Paper Presentation

Paper Presentation

Alperen Degirmenci

April 19, 2011

Liu, J.; Subramanian, K.; Yoo, T.; Van Uitert, R.

“A stable optic-flow based method for tracking colonoscopy images,”

Computer Vision and Pattern Recognition Workshops, 2008 IEEE Computer Society

Conference: pp. 1-8, June 2008.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Our Project

Using a borescope for generating a 3D reconstruction of the cochlear canal and a safe insertion path via virtual fixtures.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Background and Motivation

• A better algorithm for determining the position of the endoscopic camera during colonoscopy

• Uses optical flow

• Can be used as a part of our 3D reconstruction algorithm

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Algorithm Overview

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Sparse Optical Flow Field

2

Flow vector

1

Pixel location (x,y)

Time t

If L is the scale-space representation of image

I, then

Scale-space image

Anisotropic Gaussian Image

Anisotropic Gaussian is applied to account for the differential sampling rates across the spatial and temporal dimensions.

σ,and τ are the spatial and temporal scale parameters

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Sparse Optical Flow Field

• By applying the following Harris matrix, corners in the image are detected

• Will be used as features for tracking

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Sparse Optical Flow Field

We are interested in corresponding pairs that exhibit maximum variance in the spatial domain and minimum difference along the temporal direction.

Similarity between corresponding pairs

How distinct the selected features are in their local neighborhood

Smaller the

Θ, better the match

The numerator can be converted into the iterative Lucas-Kanade algorithm using

Taylor series approximation

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Sparse Optical Flow Field

• The relationship between spatio-temporal scale and the scale metric.

Ground truth flow vectors are in red

• Estimated flow vectors are in blue

Green cubes represent the selected feature point positions

• (a) Results with fine spatial and temporal scales

• (b) Results with optimal spatial and temporal scales

• (c) Result with relatively coarse scales

• (d) The response curve between spatiotemporal scales and the scale metric

• The scale values at points A, B and C correspond to images (a), (b), and (c) respectively.

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Sparse Optical Flow Field

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Dense Flow Field and FOE

• The characteristic spatial and temporal scales are used to compute a dense optic flow field.

• More accurate than if a single scale was chosen throughout the image sequence.

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Dense Flow Field and FOE

• Object point P: in camera coordinates (X,Y,Z)

• Projection of P, point p: in the image plane (x, y)

• Geometrically, its optical flow is:

Translation

Rotation

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Determining Camera Motion

Parameters

The vector joining two object points having different depth values and projecting on to the same pixel will point toward the focus of expansion.

Instead of solving a 6x6 linear system, the flow vectors can be transformed into polar coordinates with the focus of expansion at the origin. This gives us the rotation term, since the translation term is eliminated.

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Improving Accuracy

A sequence of

Tz’s corresponding to different feature points is computed. The median of these is chosen and outliers removed based on a threshold. The mean of the remaining values is the Tz estimate. Based on the position of the focus of expansion, Tx and Ty are then determined.

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Improving Accuracy

Figures taken from Liu et al.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Critique

• Neglected to specify the thresholds used for eliminating outliers and for choosing good tracking features.

• Didn’t explain how they have registered the phantom images, CT scans, and the endoscopic camera, or how they generated these graphics.

• How computational speed of the algorithm compares to other methods’. In order for this algorithm to be feasible, it has to run in real-time.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Relevance to Our Project

• Get scale factors, and deform images for 3D reconstruction.

• If using a non-rigid probe, can get the position of the tip.

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

Questions?

NSF Engineering Research Center for Computer Integrated Surgical Systems and Technology

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