Reading Corner

• Chapter 8: How to pick a GIS
• Chapter 10

Announcements:

• 343y Third Year Field Camp Manditory Meeting
  • Tuesday March 21, 5:05pm, SSC 2333
• Next Ombudsmen meeting will be held next week

In Today's Lecture:

• Midterm Exam Discussion
• Neighborhood Filters - Scan and Filter (see Intermediate Operations - Neighborhood Filtering Lecture)
• Digital Elevation Models (DEM); Terrain analysis and visualization
• Introduction to Remote Sensing: A Few Key Concepts
• Orbiting Earth Observation("Geographic") RS satellites

Neighborhood Filters

Scan and Filter

What they do:

• Compute the value of a cell as a function of the values of its neighbors.

GIS Tutor II hypertext example

The Scan operation: (See the MFWORKS documentation)

• Popular Scan modifiers are: Average, Total, Maximum, Minimum, Around.

The Filter Operation: (See the MFWORKS documentation)

• In the Filter operation, the LowPass modifier is particularly useful.
• other useful modifiers include HighPass and Sobel

Filtering is often used for smoothing on one hand, and for sharpening on the other.

Filter LowPass

• Engineer Speak: "Let only the low frequency information (ie. big changes) pass through the filter"
• An averaging or smoothing filter.

The default Filter LowPass and Scan Average yield similar results

• The default Filter LowPass and Scan Average Diagonally should yield identical results

One of the most commonly used filters is a change detector.

• Used for identifying where changes occur and determining their magnitude and orientation (on the 2-D plane)
• Filter HighPass1, HighPass2, Sobel

Filter HighPass

• "Let only the high frequency information (ie. small changes) pass through the filter"
• Edge, or change, detection/enhancement.

MF•Works’s High Pass1 filter (edge enhancement) operation is defined in Jensen (1986) as follows:

• HFF 5,out = (2 x BV5) - LFF 5,out
• where:
  • HFF stands for High Frequency Filter
  • LFF stands for Low Frequency Filter
  • BV5 stands for Brightness Value of Pixel 5 in a 3X3 Box:
    • 1 2 3
      4 5 6
      7 8 9

The High Pass2 filter (edge enhancement) is a Weighted Sum using the following weights:

• -1 -1 -1
  -1 9 -1
  -1 -1 -1
• Another high pass filter variant (not implemented in MF•Works) uses the following weights:
  • 1 -2 1
    -2 5 -2
    1 -2 1

Filters find use with point, line, area, and surface data.

• For instance, they can be used to:
  • identify density of points,
  • to thicken lines (a form of interpolation),
  • to smooth data, to sharpen the edges of areas,
  • or to depict the rate of change of a surface.

The user has varying control over the filtering process in different programs and modules (within programs).

For instance, by specifying parameters such as:

• filter size (Scan, some Filter(s))
• filter shape (Scan)
• applying a filter to selected areas (defined using a second map layer that acts as a mask) (Scan).
• weights (Filter)

Further sophistication: Compute the value of a cell as a function of the weighted values of its neighbors.

How are the weights represented?

• Often as an explicit tiny weights matrix ("map").
• The values are the weight coefficients.

End of Lecture: March 16, 2000

Announcements:

• Reading Corner
  • Assigned Reading: Chapter 6: “Why is it there?”
  • Read Chapter 10: “The Future of GIS”
• Final Exam
  • Tuesday April 24th
  • 7:00pm
  • 2 hours
  • SSC 2028
• Special 280b Lecture and Lab Section
  • Q & A Session
  • Tuesday April ??th
  • 3:00pm - 5:00pm
  • SSC 2322
• Next Year's 583a / 383a
  • Pazner's GIS Offering
  • not listed, but available
  • “Advanced Seminar in Geographic Information Science”
  • Seminar and Project Course

Today's Lecture

• DEM
• RS
• DIP: Next Week

Digital Elevation Models (DEM)

DEM is an important topic because:

• the environment (and geography) exists on a surface
• the methods can be used with continuous multivariate data

DEM definition: a digital representation of the continuous variation of relief over space

• DEM: “Digital Elevation Model”
• DTM - Digital Terrain Model - another term for the same thing(s)

Terrain was/is traditionally represented by contours

• Terrain is continually varying
• Therefore it does not lend itself to modeling using the choropleth map model
• Contours (isolines) can represent continuous variation
• Conceptually a contour is a closed nested polygon

Contours are an old, and in many cases inferior, method

• They have relative limited use for processing, analysis, modelling, and visualization
• Important for representing terrain using a sparse (non area-filling) line-based representation

Problems with contour lines

• often made using older more limited and subjective techniques
• sub-optimal sampling guided by contour making objectives
• need to be converted to a point model such as discrete altitude matrix
• produce poorer quality DEMs than direct spot elevation measurements

The new dominant DEM model

• a dense matrix or array representing a surface
• to the exclusion of contours and spot elevations

PinPoint II: The Rock....

Disadvantages of DEM

• large amount of redundancy in areas of uniform terrain
• inability of fixed grid cell size to adapt to variations in relief complexity
• eg. matrix too coarse to represent all the critical terrain features such as peaks, pits, passes, ridge lines and stream courses
• the exaggerated emphasis along the axes of the grid for certain kinds of computation such as line-of-sight calculations

Useful beyond the bounds of physical space...

• while DEM originated from, and is mostly used for, terrain modeling
• they can be used to model the continuous variation of any other attribute Z over a two-dimensional surface (Burrough, 1986)
• ie. it can be used for any data grids where it is assumed the data is continous

DEM input-processing-output is versatile

• this introduces complexity
• and hence mastering this sub-area is a challenge

DEM input

• Data sources for DEMs:

import (e.g. from the Internet)

• Import an existing DEM
• Import digital contour data (e.g. DLG hypsography layer)

Contour data from topographic maps, hypsographic ‘color’ separates

• digitizing, heads-up (screen) digitizing, manual-trace-scan-process

Softcopy Photogrammetry: aerial photos, sonar, radar, satellites

• e.g. process DEM and orthophoto from air-photo stereo-pairs

GPS ground survey

• sampling spot elevations
• mobile (air, sea, land) ‘kinematic mode’
• GPS/GIS processing
• interpolation

Terrain Analysis and Visualization

The Need for DEM

Storage of elevation base data for digital topographic maps in databases

• Case in point: our TopoDEM file

As a background for displaying thematic information

• Case in point: our TopoLandscape file

3-D display of landforms

• landscape design and planning (landscape architecture)
• for military purposes (weapon guidance systems, pilot training)

Cut-and-fill problems in road design and other civil and military engineering projects

For analysis of cross-country visibility (civil & military applications)

For planning routes of roads, locations of dams, etc. (siting problems)

For computing elevation data derivative maps

• slope maps, aspect maps, and slope profiles
• creating shaded relief maps
• estimate erosion and runoff

For statistical analysis and comparison of different terrains (Physical Geography)

Provide data for landscape and landscape process simulation models

To represent other continually varying surfaces

• by replacing altitude with another appropriate attribute,
• the DEM can represent surfaces of:
• travel time, cost, population, indices of visual beauty, levels of pollution, groundwater levels, etc.

Question: could it be that the greatest future need for DEM will be with non-spatial data?

Products derived from DEM

Shaded relief maps:

• based on a model of what the terrain might look like illuminated from a given direction
• can be produced very simply using pseudo shaded relief filters
• and with physical algorithms which use slope gradient and slope aspect, and a reflectance model

Applications of shaded relief maps:

• done to visualize the terrain
• in combination with thematic information: they can show the results in a realistic way
• ‘drape over landscape’: technique for overlaying image or thematic information onto shaded relief maps

Contour maps (as a DEM product)

*** Possible Exam Question: Why do a contour map when you already have a DEM?

Maps of slope gradient, aspect, convexity, concavity:

• slope comprises two main components:
  • gradient: the rate of change of altitude
  • aspect: the compass direction of this rate of change

Line-of-sight maps:

• intervisibility of points in a landscape is important for
  • military applications

• planning microwave communication networks
• and for recreational studies

note that DEMs often do not take land cover (e.g. woods, buildings, true landform) into account.

• The results need to be interpreted with care

Block diagrams, profiles and horizons:

• block diagrams are visually appealing and useful for landscale design and simulation
• and for any Z data
• rendered as line drawings or as shaded relief

the computation usually requires that the observer specify a viewing point and scale factors for the vertical exaggeration

inclusion of perspective in the computation improves the results

Volume estimation in cut-and-fill problems

creation of before and after DEMs to show the proposed changes in area

the DEM obtained by differencing is that of the material removed or added

Automated landform delineation from DEM:

• detecting ridges and stream lines
• determining the boundary of a catchment
• determining lengths of slopes (e.g. for calculating soil loss with the USLE)

Take a little break here...

Introduction to Remote Sensing: A Few Key Concepts

History of Remote Sensing:

• Roots in aerial photography
• IR camouflage detection
• NASA'a space program
  • Gemini
  • Apollo
  • Skylab
  • etc.

The technical/engineering field of Remote Sensing and the growing AeroSpace Business.

This section is based in part on Strahler & Strahler: Modern Physical Geography - 3rd Ed and up

• Special Embedded Section on "Remote Sensing for Physical Geography".
  • You may use it for additional reference.

The Electromagnetic Spectrum

• Visible Light
• TV/Radio waves

Two kinds of sensing systems: active and passive

Microwaves and Radar-RadarSat

• cloud and rain penetration
• penetration of solid (eg. sand)
• forest topography (canopy radar "shadows")
• cons: complex systems, data (content and geometry)

Absorption of Electromagnetic Energy by the Atmosphere

• Sunset
• Mie scattering

Aerial Photography

• high altitude
• mid altitude
• low altitude

Color Infrared Photography

• Military legacy and ongoing importance (re vegetation)

Digital Images

• Image processing (IP).
  • The pixel (picture element) as the basic, or 'atomic' image building block.

Scanning Systems

• Multispectral Scanners

The four types of Resolution (R):

• spatial (s)
• spectral (l)
• radiometric (r)
• temporal (t)

Multispectral Images

Spectral Signatures. MSS bands versus 'features'; the basis for image classification

• multispectral response of a single 'feature' ("spectral signature")
• multifeature representation in a single spectral 'band'
• (1) & (2) above combined: multifeature representation in multispectal bands.

Why the complexity?

• Two general geographic "laws" apply:
  • phenomena tend to be localized (in space, time, and characteristics)
  • the environment is highly complex

End of Lecture: March 23, 2000

Announcements

• Reading
  • Chapter 9 “GIS in Action”
  • Chapter 6: “Why is it there”
    • Any Questions?

• Final Exam
  • Tuesday April 24, 7:00pm
  • 2 Hours
  • SSC 2028
• Next Week
  • No Lecture
  • No Lab
  • No Office Hours
• Next Year's 583a / 383a
  • Pazner's GIS Offering
  • not listed, but available
  • “Advanced Seminar in Geographic Information Science”
  • Seminar and Project Course

Today's Lecture

• Final Exam Format and sample questions
• Zonal Transformations
• Summary Statement
• Geographic Information Science
• RS
• DIP

Final Exam Format and Sample Questions

• Click here to see the Sample Final Exam
• Worth 40% of course mark
• What to study:
  • Textbook: Chapters 6, 8, 9 & 10
  • Lecture Notes
  • Lab Assignments
  • Lab Handouts

How to Answer Exam Questions

• Read the Question Carefully
• Make sure you understand what it is asking
• Can I answer this question?
• With essay Question: Do a quick outline
• Manage your time carefully: You have 2 hours (120 minutes, 100 marks...)

Zonal Transformation — Score

What it does

• Spatial processing by cartographic districts defined using the zones in a second map layer.

Tomlin distinguishes between 2 main types

• Functions of entire zones and Functions of partial zones.
• Fragmented zones result from a 2 step process of tallying and then contrasting the tallied result with the original value and recording the contrasted result.

It is common for the “Report”, a side effect often provided by this operation, to be a most useful output.

This operation is sometimes thought of as an end product; to produce tallied results.

Score can be used as a means rather than as an end

• By incorporating it in procedures in clever ways

Since there are 2 layers it is possible to cross tabulate, ie. to alternate (or reverse) the information and the districting layer designation.

Examples:

• Tomlin’s HomesPerBlock (pp. 157, Fig. 6-2)
• Tomlin’s BlockProximity (pp. 158, Fig. 6-3)
• Tomlin’s ProximityByBlock (pp. 161, Fig. 6-5)

A non-spatial Example. Tallying occurrences in graphs by groups of rows or columns (representing space, time, or any other variable)

The ZonalCentroid Problem (the general case)

• Find the spatial centre of a zone.

The Zonal Centroid PinPoint Problem

• Pretend you are cutting out a zone with scissors
  • Where should we place a pin underneath the zone so that the zone cut-out would be balanced on this pin?

Tomlin describes a cartographic model for solving this problem

• Zonal Transformation plays an important role in this model.
• the Zonal centroid procedure from Tomlin’s book (Part III, Ch.7, p. 169) uses a RowNumber map and a ColNumber map.

Summary Statement...

Raster GIS work lies on the 4-way intersection of:

• Tool: image processing (subfield of computer science)
• Method: quantitative and symbolic techniques (mathematics and statistics, logic, common sense)
• Strategy: problem solving strategies (modeling (science), information science)
• Presentation: cartographic design and visualization (graphic design)

Geographic Information Science

• a more simple name: Computer Geography

In either case, these are modern Geographic (or Spatial) Techniques

• the science and technology behind them
• and the applications they are used for

These Geographic Techniques include:

• Cartography
• Remote Sensing
• Global Positioning Systems — GPS
• Spatial Data Bases (SDB)
• Geographic Information Systems — GIS
• Spatial Analysis and Modeling
• Spatial Decision Support Systems (SDSS)

Applications are in the following major branches:

• Environmental Modeling
• Business Geographics

I invite you to join the field of GI Science

• which is about —
  • thinking spatially
  • ... and being able to actually do something about it
  • due to modern technologies and economies

As a Geo280b graduate, I would like to welcome you to the world of Computer Geography!

• which meshes our love of nature with our fascination with science, technology, and culture

Catch-Up

Thermal Infrared Sensing (night-time)

Infrared Imagery

• James Bond Movies are highly educational ;-)

Radar Sensing Systems: SLAR, SAR, (SIR)

Orbiting Earth Observation(“Geographic”) RS satellites

The Landsat Program

Future additions: 15m panchromatic, stereo-based DEM capability (5m resolution suggested)

The SPOT Satellite

Products

• images: on tape, on floppy, CD, Internet, and hard copy
• imagemaps (ortho): custom mosaicked, Topo-quad corresponding,
• DEM images (from SPOT stereo-pairs)

Imagemaps (ortho)

• quad corresponding
• custom mosaicked

Landsat TM vs. SPOT

• Landsat TM merged with SPOT

Orbital Radar Sensing: RADARSAT; Ice, Geology, (Forestry?)

AVHRR Imagery (global scale) 4x4 km

New Future Satellite Systems

• both centralized and commercialized
• specialized
• improved spatial resolution(s)
• Hyper Spectral Resolution Remote Sensing
• stereo

*** End of Lecture, End of Course ***

Self Study Material

Remote Sensing Digital Image Processing (RS DIP)

• Image Interpretation
• Manual vs. Machine Assisted Image Interpretation/Analysis
• The ELEMENTS of image interpretation:
• Primary:
• Tone
• Color
• Secondary:
• Size
• Shape
• Texture
• Tertiary:
• Pattern
• Height, Shadow
• Higher:
• Site & Association ("Context")
• Three levels of image feature understanding:
• detection
• identification
• interpretation/analysis
• Digital Image Processing
• Enhancement vs. Analysis: differences
• Image Enhancement
• more subjective, emphasis on visual display
• Image Analysis
• more objective, emphasis on quantitative transformations
• Enhancement vs. Analysis: reciprocal support
• enhancement to guide the analysis (visualization oriented)
• analytical transformations to give enhanced views
• Mixed use for problem solving and modeling
• partial classifiers
• soft classifiers
• (e.g. VIS = Vegetation , Impervious , Soil)
• Types of DIP Processing:
• Initial statistics extraction
• Initial display alternatives
• single bands
• false color composites
• Image preprocessing
• radiometric correction
• detector response
• atmospheric effects
• geometric correction
• Image enhancement
• image reduction and magnification
• contrast enhancement
• spatial filtering (image & feature enhancement)
• edge enhancement
• smoothing
• Special transformations
• principal components analysis
• vegetation indices
• texture transformations
• band ratios
• transects
• Thematic information extraction
• unsupervised classification
• cluster building
• supervised classification
• training sites
• minimum distance to means classifier
• parallelepiped classifier
• maximum likelihood classifier
• incorporating ancillary and contextual data
• accuracy assessment
• change detection
• End of Lecture
• Zonal Transformation-Score, Other Topics
• Today's Lecture:
• How to Answer Essay Exam Questions
• Zonal Transformation-Score
• Other Topics: Appendices
• How to Answer Exam Questions
• Zonal Transformation-Score
• What it does: Spatial processing by cartographic districts defined using the zones in a second map layer.
• Tomlin distinguishes between 2 main types.
• Functions of entire zones and Functions of partial zones.
• Fragmented zones result from a 2 step process of tallying and then contrasting the tallied result with the original value and recording the contrasted result.
• It is common for the "Report", a side effect often provided by this operation, to be a most useful output.
• This operation is sometimes thought of as an end product; to produce tallied results.
• Score can be used as a means rather than as an end.
• By incorporating it in procedures in clever ways.
• Since there are 2 layers it is possible to cross tabulate, ie. to alternate (or reverse) the information and the districting layer designation.
• In addition, cross tabular measures are possible; whereby a measure is provided that takes into account the combined dual tallying.
• Examples.
• Tomlin's HomesPerBlock (pp. 157, Fig. 6-2)
• Tomlin's BlockProximity (pp. 158, Fig. 6-3)
• Tomlin's ProximityByBlock (pp. 161, Fig. 6-5)
• A non-spatial Example. Tallying occurrences in graphs by groups of rows or columns (representing space, time, or any other variable)
• The ZonalCentroid Problem (the general case)
• Find the spatial centre of a zone.
• The Zonal Centroid PinPoint Problem
• Pretend you are cutting out a zone with scissors
• Where should we place a pin underneath the zone so that the zone cut-out would be balanced on this pin?
• Tomlin describes a cartographic model for solving this problem
• Zonal Transformation plays an important role in this model.
• the Zonal centroid procedure from Tomlin's book (Part III, Ch.7, p. 169) uses a RowNumber map and a ColNumber map.
• Other Topics: Appendices
• Appendices-Table of Contents
• Allied Courses
• Modern Allied Areas
• Input, Output, Error
• CAF
• Cartography: Graphic Design, Visualization
• Allied Courses
• allied in Geography
• Remote Sensing: Intro and Advanced
• Cartography: Intro and Advanced
• SDSS
• Quantitative Methods (Stats)
• allied outside of the department
• Quantitative Methods (Stats)
• Info Sci., Modelling
• Visual Arts
• Computer Science
• Modern Allied Areas
• 3-D Rendering
• Visualization
• Animation
• Interactive Animation (-> "Virtual Reality")
• Multimedia
• Hypermedia
• Input, Output, Error
• Input: How is the spatial data entered into a GIS SDB?
• (Digital BlackBoard Discussion)
• Entering the non-spatial Attribute Data in the DB
• and then what?
• tasks to consider next include:
• linking
• verifying
• editing
• updating
• querying
• Output: What kinds of output are there?
• (Digital BlackBoard Discussion)
• Error
• Error can be thought of as "anti data"
• error is to data what anti-matter is to matter
• 2 types of errors
• syntactic errors
• content errors
• data verification: finding and dealing with error
• using printouts/displays
• Data Quality and Error
• major concern of science
• an importnat subfield in an emerging Geog. Info. Science.
• What are the sources for error?
• (Digital BlackBoard Discussion)
• CAF
• GPS
• what it is
• what it is used for: primary data collection
• links to RS
• links to GIS
• links to mobile computing: slates, SDBs, hand-held (palm-top)
• Characterizing Computer Assisted Fieldwork (CAF):
• appropriate computer tools for conducting fieldwork,
• ie. portable, rugged, inexpensive and easy to use.
• Fieldwork computing software
• outline processors and word processors
• spreadsheets
• drawing programs and GIS
• filing or database systems
• statistical packages and other
• special fieldwork software
• Characterizing Portable GIS
• spatial processing on the fly: in the field and on the go
• involves: field GIS concepts, tools methods and applications
• Portable GIS- general types of activities
• navigation-position and way-finding
• field data collection
• on-site image interpretation
• computer-assisted field mapping
• field spatial data processing
• Cartography: Graphic Design, Visualization
• Information visualization
• Visualization means making information accessible to human vision
• * Examples of information visualization: The map to the Doctor's Office needs help..., and Transportation Table and Graphic
• Good visualization of information requires good graphic design. What then are the primary principles of graphic design?
• There are common principles for information visualization and information organization
• Tufte's Envisioning Information ...
• about E. R. Tufte: Yale University statistician and political scientist
• He is a brilliant intellectual and eloquent author with a distinct "Tuftean" style. Tufte narrates, in his book, a fascinating, broad, and rich collection of examples of both excellent and shoddy information graphics.
• his previous book: Tufte, E. R. [1983]: The Visual Display of Quantitative Information, Graphics Press. 197p.
• Envisioning Information ("EI") is a treatise on the principles of graphic design for information visualization.
• EI's Introduction
• The main points of Tufte's Introduction to EI are as follows:
• "The world is complex, dynamic, multidimensional;"
• "...the paper is static, flat."
• "How are we to represent the rich visual world of experience and measurement on mere flatland?"
• The principles of information design are universal-like mathematics-and are not tied to unique features of a particular language or culture. "Consequently, our examples are widely distributed in space and time:..."
• Escaping Flatland - Key concepts:
• "Escaping this flatland is the essential task of envisioning information..." (p. 12)
• This chapter outlines a variety of design strategies that sharpen the information resolution, the resolving power, of paper and video screen. In particular, these methods work to increase (1) the number of dimensions that can be represented on plane surfaces and (2) the data density (amount of information per unit area). (p. 13)
• Color and Information - Key concepts:
• "Above all, do no harm" (p. 81)
• The fundamental uses of color in information design: to label, to measure, to represent or imitate reality, to enliven or decorate.
• * Example: Global AIDS Map
• slide(s) [or transp.]
• Tufte asks "What palette of colors should we use to represent and illuminate information?" and states "A grand design is to use colors found in nature"
• * Example: NW London (ON) TopSpot instructional spatial database
• * In-class Color Exercise : * Analyze the colors used in the interior design of this room, its furnishings, and the clothes of those present in it. Make notes of your observations.
• The Three Core Structural Principles Chapters
• Micro/Macro Readings
• Layering and Separation
• Small Multiples
• Micro/Macro Readings - Key concepts:
• to clarify, add detail (p. 37): information rich displays: increase data density and increase data dimensionality (cf. the stated goal at the beginning of Escaping Flatland)
• "Such [micro/macro] designs can report immense detail, organizing complexity through multiple and (often) hierarchical layers of contextual reading" (p. 38, bottom)
• "Micro/macro designs enforce both local and global comparisons and, at the same time, avoid the disruption of context switching. All told, exactly what is needed for reasoning about information." (p. 50)
• "it is not how much empty space there is, but rather how it is used. It is not how much information there is, but rather how effectively it is arranged". (p. 50)
• "Clutter and confusion are failures of design, not attributes of information" (p. 51)
• "God is in the details" (Mies Van Der Rohe) (p.51)
• Layering and Separation - Key concepts:
• "Among the most powerful devices for reducing noise and enriching the content of displays is the technique of layering and separation, visually stratifying various aspects of the data." (p. 53)
• Remember the 'graphic calculus': 1 + 1 =3 or more (Josef Albers) (p.61) "the endlessly contextual and interactive nature of visual elements" (p. 61)
• "Layering of data, often achieved by felicitous subtraction of weight, enhances representation of both data dimensionality and density on flatland..." (p. 60)
• * Examples: Train-withTrain Collisions, and Tile Maps (Gosia), Other...
• Small Multiples - Key concepts:
• At the heart of quantitative reasoning is a single question: "Compared to What?" (p. 67)
• small multiples: keep the design constant and show data variation, are inherently multivariate, are shrunken graphics, are very useful for showing temporal change
• "comparisons must be enforced within the scope of the eyespan" (p. 76)
• * Example: Sarnia map/scatterplot matrix
• * Example: Transportation Table and Graphic (revisited)

*******************************

• Interpolation (Interpolate)
• Neighborhood Filters: the Scan and Filter operations in brief.
• What they do: Compute the value of a cell as a function of the values of its neighbors.
• GIS Tutor hypertext example
• The Scan operation: (See the MFWORKS documentation)
• Popular Scan modifiers are: Around, Total, Average, Maximum, Minimum.
• The Filter Operation: (See the MFWORKS documentation)
• In the Filter operation, the LowPass modifier is particularly useful.
• Filtering is often used for smoothing on one hand, and for sharpening on the other.
• Filter LowPass
• Engineer Speak: "Let the low-pass (ie. big changes) frequency information through the filter"
• An averaging or smoothing filter.
• The default Filter LowPass and Scan Average yield similar results
• The default Filter LowPass and Scan Average Diagonally should yield identical results
• Filters find use with point, line, area, and surface data.
• For instance, they can be used to:
• identify density of points, to thicken lines (a form of interpolation), to thin lines, to smooth data, to sharpen the edges of areas, or to depict the rate of change of a surface.
• The user has varying control over the filtering process in different programs and modules (within programs).
• For instance, by specifying parameters such as:
• filter size (Scan, some Filter(s))
• filter shape (Scan)
• weights (Filter)
• Further sophistication: Compute the value of a cell as a function of the weighted values of its neighbors.
• How are the weights represented?
• Often as an explicit tiny weights matrix ("map").
• The values are the weight coefficients.
• Curious about filtering? Questions?
• Ask your instructor(s).