With the aim on making sure the learning of Digital Image Processing (DIP), the theory sustaining each process realized by Imagery is included on each module, it also appears in an extensive way in the Class Notes (pdf format) accompanying Imagery, which are used by the author in his classes of DIP for graduate students of Sciences and Engineering.

IMAGERY is a Digital-Image-Processing EduVirtualLab created by Javier Montenegro Joo. 

 IMAGERY operates on images supplied by the author and also on those of the user.

Left:   Histogram-aided edge detection of a grey-leveled image.

With Imagery the histograms of three images may be extracted and compared

This module shows an algorithm for Image Segmentation. The input image contains several objects and these have been extracted one-by-one with a segmentation algorithm.

Controlled Image fusion:  The two images at the top are the input images to be fused. Below are the output images.  The user sets the percentage of each image in the fusion.  It is also possible to ignore one of the colors in the input images.  With Imagery up to three images may be fused in the proportions set by the user.

The modules of Imagery include the pertinent theoretical background of the themes it covers, in this way the user knows at every moment the mathematical transformations operating on the images and how they operate.

Grey-leveled image edge detection with the Sobel's Gradient (first derivative).  Three different gradient thresholds set by the user can be appreciated at a  time.

User defined Convolution filters.

Modules in Imagery   ( 44 )

Color (05)
          01 Color Synthesis
          02 RGB Color mixing
          03 Color To Grey-Level Transformation
          04 Color Filtering in images
          05 Image Brightness and Darkness
Edges (09)
          01 Edge Enhancement by First Derivatives and Gradient
          02 Edge Enhancement by Gradient: The Roberts Operator
          03 The Prewitt Operator
          04 The Sobel Operator
          05 Generalized Sobel Operators
          06 Edge Direction Detection through Gradient
          07 Edge Enhancement via the Laplacian Operator
          08 High Boost Filter (Fine detail enhancement)
          09 Comparison of Sharpening Filters
Convolution (02)
          01 Spatial Operators (Convolution Filters)
          02 User-Defined Convolution Filters
Geometry (06)
          01 Representing a Straight Line
          02 Circularity (Binary images)
          03 Translations
          04 Rotations
          05 Size Scaling
          06 Shearing
Masks (03)
          01 Point && Small Hole Detection Mask
          02 Line Detection Masks
          03 Noise-Reduction Median Filter
Transformations (07)
          01 Image Transformations
          02 Erosion of Binary Images
          03 Dilation of Binary Images
          04 Image Subtraction
          05 Thresholded Image Difference
          06 Controlled Image Fusion (2 images)
          07 Controlled Image Fusion (3 images)
Histograms (05)
          01 Histograms (Grey-leveled images)
          02 Histograms: Compare the histograms of three grey-leveled images
          03 RGB Histograms
          04 Binarizer: Conversion of grey-level to binary images. Thresholding
          05 Borderliner: Histogram-Assisted Edge Detection of grey-leveled Images
Segmentation (01)
          01 Binary Image Segmentation through Wrapping
Miscelaneous (01)
          01 Binary Image Boundary Detector
Pattern Recognition (05)
          01 Signatures: Pattern Centroidal Profile Representation
          02 Massive RTS-Invariant Moments
          03 Boundary RTS-Invariant Moments
          04 The Polar Hough Transform
          05 Hough-Transform-based Line Detector
 

Download Demo:  Imagery: Digital Image Processing

 Back to Table of Contents        Order online  - Downloads 

EconoModeler :   Analytic Geometry for Economics Applications

Analytic Geometry for Economists and for Economic Analysis

Economic Models - Mathematical Economics

EconoModeler  

This is an Analytic Geometry EduVirtualLab for Computer Assisted Teaching and Learning with applications to Economics.

EconoModeler is also used in professional applications.   

As it can be seen with EconoModeler just by clicking and dragging the mouse the user can very easily and very quickly design Points, Lines, Circles, Ellipses, Parabolas, Hyperbolas and Circular Arcs. As the user makes the curves on the black-color region, the corresponding coordinates, equations and pertinent data are shown on the left side text column.    

At any moment the position of the origin of coordinates can be placed wherever the user needs it to be (ideal for those applications where only the first quadrant is used). The names of the X and Y axes can be changed at will. The black-color region can be printed (on a black background so that color ink is saved). The left side column with results may also  be printed alone. EconoModeler exists in English and in Castellano.

EconoModeler calculates and reports the following intersections:  line-line, line-circle, line-parabola, line-elipse, line-Hyperbola, parabola-parabola. 

The user's imagination is the limit.

Prices (USA dollars)  >>> Personal use:  35.00 ...... institutional use:  140.00

Easy Viewing Plane Analytic Geometry,   The best way of really learning while visualizing the solution to problems.  This is an EduVirtualLab for the person who really wants to learn Plane Analytic  Geometry (PAG), or for the person who loves visualizing it.  This is a tool that helps to grasp a conceptual understanding of  PAG while visualizing the solution to problems by hundreds in a very short time. 

The range of problems solved by Curvlinear goes from the most simple up to for example finding the  linear-equations of the heights of a triangle, or the equation of the line through the intersections of two circles, Or the extended  equation of the circle passing by three given points (see the icons).  

Admits two types of  coordinates input: either mouse or keyboard.   

The image on screen as well as the textual reports may be printed at will, just click a button.

Prices (USA dollars) Curvilinear >>> Personal use:  35.00 ...... institutional use:  140.00

Plane-Analytic-Geometry Problem Solver, is for the user who already knows the subject and wants to verify his/hers solutions, or for the teacher or student who needs to solve hundreds of problems in a very short time.

 Teachers may use this software to quickly prepare classes and also to propose and try  problems for tests and exams.  Students may verify their hand-made solutions with this tool.

Multiple keyboard-input modes. Reads and interprets many types of equations supplied by the user.  Includes a quadratic equation solver. 

The image on screen as well as the textual reports may be printed at will, just click a button.

Panageos is Not recommended for beginners. 

MathPhysicsGames:  

Mathematical Physics Computer Games

MathPhysicsGames:   This is a set of interactive and audio-visual Computer Games based on Mathematical Physics Modeling.  This software allows the user to assess the application of Physics and Mathematics in the development of amusing Computer Games, these kind of Computer Games not only improve the alertness and speed of reaction of the user,  they also boost his/her interest in Physics and Mathematics.   These games make use of Physics and Mathematics topics like Parabolic Motion, Velocity, Acceleration, Velocity components, equations, curve intersections, etc, etc.

List of Computer Games in MathPhysicsGames:

(1) Shoot Down The Ufo:  the Ufo flies on Parabolic, Sinusoidal, or lineal orbits. The user controls the Cannon elevation angle with the mouse and fires at will.  

(2) Shoot Down the Airplane:   User-controlled cannon and firing.

(3) Hit the Tank:  The user drops bombs from the flying airplane on a moving tank. 

(4) Bouncings: a ball bounces on the borders of a table, only if these are activated by the user.

Games have four levels of difficulty and constitute a serious challenge to the user.

Warning:    

 Use with caution, these Computer Games might boost your attention and alertness,   increase your speed of reaction and coordination and foster your interest in Physics and Mathematics

These games are included in the Physics Virtual Laboratory, PVL                        

   Back to Table of Contents                                               See the PVL       

Physics Virtual Lab (PVL):  Mechanics

These are some of the Mechanics simulation modules included in the PVL

<<< Elastic Collisions: The Bouncing Ball

The user sets the Coefficient of Restitution, The Initial Height and the first Bouncing Angle.  The module makes the simulation along with the visualization and reports successive bouncing angles, heights and velocities.

Friction on a tilted plane.

The user sets the Mass Weight and the Kinetic Friction Coefficient, then he/she clicks a button to little by little tilt the plane, the block slides down when the elevation angle reaches the corresponding sliding angle. 

Wheel Gearing

The user sets the number of wheels ( 2, 3 or 4 ), their radii, the linear velocity and the rotation direction.  The wheels rotate the angles corresponding to their actual Angular Velocities so that its dependence on radius length is evident. As the wheels rotate, the module reports: Angular Velocities, Number of turns, Angular displacement and linear displacements (same for all wheels). 

Projectile Flight Simulator     (parabolic Motion)

The user sets the shooting velocity, cannon elevation angle, horizontal and vertical air resistance, and acceleration of gravity. The simulator makes the corresponding simulation and visualization. Reported data: Horizontal range, Highest altitude, flight time.

Whenever the projectile flight is paused (at user's will),  the velocity vectors are displayed. Several trajectories can be displayed simultaneously.

Uniformly Accelerated Motion Data Plots Generator

The user sets the Initial Velocity, Positive or Negative Acceleration, Delta Time, and Number of Steps, and the software generates the numerical results and plots of:  

(1)  x(t) = Vo t + (1/2) a t ²

(2) V(t) = Vo + a t

(3) Delta X(t)

(4) V(x) = Sqrt[ Vo ² + 2 a x ]

thus the user can analyze the resulting data and plots. It is also possible to generate "Real-Life, Experimental" data,  these can be saved and used to feed a plotter.

Behavior of velocities (V, Vx, Vy) in the Parabolic Motion

The user sets the Elevation angle of a cannon in the origin of coordinates and its shooting velocity Vo, the module makes the plottings of projectile velocities V, Vx, Vy,  as time goes by

These are some of the Electricity & Magnetism simulation modules in the PVL

<<< Electric Fields and Equipotential Surfaces due to point charges.   The user places any number of point charges (positive or negative) by clicking with the mouse on screen, the charge-disposition is fixed also by the user, then  clicks a button to get either the Electric Field or the Equipotential Surface of the group of charges. 

The Electric Transformer

Computes input/output Voltages, Number of Spires, Power and Electric Currents.

Resistance and Dissipated Power in an Electric Circuit.  The user controls the Resistances, the Emf, the internal resistance. 

Induced Electromotive Force on a square loop traversing a magnetic field. 

The loop displaces either automatically or manually (the user moves it with the mouse).

Works with inwards or outwards magnetic fields.  Plots magnetic flux on loop, shows clockwise, null and anticlockwise induced electric currents.

The user sets the values of the magnetic induction B, loop side length and velocity.

Electric circuits

Left: As the user sets the Electromotive force, the internal resistance and the resistances in the resistors, the program reports the  electric currents, voltage drops, dissipated powers in the whole circuit and in individual resistors.

Left: Charged particle Deflection by an Electric Field, the user sets the E-Field intensity, mass, charge and initial velocity of the charged particle.

EduVirtualLab on Waves and Oscilations

These are some of the Waves & Oscillations simulation modules in the PVL

<<< The Damped Oscillator:  In order to appreciate the effect of the damping, the oscillation starts in a free environment, then on a sudden a damping material surrounds the oscillator.

Total Energy Distribution in the Simple Harmonic Motion.  

The exchange between the Kinetic and the Potential energies is appreciated as the Spring oscillates conserving its Total Energy.  The user controls the Mass, and the Elastic constant k.

Standing (Stationary) waves

Clearly visualizes a wave traveling to the right side, another wave going to the left side, and the standing wave produced by their  interference. Obviously the user controls the Amplitude, Wavelength, Frequency, etc.  Also it is possible to freeze the time, and to visualize the motion of individual waves

Damped Harmonic Oscillations Analyzer

Under damping, Over damping and Critical Damping.

The user sets the Mass, Elastic constant k, Viscosity b, Initial Phase, Delta Time and Number of events, the module generates the data and makes the corresponding plotting.

The user may analyze the generated numerical data and the plots.  Prints the whole image or only the generated numerical results.  

Simple Harmonic Motion: The Rotor

Superposition of two Simple Harmonic Motions in the same direction

Physics Virtual Lab,  PVL       ( 167  Simulators )

Besides hundreds of individual users around the world, the following Universities and High Schools have purchased Institutional Licenses of the PVL for students instruction:   

- Physics Dept of Central Connecticut State University (CCSU - USA)

- Universidad ESAN (Lima Peru)

- UCAN ( Angola, Africa)

- St Petersburg High (FL, USA)  

Download PVL Demo:          Physics Virtual Lab, PVL: PVL_Demo

The PVL is the Non-Plus-Ultra of the Physics Simulation Softwares, this Virtual Lab includes detailed simulation modules dealing with Mechanics, Waves, Oscillations, Thermodynamics, Electricity, Magnetism, Light, Optics, Hydrostatics, Applications, etc.   The main feature of PVL is that every user can adapt it to his/her own level.   The PVL is mainly addressed to the university student / teacher of Sciences and Engineering, however, since a variety of different-level books have been used to develop PVL, it becomes also suitable for Physics courses in Colleges and International Baccalaureate Programs.  High School students will find many modules of PVL helpful to simulate and visualize many Physics topics covered in their courses.

Physics lovers and amateurs will find in PVL very stimulating and enlightening experiences while learning at their own pace.  

VirtualDynamics Professional and Rigorous Simulators execute Mathematical Models:  whenever there is an equation or  mathematical model to represent an experiment or physical event, it has been used in  PVL  to produce its simulation. In order to visualize the simulation while this takes place the more advanced techniques have been used, the result is a professional and robust software.

See some of the Mechanics modules of the PVL     PVL Mechanics 

See some of the Waves and Oscillations modules of the PVL     PVL Oscillations  

See some of the PVL Electricity & Magnetism simulators   PVL Electromagnetics 

The  PVL  is an EduVirtualLab of Physics, is Audio-Visual, it contains detailed simulators of phenomena from Mechanics, Hydrostatics, Waves, Hydrodynamics,  Electricity, Magnetism, Thermodynamics, Optics, Applications, etc, etc.   

PVL is a professional virtual lab that leaves behind simple demonstrations and rather puts emphasis on very precise simulations under the direction of the user.     

Here only a few of the simulators from the package are shown, the complete list of simulators is included below. 

<<< PVL : Stereo Sounds >>>

Deviation by a Prism.-

The user sets the Refractive Index of the prism and its top angle.  As the angle of the Incident Ray is varied with the mouse, the Refracted Rays and the Total Deviation Angle are shown, also their numerical values are reported. The Minimum Deviation of the prism is clearly appreciated when the ray inside the prism is parallel to its base. 

This module plots Total Deviations  vs   Incident Angles for user-fixed values of the refractive indices  

Physics Virtual Lab, PVL,  is  interactive and very easy to use, there is no need of either manuals or training or tutorials. 

This is a tool recommended not only to students and teachers but also to the persons fond of Physics, those who really love this subject.  Obviously secondary schools with ambitious teaching programs and universities, may use this software instead of the traditional laboratories, which are expensive, fragile, hard to maintain, limited, ....

Left: Operation of the Four-Cycle Piston Motor.

Intuitively Easy-To-Use simulators.

Users do not need to get trained to operate these simulators. At any moment during use, non-applicable controls (options,  buttons, parameter changers) are disabled and only appropriate controls are enabled, in this way there is no chance to activate a non-opportune control.  For instance the buttons to abort or pause an experiment are disabled at any time except while an experiment is running.

<<< The Carnot Engine: Converting Heat into Work.  As the piston displaces due to the expansion or  compression of the gas inside the cylinder, the two Isothermals and two  Adiabatics of the Carnot Cycle are plotted.  Pertinent theoretical explanations are shown as every stage of the Carnot cycle takes place.

Mass Falling Down due to the Gravity in a Medium whose Resistance is Proportional to the Velocity of the Mass.

The user sets the Resistance of the medium, the initial velocity of the falling mass, the number of events and the delta time, the software makes the corresponding data generation and plots Position, Velocity, Acceleration and Delta Position.    Allows data collection from simulated real-life experiments.

A similar module dealing with Motion against a Resistance proportional to  V ² (squared Velocity) is also included in PVL

Tri-Dimensional Lissajous

Superposition of Three Simple Harmonic Perpendicular Oscillators. The user controls oscillator amplitudes, frequencies and phase varying, as well as image orientations, displacements and animation speed.  Several animations (manual and automatic) are possible. Lissajous orbits may be seen from any angle. 

PVL is Audio-Visual:  whenever it is pertinent, simulators include stereo sounds, for instance when a bomb hits the ground, the sound of a explosion is produced, a collision of two cars on the air track is accompanied by a knocking sound.

Learning by comparison.- 

Tracks of experiments on screen have different colors (for instance, projectile trajectories) and them may be kept for comparison, in this way the effect of changing parameters can be easily observed.  The data associated to every experiment is displayed with the color of the track of that experiment, in this way, tracks and data are easily identified and compared.

No passive user.-  The PVL  is strongly dedicated to animation and simulation with user's data. For instance in the case of the Doppler Effect, up to twelve wave fronts are generated one after other and their expansion process is visualized while the wave source keeps displacing.  Obviously time may be frozen for as long as the user wants, so that he/she can see what is taking place and analyze the situation. This module includes a collection of sounds that when activated by the user, reproduce examples of the Doppler effect.

Use the screen as a blackboard ....

Whenever an experiment or demonstration occupies small space, several instances of it may be displayed wherever the user wants on screen, like on a blackboard.  In this way several cases of a  topic  may be appreciated at once on screen, thus facilitating understanding and learning, obviously the instructor's work becomes easier and much more productive.

Pre-defined examples.-  In general, whenever the objective of  an experiment is not obvious, the simulators include a set of pre-defined examples, in this way the user may execute first these examples and then after the experiment is understood, he/she may try with his/her own parameters.

Time freezing

Time can be frozen at any moment during simulation, it is then when pertinent vectors (velocity, force, etc) are displayed.  In real-life experiments neither time can be frozen nor vectors are seen, by the other hand, on a blackboard, vectors are seen only where the teacher depicts them. These simulators enable users to watch pertinent vectors wherever and whenever they want and as many times as desired by just clicking a button.

Unrestricted experimentation.-   Unrestricted experimentation leads to learning through extreme-situations exploration.  Physics Virtual Lab allows for this type of experimentation since the user may try experimenting with data sets that in real life may be impossible or may even harm the user.  For instance, in a conventional laboratory it may be impossible an exaggerated elongation of a spring, since it may break the instruments, or may encounter obstacles or may even hurt the user if suddenly released.

A Laboratory at home

For the person who enjoys physics and wants to appreciate it comfortably at home, this software is the ideal tool.

Screen Printing

Screen images may be printed, just click a button (see included images). 

Text Printing

Some modules generate abundant data in text form, this can be printed as a text file with just a click on a button.

Author easy to reach

Users may contact the author by e.mail or telephone at any time, for suggestions and doubts.  The author thanks in advance for  ideas and criticism to improve this material.

The user sets Amplitudes Ex and Ey of electric fields, their  initial phases and wave front polarization type.  Every time the experiment is paused the electric field E and its components Ex and Ey may be seen. Pre-defined examples are also included. Up to four cases may be conserved on screen with their respective parameters.

Left : Adiabatic Compression or Expansion of an Ideal Gas.- The user sets Cp / Cv, temperature and pressure, a button click starts the piston movement. The plots are made as the piston displaces. The gas inside the cylinder changes color as its pressure is varied.

Theory and Equations

Every PVL module includes pertinent theoretical information like some very specific description of the phenomenon under study and the equations used to execute the simulation. Generally space is not enough on the screen to show all this, then an information window is displayed on the click of a button.

Left : Ball - Wedge Elastic Collision.   The user sets ball velocity, ball and block mass, the program makes the simulation. As in all of these simulators slow motion and sound are at user's will.

Left: The Ballistic pendulum.-   The user controls bullet mass and velocity as well as block altitude.  A mouse click starts the simulation which may be visualized even in slow motion if the user wants.  

Cannon-Bullet and Falling-Mass Encounter.-

The user controls the cannon elevation angle, the bullet initial velocity and the horizontal distance from the cannon to the vertical along which the mass falls down since the moment the cannon makes fire.

The software calculates the corresponding mass-releasing altitude so that the bullet hits the falling mass. 

In the figure several cases are shown, each with a different color.

Bi Convex (Converging) Lens

The user sets the object distance to the lens and its size, the software computes the generated image size, position and other magnitudes and generates the corresponding visualization.

All  PVL  modules include theory, equations and relevant information.

Forces acting on a hanging picture. 

With the mouse the user places the picture wherever he wants on screen, all the involved forces appear automatically.  The  user controls picture weight and position.

Lissajous Orbits (Motion in two dimensions).

The superposition of two perpendicular Simple Harmonic Motions generates the Lissajous Orbits.  Freeze time at any moment to see why a central force is the resultant of the combined forces of two oscillating springs.  In this case the tracks of up to four experiments may be conserved on screen together with their generating parameters. The user sets the  Amplitudes, frequencies and initial phases of the oscillators.

The module dealing with Tri-Dimensional Lissajous shows the motion of Lissajous orbits in three dimensions. 

Light refraction through parallel plates

The user sets the refraction index of each slab and the module makes the computations and shows the light trajectory through the slabs

Light refraction through a semi circular slab

Prices (US dollars) >>> PVL:  personal use:  100.00  --------------  Institutional use: 450.00 (Quantity discounts)                  

   Order online  - Downloads                                                      Back to Table of Contents     

This is an ultra quick Audio Visual File Explorer dealing strictly with the most commonly used file formats (this is why it is ultra quick), permits to very quickly and with only a single mouse click visualize (or listen to) hundreds of images and files containing textual information, also explores by executing animated-Gif images,  audio (sound) and video  files.
Very quickly can explore hundreds of sound, image and textual files.  Useful when the user wants to very quickly get to know the contents of many files (text, sound, images, video) in a very short time. There is absolutely no waiting when shifting files.

Supported File formats... Image Files: Bmp, Jpg, Gif, Ico, Emf, Wmf, Animated Gif. Video Files: Avi. Sound Files: Wav, Mid.  
Exe-type files are executed.  All other file formats ( .pas, .cpp, .dsk, etc, etc) are displayed as .txt 
Files may be deleted, renamed, and printed.                                                         

AudioVisualizer ---- Price  US dollars:  35.00