Ter Haar Romeny, FEV Scale-time. ter Haar Romeny, FEV Time measurements can essentially be processed in two ways: as pre-recorded frames or instances,

Slides:

Advertisements

Similar presentations

Sampling Design, Spatial Allocation, and Proposed Analyses Don Stevens Department of Statistics Oregon State University.

Advertisements

What is the neural code? Puchalla et al., What is the neural code? Encoding: how does a stimulus cause the pattern of responses? what are the responses.

What is the neural code?. Alan Litke, UCSD Reading out the neural code.

Ter Haar Romeny, EMBS Berder 2004 Deblurring with a scale-space approach.

Ter Haar Romeny, FEV Nuclei of fungus cell Paramecium Caudatum Spatial gradient Illumination spectrum -invariant gradient Color RGB original Color-Scale.

Ter Haar Romeny, MICCAI 2008 Regularization and scale-space.

Ter Haar Romeny, FEV 2005 Curve Evolution Rein van den Boomgaard, Bart ter Haar Romeny Univ. van Amsterdam, Eindhoven University of technology.

Ter Haar Romeny, EMBS Berder 2004 Gaussian derivative kernels The algebraic expressions for the first 4 orders:

Ter Haar Romeny, FEV Geometry-driven diffusion: nonlinear scale-space – adaptive scale-space.

Ter Haar Romeny, EMBS Berder 2004 How can we find a dense optic flow field from a motion sequence in 2D and 3D? Many approaches are taken: - gradient based.

Ter Haar Romeny, ICPR 2010 Introduction to Scale-Space and Deep Structure.

The linear/nonlinear model s*f 1. The spike-triggered average.

Johann Radon Institute for Computational and Applied Mathematics: 1/38 Mathematische Grundlagen in Vision & Grafik ( ) more.

Ter Haar Romeny, FEV Vesselness: Vessel enhancement filtering Better delineation of small vessels Preprocessing before MIP Preprocessing for segmentation.

for image processing and computer vision

EXAMPLE 4 Use the change-of-base formula SOLUTION 3 log 8 Evaluate using common logarithms and natural logarithms. Using common logarithms: Using natural.

DMEC Neurons firing Black trace is the rat’s trajectory. Red dots are spikes recorded from one neuron. Eventually a hexagonal activity pattern emerges.

Aula 5 Alguns Exemplos PMR5406 Redes Neurais e Lógica Fuzzy.

Ter Haar Romeny, FEV Nuclei of fungus cell Paramecium Caudatum Spatial gradient Illumination spectrum -invariant gradient Color RGB original Color-Scale.

Spike-triggering stimulus features stimulus X(t) multidimensional decision function spike output Y(t) x1x1 x2x2 x3x3 f1f1 f2f2 f3f3 Functional models of.

Methods and Techniques of investigating user behavior Introduction - why M & T? Gerrit C. van der Veer aims theory methods planning presentation.

Paul Heckbert Computer Science Department Carnegie Mellon University

Chapter 12 Fourier Transforms of Discrete Signals.

Optic flow from dynamic anchor point attributes a feasibility study Bart Janssen.

Microarray Gene Expression Data Analysis A.Venkatesh CBBL Functional Genomics Chapter: 07.

Logarithmic Functions and Their Graphs

Johann Radon Institute for Computational and Applied Mathematics: 1/48 Mathematische Grundlagen in Vision & Grafik ( ) more.

1 Methods in Image Analysis – Lecture 3 Fourier U. Pitt Bioengineering 2630 CMU Robotics Institute Spring Term, 2006 George Stetten, M.D., Ph.D.

EXAMPLE 4 Use the change-of-base formula SOLUTION 3 log 8 Evaluate using common logarithms and natural logarithms. Using common logarithms: Using natural.

Chapter 1: Introduction to Statistics

1 Image Basics Hao Jiang Computer Science Department Sept. 4, 2014.

Logarithmic Functions

Optical Flow Donald Tanguay June 12, Outline Description of optical flow General techniques Specific methods –Horn and Schunck (regularization)

Low Level Visual Processing. Information Maximization in the Retina Hypothesis: ganglion cells try to transmit as much information as possible about the.

Ch 111 Sensation & Perception Ch. 11: Sound, The Auditory System, and Pitch Perception © Takashi Yamauchi (Dept. of Psychology, Texas A&M University) Main.

FMRI Methods Lecture7 – Review: analyses & statistics.

Review of Ultrasonic Imaging

Systems (filters) Non-periodic signal has continuous spectrum Sampling in one domain implies periodicity in another domain time frequency Periodic sampled.

Monday August 24, Essential Question How are relationships between components on a scatter-plot graph determined? What is a “line of best fit” or.

Introduction. Spatial sampling. Spatial interpolation. Spatial autocorrelation Measure.

1 Motion Analysis using Optical flow CIS601 Longin Jan Latecki Fall 2003 CIS Dept of Temple University.

Ter Haar Romeny, CASIA 2015 scale-space The retina measures on many resolutions simultaneously.

1 Intensity Scales Exponents Logarithms dB dB SPL.

Measurements and Scale Arjan Kuijper

Model-based learning: Theory and an application to sequence learning P.O. Box 49, 1525, Budapest, Hungary Zoltán Somogyvári.

1 Methods in Image Analysis – Lecture 3 Fourier CMU Robotics Institute U. Pitt Bioengineering 2630 Spring Term, 2004 George Stetten, M.D., Ph.D.

State Estimation and Kalman Filtering Zeeshan Ali Sayyed.

CS Spring 2014 CS 414 – Multimedia Systems Design Lecture 3 – Digital Audio Representation Klara Nahrstedt Spring 2014.

Forecasting is the art and science of predicting future events.

Introduction to Scale Space and Deep Structure. Importance of Scale Painting by Dali Objects exist at certain ranges of scale. It is not known a priory.

Fundamentals of Multimedia Chapter 6 Basics of Digital Audio Ze-Nian Li and Mark S. Drew 건국대학교 인터넷미디어공학부 임 창 훈.

7.3 Logarithmic Functions as Inverses Objective(s): To write and evaluate logarithmic expressions To graph logarithmic functions.

1 Computational Vision CSCI 363, Fall 2012 Lecture 32 Biological Heading, Color.

Copyright © 2011 Pearson, Inc. 3.3 Logarithmic Functions and Their Graphs.

Automatic Picking of First Arrivals

Smoothing the intensities

Apply Properties of logarithms Lesson 4.5

BIVARIATE ANALYSIS: Measures of Association Between Two Variables

The Neural Code of the Retina

Volume 55, Issue 3, Pages (August 2007)

Binocular Disparity and the Perception of Depth

Attentional Modulations Related to Spatial Gating but Not to Allocation of Limited Resources in Primate V1 Yuzhi Chen, Eyal Seidemann Neuron Volume.

Bartlett D. Moore, Caitlin W. Kiley, Chao Sun, W. Martin Usrey Neuron

BIVARIATE ANALYSIS: Measures of Association Between Two Variables

A Scalable Population Code for Time in the Striatum

Evaluate the logarithm.

Stochastic Hydrology Simple scaling in temporal variation of rainfalls

End-Stopping and the Aperture Problem

Sensation and Perception

Definition and essential features of population and housing censuses

Presentation transcript:

ter Haar Romeny, FEV Scale-time

ter Haar Romeny, FEV Time measurements can essentially be processed in two ways: as pre-recorded frames or instances, or real-time. Humans are real-time, they continuously perform a temporal analysis with their senses. The scale-space treatment of these two categories will turn out to be essentially different. The prerecorded sequences are treated as regularly sampled points, leading to a regular causal time-scale-space, with temporal apertures and Gaussian temporal differential operators.

ter Haar Romeny, FEV We can never reach the present moment: A measurement aperture (operator) with infinitesimally short duration will be needed. In the real-time measurement and analysis of temporal data we have a serious problem: the time axis is only a half axis: the past. There is a sharp and unavoidable boundary on the time axis: the present moment.

ter Haar Romeny, FEV Koenderink proposed to reparametrize the time axis in a logarithmic Fashion, thus maintaining causality. The log time axis is now a full axis, allowing diffusion, i.e. causal operators. present

ter Haar Romeny, FEV Dimensionless elapsed time present

ter Haar Romeny, FEV The receptive fields become skewed: time

ter Haar Romeny, FEV It is interesting to study if the temporal receptive field (RF) sensitivity profiles match the predicted skewness for the different differential order. Many neurophysiology labs have recorded time sequences of neural RF’s, e.g. by the reverse correlation technique.

ter Haar Romeny, FEV DeAngelis, Ohzawa, Freeman, 1991 Cat V1 simple cell, 5 ms interframe interval

ter Haar Romeny, FEV De Valois, Cottaris, Mahon, Elfar and Wilson, 2000 space time A clear skewness is observed in the time direction.

ter Haar Romeny, FEV A time-scale model of skewed receptive field profiles on a logarithmic axis.

ter Haar Romeny, FEV From group theory: Any half-axis should be parameterized logarithmically to enable linear addition of a multiplication property for the measurement convolution. Examples: The scale axis (Powers of Ten: ‘orders of magnitude’); The intensity axis (retina log mapping, gamma-corrections); The time axis; The sound pressure axis (decibels); Etc.