Signal processors and methods for estimating transformations between signals with least squares

Patent metadata

Field	Value
Publication number	US-10402929-B2
Application number	US-201815959992-A
Country	US
Kind code	B2
Filing date	Apr 23, 2018
Priority date	Sep 3, 2010
Publication date	Sep 3, 2019
Grant date	Sep 3, 2019

Abstract

Signal processing devices and methods estimate transforms between signals using a least squares technique. From a seed set of transform candidates, a direct least squares method applies a seed transform candidate to a reference signal and then measures correlation between the transformed reference signal and a suspect signal. For each candidate, update coordinates of reference signal features are identified in the suspect signal and provided as input to a least squares method to compute an update to the transform candidate. The method iterates so long as the update of the transform provides a better correlation. At the end of the process, the method identifies a transform or set of top transforms based on a further analysis of correlation, as well as other results.

First claim

We claim:

1. A method of determining a geometric transformation of an image, the method comprising:
receiving an electronic image sampled from a physical object;
with one or more processors:
determining a candidate geometric transform between a digital watermark signal and the electronic image;
refining the candidate geometric transform by transforming coordinates of the digital watermark signal with the candidate geometric transform, determining peak locations within the electronic image that are within a neighborhood of the transformed coordinates of the digital watermark signal, updating locations of the transformed coordinates to the peak locations, determining a new geometric transform that maps the digital watermark signal to the updated locations, and determining whether correlation has increased between the electronic image and the digital watermark signal, transformed by the new geometric transform;
from the electronic image, estimating phase at non-integer coordinates corresponding to coordinates of the digital watermark signal transformed with the new geometric transform; and
determining deviation between estimated phase and expected phase of the digital watermark signal.

2. The method of claim 1 wherein the candidate geometric transform comprises two or more affine transform parameters.

3. The method of claim 2 wherein the two or more affine transform parameters comprise rotation, differential scale and shear.

4. The method of claim 1 wherein the digital watermark signal comprises peaks at the coordinates of the digital watermark signal.

5. A digital watermark detector comprising:
a memory for storing an electronic image sampled from a physical object;
a processor in communication with the memory, the processor configured to obtain a candidate geometric transform, and configured to refine the candidate geometric transform by transforming coordinates of the digital watermark signal with the candidate geometric transform, determining peak locations within the electronic image that are within a neighborhood of the transformed coordinates of the digital watermark signal, updating locations of the transformed coordinates to the peak locations, determining a new geometric transform that maps the digital watermark signal to the updated locations, and determining whether correlation has increased between the electronic image and the digital watermark signal, transformed by the new geometric transform;
the processor further configured to obtain phase estimates of a digital watermark signal in the electronic image by estimating phase at non-integer coordinates corresponding to coordinates of the digital watermark signal transformed with the new geometric transform, the estimating employing point spread function parameters to estimate phase at the non-integer coordinates based on frequency domain data at neighboring integer coordinates; and
the processor further configured to determine deviation between estimated phase and expected phase of the digital watermark signal.

6. The digital watermark detector of claim 5 wherein the candidate geometric transform comprises rotation, differential scale, and shear.

7. The digital watermark detector of claim 5 wherein the digital watermark signal comprises peaks at the coordinates of the digital watermark signal.

8. A non-transitory, computer readable medium on which is stored instructions, which, when executed by a processor, perform a method of determining a geometric transformation of an image, the method comprising:
obtaining an electronic image sampled from a physical object;
determining a candidate geometric transform between a digital watermark signal and the electronic image;
refining the candidate geometric transform by transforming coordinates of the digital watermark signal with the candidate geometric transform, determining peak locations within the electronic image that are within a neighborhood of the transformed coordinates of the digital watermark signal, updating locations of the transformed coordinates to the peak locations, determining a new geometric transform that maps the digital watermark signal to the updated locations, and determining whether correlation has increased between the electronic image and the digital watermark signal, transformed by the new geometric transform;
from the electronic image, estimating phase at non-integer coordinates corresponding to coordinates of the digital watermark signal transformed with the new geometric transform; and
determining deviation between estimated phase and expected phase of the digital watermark signal.

9. The computer readable medium of claim 8 wherein the candidate geometric transform comprises two or more affine transform parameters.

10. The computer readable medium of claim 9 wherein the two or more affine transform parameters comprise rotation, differential scale and shear.

11. The computer readable medium of claim 8 wherein the digital watermark signal comprises peaks at the coordinates of the digital watermark signal.

12. The computer readable medium of claim 8 further comprising instructions that configure a processor to perform acts of: estimating phase of the digital watermark signal, when transformed by the geometric transform, by sampling phase from neighboring image samples at integer locations within the electronic image signal, and using the phase estimates of the digital watermark signal to assess whether the geometric transform improves correlation between the electronic image and the digital watermark signal, as transformed by the geometric transform.

Assignees

• Digimarc Corp

Inventors

• Sharma Ravi K
• Lord John D
• Lyons Robert G

Classifications

• G06V10/754

  involving a deformation of the sample pattern or of the reference pattern; Elastic matching · CPC title

• G06T1/0064 Primary

  Geometric transfor invariant watermarking, e.g. affine transform invariant · CPC title

• G06F1/02

  Digital function generators · CPC title

• G06T1/0021

  Image watermarking · CPC title

• G06T3/0056

  Physics · mapped topic