used to determine defects in the data
More informationLine Drawing. Introduction to Computer Graphics Torsten Möller / Mike Phillips. Machiraju/Zhang/Möller
Line Drawing Introduction to Computer Graphics Torsten Möller / Mike Phillips Rendering Pipeline Hardware Modelling Transform Visibility Illumination + Shading Perception, Color Interaction Texture/ Realism
More informationScanner Parameter Estimation Using Bilevel Scans of Star Charts
ICDAR, Seattle WA September Scanner Parameter Estimation Using Bilevel Scans of Star Charts Elisa H. Barney Smith Electrical and Computer Engineering Department Boise State University, Boise, Idaho 8375
More informationComputer Graphics and Image Processing
Computer Graphics and Image Processing Lecture B2 Point Processing Joseph Niepce, 1826. The view from my window 1 Context How much input is used to compute an output value? Point Transforms Region Transforms
More informationSegmentation and Grouping
Segmentation and Grouping How and what do we see? Fundamental Problems ' Focus of attention, or grouping ' What subsets of pixels do we consider as possible objects? ' All connected subsets? ' Representation
More informationPeripheral drift illusion
Peripheral drift illusion Does it work on other animals? Computer Vision Motion and Optical Flow Many slides adapted from J. Hays, S. Seitz, R. Szeliski, M. Pollefeys, K. Grauman and others Video A video
More informationData products. Dario Fadda (USRA) Pipeline team Bill Vacca Melanie Clarke Dario Fadda
Data products Dario Fadda (USRA) Pipeline team Bill Vacca Melanie Clarke Dario Fadda Pipeline (levels 1 à 2) The pipeline consists in a sequence of modules. For each module, files are created and read
More informationRobotics. Lecture 5: Monte Carlo Localisation. See course website for up to date information.
Robotics Lecture 5: Monte Carlo Localisation See course website http://www.doc.ic.ac.uk/~ajd/robotics/ for up to date information. Andrew Davison Department of Computing Imperial College London Review:
More informationImage Processing. Overview. Trade spatial resolution for intensity resolution Reduce visual artifacts due to quantization. Sampling and Reconstruction
Image Processing Overview Image Representation What is an image? Halftoning and Dithering Trade spatial resolution for intensity resolution Reduce visual artifacts due to quantization Sampling and Reconstruction
More informationBiometrics Technology: Image Processing & Pattern Recognition (by Dr. Dickson Tong)
Biometrics Technology: Image Processing & Pattern Recognition (by Dr. Dickson Tong) References: [1] http://homepages.inf.ed.ac.uk/rbf/hipr2/index.htm [2] http://www.cs.wisc.edu/~dyer/cs540/notes/vision.html
More informationFourier Transform in Image Processing. CS/BIOEN 6640 U of Utah Guido Gerig (slides modified from Marcel Prastawa 2012)
Fourier Transform in Image Processing CS/BIOEN 6640 U of Utah Guido Gerig (slides modified from Marcel Prastawa 2012) 1D: Common Transform Pairs Summary source FT Properties: Convolution See book DIP 4.2.5:
More informationTheoretically Perfect Sensor
Sampling 1/67 Sampling The ray tracer samples the geometry, only gathering information from the parts of the world that interact with a finite number of rays In contrast, a scanline renderer can push all
More informationSpatial Interpolation & Geostatistics
(Z i Z j ) 2 / 2 Spatial Interpolation & Geostatistics Lag Lag Mean Distance between pairs of points 1 Tobler s Law All places are related, but nearby places are related more than distant places Corollary:
More informationLecture 4: Spatial Domain Transformations
# Lecture 4: Spatial Domain Transformations Saad J Bedros sbedros@umn.edu Reminder 2 nd Quiz on the manipulator Part is this Fri, April 7 205, :5 AM to :0 PM Open Book, Open Notes, Focus on the material
More informationEE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 WRI C225 Lecture 04 130131 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Histogram Equalization Image Filtering Linear
More informationPoints Lines Connected points X-Y Scatter. X-Y Matrix Star Plot Histogram Box Plot. Bar Group Bar Stacked H-Bar Grouped H-Bar Stacked
Plotting Menu: QCExpert Plotting Module graphs offers various tools for visualization of uni- and multivariate data. Settings and options in different types of graphs allow for modifications and customizations
More informationImage Processing, Warping, and Sampling
Image Processing, Warping, and Sampling Michael Kazhdan (601.457/657) HB Ch. 4.8 FvDFH Ch. 14.10 Outline Image Processing Image Warping Image Sampling Image Processing What about the case when the modification
More informationA METHOD FOR OPTIMAL IMAGE SUBTRACTION.
A METHOD FOR OPTIMAL IMAGE SUBTRACTION. C. Alard 1,2,R.H.Lupton 3 ABSTRACT We present a new method designed for optimal subtraction of two images with different seeing. Using image subtraction appears
More informationDiffuse Source Absolute Sensitivity and Point Source Relative Sensitivity as a Function of Extraction Slit Height for STIS First-Order Modes
Instrument Science Report STIS 98-01 Diffuse Source Absolute Sensitivity and Point Source Relative Sensitivity as a Function of Extraction Slit Height for STIS First-Order Modes Ralph Bohlin, Space Telescope
More informationHOUGH TRANSFORM CS 6350 C V
HOUGH TRANSFORM CS 6350 C V HOUGH TRANSFORM The problem: Given a set of points in 2-D, find if a sub-set of these points, fall on a LINE. Hough Transform One powerful global method for detecting edges
More informationALMA Memo 386 ALMA+ACA Simulation Tool J. Pety, F. Gueth, S. Guilloteau IRAM, Institut de Radio Astronomie Millimétrique 300 rue de la Piscine, F-3840
ALMA Memo 386 ALMA+ACA Simulation Tool J. Pety, F. Gueth, S. Guilloteau IRAM, Institut de Radio Astronomie Millimétrique 300 rue de la Piscine, F-38406 Saint Martin d'h eres August 13, 2001 Abstract This
More informationWatershed Sciences 4930 & 6920 GEOGRAPHIC INFORMATION SYSTEMS
HOUSEKEEPING Watershed Sciences 4930 & 6920 GEOGRAPHIC INFORMATION SYSTEMS CONTOURS! Self-Paced Lab Due Friday! WEEK SIX Lecture RASTER ANALYSES Joe Wheaton YOUR EXCERCISE Integer Elevations Rounded up
More informationFiltering Applications & Edge Detection. GV12/3072 Image Processing.
Filtering Applications & Edge Detection GV12/3072 1 Outline Sampling & Reconstruction Revisited Anti-Aliasing Edges Edge detection Simple edge detector Canny edge detector Performance analysis Hough Transform
More informationComputer Vision: 4. Filtering. By I-Chen Lin Dept. of CS, National Chiao Tung University
Computer Vision: 4. Filtering By I-Chen Lin Dept. of CS, National Chiao Tung University Outline Impulse response and convolution. Linear filter and image pyramid. Textbook: David A. Forsyth and Jean Ponce,
More informationPart 3: Image Processing
Part 3: Image Processing Image Filtering and Segmentation Georgy Gimel farb COMPSCI 373 Computer Graphics and Image Processing 1 / 60 1 Image filtering 2 Median filtering 3 Mean filtering 4 Image segmentation
More informationEdge Detection. EE/CSE 576 Linda Shapiro
Edge Detection EE/CSE 576 Linda Shapiro Edge Attneave's Cat (1954) 2 Origin of edges surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity Edges are caused
More informationDrawing a Triangle (and an introduction to sampling)
Lecture 4: Drawing a Triangle (and an introduction to sampling) Computer Graphics CMU 15-462/15-662, Spring 2017 Assignment 1 is out! https://15462-s17.github.io/asst1_drawsvg/ Let s draw some triangles
More information