Digital pen calibration by local linearization

• US 20060182343A1
• Filed: 02/17/2005
• Published: 08/17/2006
• Est. Priority Date: 02/17/2005
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Wang, Jian, Chen, Liyong, Lin, Zhouchen
• Granted Patent: US 7,536,051 B2
• Time in Patent Office: Days
• US Class Current: 382/181
• CPC Class Codes: G06V 30/1423 the instrument generating sequences of position coordinates corresponding to handwriting preprocessing or recognising digital ink G06V30/32

Abstract

X-y positions of a digital pen'"'"'s tip may be determined by using a calibration parameter to map the x-y positions of the respective centers of images captured by the pen'"'"'s camera. The calibration parameter may be generated by iteratively calculating estimates of the calibration parameter. The iteratively calculated estimates may be based on a gradient of an error function of the iteratively generated estimates. Calibration input data may be produced by a user placing the pen tip in a fixed location on a surface, which may be a positionally encoded medium, such as paper, and then rotating the pen and/or moving the opposite end of the pen in various directions to capture multiple images for use in generating the calibration parameter. A user may perform such a calibration procedure without the need for complicated calibration equipment typically used in connection with conventional calibration techniques.

Claims

1. A method of calibrating a digital pen, which includes a pen tip and a camera, and of mapping a location of a center of a camera-captured image to a location of the pen tip, the method comprising:

generating a calibration parameter based on a plurality of images captured by the digital pen'"'"'s camera by placing the pen in a plurality of different orientations while keeping the pen tip at a substantially fixed location L_pentip on a positionally encoded surface, wherein the calibration parameter is generated based on a plurality of iteratively generated estimates of the calibration parameter, wherein the iteratively generated estimates are based on a gradient of an error function of the iteratively generated estimates; and

using the calibration parameter to map the location of the center of the camera-captured image to the location of the pen tip so that a stroke written by a user on the positionally encoded surface can be recovered at a location within an electronic copy of the positionally encoded surface, wherein the position of the recovered stroke within the electronic copy corresponds to a plurality of locations of the pen tip as the user was writing the stroke on the positionally encoded surface.

2. The method of claim 1, further comprising:

finding a fixed point

p=(p₁p₂1)^t,

such that

$g<br><br>\left(p\right)=\frac{1}{2<br><br>n}<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{<br><br>{\mathrm{\lambda <br><br>}}_i<br><br>H_i<br><br>p-\stackrel{\_}{p}<br><br>}^2,$

is minimized, given

$H_i=\left(\begin{array}{ccc}{h}_{11}^{\left(i\right)}& h_{12}^{\left(i\right)}& h_{13}^{\left(i\right)}\\ h_{21}^{\left(i\right)}& h_{22}^{\left(i\right)}& h_{23}^{\left(i\right)}\\ h_{31}^{\left(i\right)}& h_{32}^{\left(i\right)}& h_{33}^{\left(i\right)}\end{array}\right),$

for each of the plurality of captured images.

3. The method of claim 2, further comprising:

initializing p as

$\left(\begin{array}{c}\hat{p}\\ 1\end{array}\right)$ $\mathrm{where}$ $\hat{p}=-{\left(\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\hat{H}}_i^t<br><br>{\hat{H}}_i-\frac{1}{n}<br><br>{\stackrel{\_}{\hat{H}}}^t<br><br>\stackrel{\_}{\hat{H}}\right)}^{-1}<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\hat{H}}_i^t<br><br>\left(h_3^{\left(i\right)}-{\stackrel{\_}{h}}_3\right).$

4. The method of claim 3, further comprising:

updating p in accordance with

p ^(k+1) =p ^(k) +δ

p

where

$\mathrm{\delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>p=-{\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>\nabla <br><br>g_i\right]}^{-1}<br><br>\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>g_i<br><br>\left(p\right)\right].$

5. The method of claim 4, further comprising:

repeating the step of claim 5 a plurality of times such that p converges to a substantially accurate result.

6. The method of claim 5, further comprising:

using p as the calibration parameter for mapping the location of the center of the camera-captured image to the location of the pen tip.

7. A computer-readable medium containing computer-executable instructions that generate a calibration parameter for a digital pen, which includes a pen tip and a camera, wherein mapping, the location of the image center to the location of the tip of the pen on a positionally encoded surface, depends on the calibration parameter, by performing steps comprising:

generating the calibration parameter based on a plurality of images captured by the digital pen'"'"'s camera by placing the pen in a plurality of different orientations while keeping the pen tip at a fixed location L_pentip on the positionally encoded surface, wherein the calibration parameter is generated based on a plurality of iteratively generated estimates of the calibration parameter, wherein the iteratively generated estimates are based on a gradient of an error function of the iteratively generated estimates.

8. The computer-readable medium of claim 7, containing further computer-executable instructions that finding a fixed point

p=(p₁p₂1)^t,

such that

$g$

(p)=12⁢

n⁢

 

⁢

∑

i=1n⁢



λ

i⁢

Hi⁢

p-p_

2,

is minimized, given

$H_i=\left(\begin{array}{ccc}{h}_{11}^{\left(i\right)}& h_{12}^{\left(i\right)}& h_{13}^{\left(i\right)}\\ h_{21}^{\left(i\right)}& h_{22}^{\left(i\right)}& h_{23}^{\left(i\right)}\\ h_{31}^{\left(i\right)}& h_{32}^{\left(i\right)}& h_{33}^{\left(i\right)}\end{array}\right),$

for each of the plurality of captured images.

9. The computer-readable medium of claim 8, containing further computer-executable instructions for initializing p as

$\left(\begin{array}{c}\hat{p}\\ 1\end{array}\right)$ $\mathrm{where}$ $\hat{p}=-{(\sum _{}^{}}^{}$

i = 1 n ⁢

H ^ i t ⁢

H ^ i - 1 n ⁢

H ^ _ t ⁢

H ^ _ ) - 1 ⁢

 

⁢

∑

i = 1 n ⁢

H ^ i t ⁡

( h 3 ( i ) - h _ 3 ) .

10. The computer-readable medium of claim 9, containing further computer-executable instructions for updating p in accordance with

p ^(k+1) =p ^(k) +δ

p

where

$\mathrm{\delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>p=-{\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>\nabla <br><br>g_i\right]}^{-1}<br><br>\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>g_i<br><br>\left(p\right)\right].$

11. The computer-readable medium of claim 10, containing further computer-executable instructions for repeating the calculations of claims 13 a plurality of times such that p converges to a substantially accurate result.

12. The computer-readable medium of claim 11, containing further computer-executable instructions for using p as the calibration parameter L_{virtual-pentip} for mapping the location of the image center to the location of the tip of the pen.

13. A system that calibrates a digital pen, which includes a pen tip and a camera, and that maps a location of a center of a camera-captured image to a location of the pen tip, the system comprising:

a calibration module that generates a calibration parameter based on a plurality of images captured by the digital pen'"'"'s camera with the pen in a plurality of different orientations while the pen tip is at a substantially fixed location L_pentip on the positionally encoded surface, wherein the calibration parameter is generated based on a plurality of iteratively generated estimates of the calibration parameter, wherein the iteratively generated estimates are based on a gradient of an error function of the iteratively generated estimates; and

a mapping module that uses the calibration parameter to map the location of the center of the camera-captured image to the location of the pen tip so that a stroke written by a user on the positionally encoded surface can be recovered at a location within an electronic copy of the positionally encoded surface, wherein the position of the recovered stroke within the electronic copy corresponds to a plurality of locations of the pen tip as the user was writing the stroke on the positionally encoded surface.

14. The system of claim 13, wherein the calibration module calculates a transform F_S→

P and an inverse transform F<sub>P→

S</sub>=F<sub>S→

P</sub><sup>−

1</sup>, by image matching, for each image of the plurality of captured images.

15. The system of claim 14, wherein the calibration module finds a fixed point

p=(p₁p₂1)^t,

such that

$g$

(p)=12⁢

n⁢

 

⁢

∑

i=1n⁢



λ

i⁢

Hi⁢

p-p_

2,

is minimized, given

$H_i=\left(\begin{array}{ccc}{h}_{11}^{\left(i\right)}& h_{12}^{\left(i\right)}& h_{13}^{\left(i\right)}\\ h_{21}^{\left(i\right)}& h_{22}^{\left(i\right)}& h_{23}^{\left(i\right)}\\ h_{31}^{\left(i\right)}& h_{32}^{\left(i\right)}& h_{33}^{\left(i\right)}\end{array}\right),$

for each of the plurality of captured images.

16. The system of claim 15, wherein the calibration module initializes p as

$\left(\begin{array}{c}\hat{p}\\ 1\end{array}\right)$ $\mathrm{where}$ $\hat{p}=-{(\sum _{}^{}}^{}$

i = 1 n ⁢

H ^ i t ⁢

H ^ i - 1 n ⁢

H ^ _ t ⁢

H ^ _ ) - 1 ⁢

∑

i = 1 n ⁢

H ^ i t ⁡

( h 3 ( i ) - h _ 3 ) .

17. The system of claim 16, wherein the calibration module updates p in accordance with

p ^(k+1) =p ^(k) +δ

p

where

$\mathrm{\delta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>p=-{\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>\nabla <br><br>g_i\right]}^{-1}<br><br>\left[\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>{\left(\nabla <br><br>g_i\right)}^t<br><br>g_i<br><br>\left(p\right)\right].$

18. The system of claim 17, wherein, the calibration module repeats the calculations of claim 17 a plurality of times such that the estimate of p converges to a substantially accurate result.

19. The system of claim 18, wherein, the calibration module outputs p as the calibration parameter for use by the mapping module to map the recovered image-center stroke to the recovered pen-tip stroke.

20. The system of claim 13, wherein the mapping module uses a virtual pen tip to map a recovered camera-captured stroke to a recovered pen-tip stroke, wherein a location of the virtual pen-tip on an image-sensing plane of the digital pen depends on a predetermined relationship between the tip of the pen and the pen'"'"'s camera, wherein the predetermined relationship is based on the configuration of the pen.