Rubik s Cube Recognition and Identification using Computer Vision

Transcription

1 Rubik s Cube Recgnitin and Identificatin using Cmputer Visin Saichand Bandarupalli and Rahul Dev Appapgu Curse N: CSCI507 Clrad Schl f Mines

2 Intrductin Named after Ern Rubik, its inventr (in 1947) Has always been an interest fr mathematicians and engineers Quick Facts: Official Rubik s cube (3x3) cnsists f 6 slid clrs. Each small cube is called a cubie Has 8 crner cubies,12 edge cubies and 6 center cubies (immvable) Pssible number f cnfiguratins: 43,252,003,274,489,856,000 Gd s Number: 20

3 Key Objectives Recgnitin and Identificatin f Rubik s cube using Cmputer Visin techniques/algrithms 3D mdel recnstructin f the Rubik s cube Slving the identified Rubik s cube using Matlab

4 Existing Wrk Rubik's Cube Slver using an Arduin and MATLAB Rubik's Cube Simulatr and Slver Nt pen surce Mstly used feature extractin

5 Our Apprach Recgnitin: Each face has t be identified separately 9 cubie clrs in a given face have t be detected Repeat fr all 6 faces 1. Fixed Lcatin in the FOV f a Camera Place ne face f the cube in a given lcatin Crp the face f the cube part Divide int 9 regins fr identifying clr Nn - Rbust

6 Our Apprach Recgnitin f cube in any randm psitin Extract R, G, B images frm a given image Transfrm all 3 images int black and white images adjusting threshld Extract blb features (Area, Centrid, MajrAxis, MinrAxis) Set threshld range fr area, and identify blbs in that range (t1<area<t2) Calculate difference between majr and minr axes. (Fr ideal square, it is 0) If the difference is less than a given threshld, identify it as a square. Identify all squares Extract minimum and maximum centrid crdinate values. Draw a bunding bx using the crdinate, thus identifying the face. Crp the face.

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8 Our Apprach Clr Identificatin Divide the face f the cube int 9 regins Cnvert the image frm RGB space t HSV space Take the median HSV value f a given regin Identify the clr using the Hue Hue values accunt fr bth dark and bright images Repeat fr all 6 faces and stre clrs in a 3x3x6 matrix Clr Hue Min Hue Max Orange Yellw Green Blue White Red Use the matrix and fill3 functin frm Matlab in rder t plt the cube

9 Results Obtained

10 Limitatins Reflective Surface Incident Light is reflected back t the camera. Leads t Bad Clr Identificatin External squares in the backgrund Other Squares may lead t bad detectins. Slutin: Median Distance Estimate Bad Lighting Cnditin Slutin: May adjust intensity Extreme distance between cube and camera may lead t pr identificatin Squares very clse t the cube squares

11 Limitatins Lighting Cnditins Red Face Bad Lighting Red Face Gd lighting

12 Slving the cube Des nt invlve cmputer visin Brute frce apprach All pssible permutatins Standard 7-step algrithm Thistlethwaite s Algrithm Almst impssible fr a human t execute Called, the first genuine math attempt t slve the Rubik s Cube Can slve under 45 mves

13 Thistlethwaite s Algrithm Permits nly fixed number f mve set / states - (G0,G1,G2,G3,G4) A cube in any cnfiguratin can be classified in ne f the abve 5 categries Any mve sequence can be cnstructed using G0,if cube is in G0 Idea is t bring cube t the final state frm a given state using the fixed mve sets. (G0 t G4,G4 being the final state, which is the slved state) Generate Pruning Tables

14 Thistlethwaite s Algrithm Cntinued Pruning table hlds pssible Gi -> the current cnfiguratin and all pssible G(i+1)s, the next pssible states. In rder t generate pruning table, ne has t back iterate frm the slved state, applying the pssible fixed mve sets Once we have a fully ppulated Pruning Table, we fixed the rientatin f the edge and crner cubies. Lk thrugh the pruning table and apply pssible mves fr a given fixed rientatin until the cube is slved

15 References