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Sparse representation for coarse and fine object recognition. Thang V. Pham & Arnold W. M. Smeulders ISIS research group University of Amsterdam, the Netherlands. AIO-SOOS. Content. Coarse and fine recognition with PCA A new representation Gaussian derivative bases Experimental results

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sparse representation for coarse and fine object recognition

Sparse representation for coarse and fine object recognition

Thang V. Pham & Arnold W. M. Smeulders

ISIS research group

University of Amsterdam, the Netherlands

AIO-SOOS

content
Content
  • Coarse and fine recognition with PCA
  • A new representation
    • Gaussian derivative bases
  • Experimental results
  • Conclusions
coarse and fine recognition
Coarse and fine recognition

Bear

90 degree

0 degree

Car

Name?

Pose?

Duck

Training

Testing

with pca
… with PCA

project

bear

project

eigenspace

car

duck

our assessment of pca based
Our assessment of PCA-based
  • Storage space is huge
  • Recognition time is large
  • Spatial coherent not exploited
    • identical result by permuting the pixels
  • Incremental learning absent
    • large datasets
  • Inefficient when unknown object localization
our idea
Our idea
  • Sparsity

Each object uses a small number of N bases from a potentially very large dictionary.

Typically N could go up to 1000

… from a dictionary up to 2003.

coarse and fine recognition1
Coarse and fine recognition

To model orientation, an image is modeled as a 3D function

Each basis is separable

Each 1D basis is a Gaussian derivative

with local bases
… with local bases

Reconstruct

Compare

new object

duck space

bear space

remember our idea
Remember our idea
  • Sparsity

(Each object uses a small number of N bases from a potentially very large dictionary.)

  • by matching pursuit
    • Initialize residual = object images
    • Select the best basis for the current residual
    • Update the residual
    • Goto 2 unless the number of bases = N
so far in contrast to pca
So far, in contrast to PCA

+ Storage space is efficient

No sampled points

Not the axes, but their indices in the dictionary.

+ Spatial coherence is exploited

+ Yes, there is incremental learning

- Some loss for recognition and localization?

Is “Reconstruct and compare” inefficient?

the answer is no
The answer is NO.

Approximating bases by piece-wise polynomials, we turn matching to polynomial evaluation.

polynomial recognition
Polynomial recognition

A new image is recognized by

  • Compute the piece-wise polynomials
    • Compute the complete Njet coefficients of the test image at all locations
    • Select N coefficients for each object from the object models as learned.
    • Polynomial computation to yield polynomials (of degree 6 max).
  • Evaluating the polynomials along the orientation to find the best matching candidate.
so far in contrast to pca1
So far, in contrast to PCA

+ Storage space is efficient

No sampled points

Not the axes, but their indices in the dictionary.

+ Spatial coherence is exploited

+ Yes, there is incremental learning

+ Recognition phase is fast

- / + Njet is slower than PCA but done once

Efficient for localization

Efficient for many objects

experimental results2
Experimental results

1000

bases

6-D

eigenspace

100-D

eigenspace

conclusions
Conclusions
  • Efficient in storage space

(no sample points)

  • Efficient in recognition time

(polynomial evaluation)

  • Spatial correlation exploited

(in framework of Gaussian differentials)

  • Efficient object localization & multiple objects

(work with Njet coefficients)

  • Large dataset and incremental learning

(no re-training of existing models)