# 博士論文発表会

「Criterion for image matching with global projection transformation
correlation and its acceleration algorithms（大局的射影変換相関による画像マッチ
ングのための評価基準およびその高速計算）」

Image matching is a strong ally in computer vision field, because it outputs
the correspondence between the input images and templates. The most important
thing in image matching is the invariant matching result against adverse
conditions such as noise, color of background, geometrical transformations,
etc. Furthermore, short calculation time is also highly expected for real-world
applications. This thesis proposes a theoretical criterion of GPT (Global
Projection Transformation) correlation matching which revises the deformations
between input images and templates by 2D projection transformation. In the
thesis, we also discuss the local features and acceleration algorithm to
reinforce the stability of the proposed criterion and shorten the calculation
time.

GPT correlation matching technique is originated by Wakahara and Yamashita to
realize a projection-invariant image matching technique. However, theoretically,
there is a serious defect in the conventional criterion. So firstly, we
introduce the conventional GPT correlation matching model and point out a
problem that the conventional approach does not guarantee the conservation of
the L2 norm of the transformed images. The problem will lead mismatches during
the optimization of the criterion. To solve this problem the theoretical
criterion is proposed by introducing a norm normalization factor. Furthermore,
the conventional GPT correlation matching realizes the 2D projection
transformation by the alternative calculation of AT (Affine Transformation) and
PPT (Partial Projection Transformation), which causes the incompatibility during
the matching process. This thesis also focuses on the norm normalization of the
simultaneous calculation of AT and PPT. The mathematical derivation and
implementation algorithm of the proposed criteria are described in detail and
some demonstrations using toy image data are also illustrated. From the
demonstrations, the proposed approach achieves not only higher correlations
between the input images and template, but also faster convergence speed.

During the matching process, both the conventional approach and the proposed
approach use only the quantized gradient direction of the target pixel as a
kind of space filter to mitigate mismatches. However, in the field of natural
image matching, the quantized gradient direction is greatly affected by
deformations or distortion of the image. To achieve a more robust and stable
matching against bad conditions of the images, this thesis also proposes some
kinds of local features of the histogram of oriented quantized gradient
direction (HOG) information of a 5-by-5 block around each target pixel. For
example, we simplify the HOG features by eliminating the non-significant
directions. Or, we also perform k-means clustering to simplify the HOT features.
The comparison among matching abilities using these HOG patterns is shown by
demonstrations. From the demonstrations, in case the test images suffer from
large deformation, the matching results are stable with the assist of the local
features, while the conventional space filter does not lead to the converge
point any longer.

Furthermore, the proposed criterion is expected to be utilized into real-world
applications, so short calculation time is highly required. This thesis
introduces the acceleration algorithm of the proposed algorithm. The key idea
of the acceleration algorithm is to create two kinds of reference tables. These
reference tables can avoid the naïve search of the image domain, which
dramatically reduce the calculation time to about one hundredth. Since the
calculation time for creating the reference tables is still the fourth-order of
the image size, an acceleration algorithm for creating the reference tables
using integral images is also proposed. The same demonstrations as above-
mentioned section are conducted firstly to show the agreement of the matching
results no matter the acceleration algorithm is used or not, and as well as the
significant reduction of the calculation time than the standard algorithm about
one thousandth.

Several experiments are performed to show the advantages of the proposed
approach. The experiments can be divided into two sections, one is the image
matching part and the other is the image discrimination part. In image matching
part we perform “whole-to-whole” and “whole-to-part” template matchings using
natural images from some famous datasets vis the conventional approaches, the
proposed approach as well as the acceleration algorithm, and the state-of-the-
art methods. In image discrimination part, the image discrimination of
handwritten digit from MNIST database is performed vis the conventional
approaches and the accelerated proposed approach. The comparison of the
correlation values and the error rates output by these approaches are listed up.

From the demonstrations and experiments, we can distinguish the outstanding
performance of the proposed approach not only in image matching field but also
in image recognition field. It also has high potential to be applied to some