polynomials, trigonometric functions, simple derivatives and integrals. Client Side
. Server Side. Acknowledgements. Equation Image. Rank Filtered. Background.
Augmented Reality Equation Plotter" Salman Naqvi, Uzair Sikora"
EE368 Spring 2013
Department of Electrical Engineering, Stanford University
Motivation • • • •
Client Side
Graphical Visualization of an equation can often help better understand underlying trends of real variables. Mobile Application with the use of Android platform, OpenCV, Tesseract OCR, and Template Matching with a server to overlay a plot on top of user’s axes. Typing out a complex equation made easier Decently Complex equations can be solved including explicit equations composed of exponentials, polynomials, trigonometric functions, simple derivatives and integrals
Equation Image
Rank Filtered Background
Eqn. Solved: Data Points Sent
Canny Edge Detection
Canny Edge Detector
Template Match Form Equa%on String
Harris Keypoint Detector
Create Plot Points
Manual Correc,on
Future Work
Tesseract Math Chars • •
72(x6(2)+2x+26(x))/8(x6(3)+5x) • Bad alpha-num recognition • excessive false positives
Smart Character Fixing
•
Template Matching Database
•
y=(x^(2)+2x+2^(x))/e^((x^(5)+5x)) • Utilize region properties • Aspect Ratio, Solidity, # Holes, y-Centroid, Hole Centroid • Fixes problems with 6,(,e,0; (,l,|,t,i; s,5; 3,a; /,x; & other pairs
Create Plot
Recursively Segment Image
Create Plot
y=((x.^(2)+2.*x+2.^(x)))./(exp(x.^(5)+5.*x));
Coordinate Axis Preview Frame
Server Side
Query user for equa%on approval
Recursive Segmentation & Exponentiation
Equation Parsing
Binarize Image
Equa%on Image Capture
Experimental Results Binarized
Method
Char. Confusion Matrix
• • 5 fonts, 35 characters each • Database quickly updated • calculus can thus also be used
•
Database Characters
Perspective Insensitive plotting Robust keypoint detection for faster and efficient axis detection Skew and Perspective Insensitive OCR using RANSAC and VLFeat Handwritten equation detection capability by training an SVM. 3D plotting capability by adding plot transformation and multiple variable equation detection Interactive plot reading features by allowing the user to place dots where the plot readings are needed Detailed Confusion Matrix for addressing all edge cases in character recognition
Harris Keypoint Detection Recognized Characters
Close Operation
/*+-=^√dπ∫yx()|0123456789elsintaco.
/*+-=^√dπ∫yx()|0123456789elsintaco.
Acknowledgements
Template Matching Result y=(x^(2)+2x+2^(x))xe^(x^(s)+5x))
•
• Astounding! but still false pos. • Need character properties
•
Extremely grateful to Sam Tsai, for crafting pathway for character recognition And the TA, David Chen, continuous help along the way
