Spin Image Correlation

Steven M. Kropac

April 26, 2005

Presentation contents

Overview

Background/Motivation

Operational Concept

Functional Diagram

Software Implementation

Application

Conclusion

Overview

A spin image provides a 2D object centered description of a 3D mesh object.

Essentially, a spin image represents the radial and elevation distances to every other vertex on the mesh.

Resultant spin images can be compared (correlated) to identify similarities between vertices.

Background/MotivationObject recognition for 3D computer vision has many applications in the area of robotics and automation. Andrew Johnson works on Surface System Guidance Navigation and Control

for the mars science laboratory (2009)

“Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes” –Andrew E. Johnson and Martial Hebert (5/1999) Presents an approach for recognition of complex objects in cluttered 3-D

scenes.

Encoding relative positions of many points on the surface is not new. Others have performed explored using view-based approaches, or storing points along curves.The approach described in this presentation is different because the spin images are much more discriminating than curves and angles and is object centered, so it is not view dependant.

Operational Concept

Provide a Graphical User Interface (GUI) for loading 3D mesh models. Models are specified in .ply file format

Two operations available to user:1. Generate spin images for every vertex on a loaded 3D

mesh model2. Perform spin image correlation between a selected

vertex and every other vertex on the model. Highly correlated vertexes will be colored bright green Vertices with limited correlation will be colored very dark

green or black (background color).

Functional DiagramGenerate Spin images

Model mesh

Calculate spin images foreach vertex in the mesh

Store spin imagesin an SQL database

Spin Image calculations

Start with a selected vertex and associated normal, which we call an oriented point.

Calculate alpha, beta distances from the oriented point to every other vertex.

Alpha = perpendicular distance from surface normal

Beta = signed perpendicular distance to the plane p

Spin Image calculationsCalculating alpha,beta

p – oriented pointn – surface normalx – position of another vertex on mesh Beta – difference of x - p, then dot product with

surface normal to project on Normal.Alpha – length of vector from x to p, subtract out

Beta componentDistance between points = sum of square of differences

Spin Image calculationssample alpha, beta values

Spin Image calculationsGenerate spin images

A bin size (i,j) is selected as a multiple of the resolution of the mesh. My application uses 1x.

The alpha,beta values are then translated to the appropriate bin. Bin dimensions might be 4x20. Alpha Beta

ranges might be [0,2] and [-3,3]. When an alpha,beta pair is translated the

associated bin is incremented.

Spin Image calculationssample spin image bins

Functional DiagramPerform Spin-image Correlation

Model mesh

Select a vertex

Retrieve spin image forselected vertex and

iteratively retrieve spinimage for every other vertex

Compare selected vertexspin image with spin image

for current vertex on themodel mesh

Calculate correlationcoefficient between spin

images

Apply correlation coefficientto color of vertices (brightgreen = highly correlated)

Spin images database

Spin Image CorrelationCalculating correlation coefficient

Correlation coefficient provides the quality of a least squares fitting to the selected data set.

Software Implementatoin

The spin image application is implemented in C++ using Microsoft Visual Studio. The display of 3D mesh objects is accomplished using

OpenGL.

A MySQL database is utilized to store calculation of spin images. Database stores (filename, vertexIndex, alphaBucket,

betaBucket, intensityValue) For an image with 5000 vertices and a spin image size of 85x42

represents ~1.8 million database entries. Spin Image calculations takes several minutes The amount

of time is dependant on the number of vertices in the model.

Spin Image Application

The application provides the capability to parse .ply graphics files and display the 3D model using OpenGL.

Spin Image Applicationkeyboard commands

Left/right arrow – rotate along y axis

Up/down arrow – rotate along x axis

PgUp/PgDn – rotate along z axis

-/= zoom-out / zoom-in

Home/end – select next/previous vertex

Spin Image ApplicationPull-down menu features

File Open .ply file Exit

Operation Calculate Spin Images and store in Database Display Spin Image Correlations

View Zoom-in Zoom-out

Spin Image ApplicationResults

Selected vertex

Spin Image ApplicationResults (elephant)

5+ hours to generate spin images10 minutes to spin-correlate

Selected vertex

Conclusion

Spin images provides an interesting representation for surface matching.

More work needs to be done to fully understand how speed issues can be addressed. Ex: A 3D mesh has 5000 vertices. To calculate

all spin images for this model requires 5000 * 5000 = 25 million sets of calculations.