Local image descriptors using linear discriminant embedding
To render the comparison of image patches more efficient, the data of an image patch can be projected into a smaller-dimensioned subspace, resulting in a descriptor of the image patch. The projection into the descriptor subspace is known as a linear discriminant embedding, and can be performed with reference to a linear discriminant embedding matrix. The linear discriminant embedding matrix can be constructed from projection vectors that maximize those elements that are shared by matching image patches or that are used to distinguish non-matching image patches, while also minimizing those elements that are common to non-matching image patches or that distinguish matching image patches. The determination of such projection vectors can be limited such that only orthogonal vectors comprise the linear discriminant embedding matrix. The determination of the linear discriminant embedding matrix can likewise be constrained to avoid overfitting to training data.
1. One or more computer-readable storage media comprising computer-executable instructions for deriving a linear discriminant embedding matrix, the computer-executable instructions directed to steps comprising:
receiving multiple training image patches comprising an indication of matching training image patches;
applying one or more non-linear transformations to vectors representing the multiple training image patches to obtain multiple transformed training image patches;
identifying multiple projections of the transformed training image patches that maximize a ratio of variance between differences between pairs of transformed training image patches that are not matching and differences between pairs of transformed training image patches that are matching; and
forming the linear discriminant embedding matrix from the identified multiple projections.
2. The computer-readable storage media of claim 1 comprising further computer-executable instructions directed to determining which training image patches are matching and appending to the matching training image patches the indication of matching training image patches.
3. The computer-readable storage media of claim 1 , wherein the identifying the multiple projections is constrained by requiring that the identified multiple projections are orthogonal to each other.
4. The computer-readable storage media of claim 1 , wherein the identifying the multiple projections is constrained by requiring that the differences between pairs of transformed training image patches that are matching be limited to a fraction of a corresponding signal power.
5. The computer-readable storage media of claim 1 , wherein the identifying the multiple projections comprises identifying less than 40 multiple projections.
6. The computer-readable storage media of claim 1 , wherein the multiple training image patches are between 10,000 and 100,000 training image patches.
7. The computer-readable storage media of claim 1 , wherein the one or more non-linear transformations are based on normalized gradients obtained from normalized multiple training image patches.
8. One or more computer-readable storage media comprising computer-executable instructions for deriving a descriptor of an image patch, the computer-executable instructions directed to steps comprising
receiving an image patch;
applying one or more non-linear transformations to vectors representing the image patch to obtain a transformed image patch; and
linearly projecting the transformed image patch into a discriminant subspace using a linear discriminant embedding matrix formed from multiple projections that maximized a ratio of variance between differences between pairs of transformed training image patches that are not matching and differences between pairs of transformed training image patches that are matching.
9. The computer-readable storage media of claim 8 comprising further computer-executable instructions directed to normalizing the linearly projected transformed image patch to form the descriptor of the image patch.
10. The computer-readable storage media of claim 8 , wherein the discriminant subspace has a dimensionality equivalent to the quantity of the multiple projections, the dimensionality being less than 40.
11. The computer-readable storage media of claim 8 , wherein vectors comprising the linear discriminant embedding matrix are orthogonal to each other.
12. The computer-readable storage media of claim 8 , wherein the differences between pairs of transformed training image patches that are matching are limited to a fraction of a corresponding signal power.
13. The computer-readable storage media of claim 8 , wherein the one or more non-linear transformations are based on normalized gradients obtained from a normalized version of the image patch.
14. A computer-implemented method of generating a computer-readable linear discriminant embedding matrix comprising the steps of:
applying, by a non-linear transformer, one or more non-linear transformations to vectors representing multiple training image patches, that comprise an indication of matching training image patches, to generate multiple transformed training image patches;
identifying, by a linear projection identifier, multiple projections of the transformed training image patches that maximize a ratio of variance between differences between pairs of transformed training image patches that are not matching and differences between pairs of transformed training image patches that are matching; and
generating, by the linear projection identifier, the computer-readable linear discriminant embedding matrix from the identified multiple projections.
15. The computer-implemented method of claim 14 further comprising the steps of: determining, by an image patch matcher, which training image patches are matching; and appending, by the image patch matcher, to the matching training image patches, the indication of matching training image patches.
16. The computer-implemented method of claim 14 , wherein the identifying the multiple projections is constrained by requiring that the identified multiple projections are orthogonal to each other.
17. The computer-implemented method of claim 14 , wherein the identifying the multiple projections is constrained by requiring that the differences between pairs of transformed training image patches that are matching be limited to a fraction of a corresponding signal power.
18. The computer-implemented method of claim 14 , wherein the identifying the multiple projections comprises identifying less than 40 multiple projections.
19. The computer-implemented method of claim 14 , wherein the multiple training image patches are between 10,000 and 100,000 training image patches.
20. The computer-implemented method of claim 14 , wherein the one or more non-linear transformations are based on normalized gradients obtained from normalized multiple training image patches.