Generalized Matching

Zhang, Yu-Jin

doi:10.1007/978-981-19-7580-6_10

Yu-Jin Zhang²

Abstract

Commonly used image-related matching can be classified into two categories: One is more specific and corresponds to the lower-level pixels or sets of pixels, which can be collectively referred to as image matching; the other is more abstract, mainly related to image objects or the nature and connection of objects, or even related to the description and interpretation of the scene, which can be collectively referred to as generalized matching. This chapter will introduce some typical object matching methods, including matching with landmarks or feature points on the object, matching the contours of the two object regions with the help of string representations, and matching by using the inertia equivalent ellipse. This chapter will introduce a method of dynamically establishing the pattern for object representation during the matching process, and then matching these patterns. This chapter will use the principle of graph theory and the properties of graphs to establish the correspondence between objects, and use graph isomorphism to match scenes at different levels. This chapter will introduce the matching method that first constructs the line drawing of the object, then marking the line drawing, and finally using this mark to match the 3-D scene with the corresponding model.

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Authors and Affiliations

Department of Electronic Engineering, Tsinghua University, Beijing, China
Yu-Jin Zhang

Authors

Yu-Jin Zhang
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Self-Test Questions

The following questions include both single-choice questions and multiple-choice questions, so each option must be judged.

10.1.
Matching Overview
1. 10.1.1.
  Matching is to find the correspondence between two representations; (·).
  1. (a)
    Image matching is to find the correspondence between two image representations, such as the left and right image functions in binocular stereo vision.
  2. (b)
    Object matching is to find the correspondence between two object representations, such as two persons in the two consecutive video frames.
  3. (c)
    The scene matching is looking for the correspondence between two scene descriptions, such as the scenery on both sides of a highway.
  4. (d)
    Relationship matching is to find the correspondence between two relationship descriptions, such as the mutual positions of two persons at different moments.
  [Hint] The object hierarchy of different matches is different.
2. 10.1.2.
  Matching and registration are two closely related concepts; (·).
  1. (a)
    The concept of matching is larger than the concept of registration.
  2. (b)
    The registration considers more image properties than matching.
  3. (c)
    Image registration and stereo matching both need to establish the correspondence between point pairs.
  4. (d)
    The goal of matching and registration is to establish content correlation between two images.
  [Hint] Registration mainly considers low-level representation, while matching covers more levels.
3. 10.1.3.
  Various evaluation criteria for image matching are both related and different; (·).
  1. (a)
    For a matching algorithm, the higher the accuracy, the higher the reliability.
  2. (b)
    For a matching algorithm, the higher the reliability, the higher the robustness.
  3. (c)
    For a matching algorithm, the robustness can be judged with the help of accuracy.
  4. (d)
    For a matching algorithm, the reliability can be judged with the help of robustness.
  [Hint] Analyze according to the self-definition of the criteria.
10.2.
Object Matching
1. 10.2.1.
  Hausdorff distance (·).
  1. (a)
    Can only describe the similarity between two pixel sets.
  2. (b)
    Is the distance between the closest two points in the two point sets.
  3. (c)
    Is the distance between the two points that are the furthest apart in the two point sets.
  4. (d)
    Being 0 indicates that the two point sets do not overlap.
  [Hint] Judge according to the definition of Hausdorff distance.
2. 10.2.2.
  Suppose that the contours A and B encoded as character strings are matched. It is known that ||A|| = 10, ||B|| = 15, and (·).
  1. (a)
    If M = 5 is known, then R = 1/2.
  2. (b)
    If M = 5 is known, then R = 1/4.
  3. (c)
    If M = 10 is known, then R = 2.
  4. (d)
    If M = 10 is known, then R = 1.
  [Hint] Calculate directly according to Eq. (10.12).
3. 10.2.3.
  Inertia equivalent ellipse matching method can be applied to object matching; (·).
  1. (a)
    Each inertia equivalent ellipse corresponds to a specific object.
  2. (b)
    Representing the object with its inertia equivalent ellipse can reduce the complexity of representing the object.
  3. (c)
    When the object is not an ellipse, the inertia equivalent ellipse of the object is only equal to the area of the object.
  4. (d)
    For this, four parameters of the ellipse are calculated, which shows that an ellipse can be completely determined by four parameters.
  [Hint] See the calculation of inertia and equivalent ellipse (Chap. 12 of 2D Computer Vision: Principles, Algorithms and Applications).
10.3.
Dynamic Pattern Matching
1. 10.3.1.
  In the dynamic pattern matching method, (·).
  1. (a)
    The grayscale information of the pixels to be matched has been used.
  2. (b)
    The position information of the pixel to be matched has been used.
  3. (c)
    Two point sets can be matched.
  4. (d)
    The Hausdorff distance can be used to measure the effect of matching.
  [Hint] Analyze according to the construction method of dynamic pattern.
2. 10.3.2.
  In the dynamic pattern matching method, the absolute pattern refers to the pattern (·).
  1. (a)
    Whose number of units used is determined.
  2. (b)
    That can be realized with a fixed size template.
  3. (c)
    That is determined in space.
  4. (d)
    That is constant throughout the matching process.
  [Hint] See the pattern example in Fig. 10.9.
3. 10.3.3.
  Comparing absolute pattern and relative pattern, (·).
  1. (a)
    The representation of absolute pattern is simpler than that of relative pattern.
  2. (b)
    The absolute pattern has more units than the relative pattern has.
  3. (c)
    The absolute pattern and the relative pattern have the same properties.
  4. (d)
    The absolute pattern and relative pattern can have different pattern radii.
  [Hint] Analyze the difference between absolute pattern and relative pattern.
10.4.
Graph Theory and Graph Matching
1. 10.4.1.
  In the geometric representation of the graph, (·).
  1. (a)
    A graph with number of edges one can have an infinite number of geometric representations.
  2. (b)
    The graph with the number of vertices one can have an infinite number of geometric representations.
  3. (c)
    If edges a and b are adjacent, it indicates that edges a and b are incident with vertex A.
  4. (d)
    If vertices A and B are adjacent, it indicates that the edge e is incident with the vertices A and B.
  [Hint] Adjacent only involves any two edges or two vertices, and the incident also considers a specific vertex or a specific edge.
2. 10.4.2.
  Which of the following statement(s) about colored graphs is/are wrong? (·).
  1. (a)
    A graph is composed of two sets, and a colored graph is composed of two sets.
  2. (b)
    A graph is composed of two sets, and a colored graph is composed of four sets.
  3. (c)
    The number of edges in the colored graph is the same as the chromaticity number of the edges.
  4. (d)
    The number of vertices in the colored graph is the same as the chromaticity number of the vertices.
  [Hint] Different vertices can have the same color, and different edges can also have the same color.
3. 10.4.3.
  Which of the following statement(s) about the identity and isomorphism of graphs is/are correct? (·).
  1. (a)
    The two graphs of identity have the same geometric representation.
  2. (b)
    The two graphs of isomorphism have the same geometric representation.
  3. (c)
    Two graphs with the same geometric representation are identical.
  4. (d)
    Two graphs with the same geometric representation are isomorphic.
  [Hint] Analyze the difference between identities and isomorphism and their relationship with geometric representations.
4. 10.4.4.
  Which of the following statement(s) about graph isomorphism is/are correct? (·).
  1. (a)
    The graph isomorphism of two graphs indicates that the two graphs have the same geometric representation.
  2. (b)
    The sub-graph isomorphism of two graphs indicates that the two graphs have the same geometric expression.
  3. (c)
    The sub-graph isomorphism of two graphs indicates that the two graphs are isomorphic.
  4. (d)
    The double-sub-graph isomorphism of the two sub-graphs indicates that the two sub-graphs are isomorphic.
  [Hint] Distinguish between isomorphism and geometric representation, and distinguish between graphs and sub-graphs.
10.5.
Line Drawing Signature and Matching
1. 10.5.1.
  Some of the blades of the square in Fig. 10.23 have marks, and the remaining marks are as follows: (·).
  1. (a)
    A is ↗, B is ↙, and C is →.
  2. (b)
    A is ↗, B is ↗, and C is ←.
  3. (c)
    A is ↙, B is ↙, and C is ←.
  4. (d)
    A is ↗, B is ↙, and C is ←.
  [Hint] Pay attention to the agreement on the direction of the arrow.
2. 10.5.2.
  For the object in Fig. 10.19a, if it is to be pasted on the left wall, it should be as follows: (·).
  1. (a)
    Figure 10.24a.
  2. (b)
    Figure 10.24b.
  3. (c)
    Figure 10.24c.
  4. (d)
    Figure 10.24d.
  [Hint] The concave creases should be on the same vertical plane.
3. 10.5.3.
  When performing structural reasoning and labeling via backtracking, the issues to be noted include: (·).
  1. (a)
    Only one mark can be assigned to each edge of the line graph.
  2. (b)
    Do not use the join types not shown in Fig. 10.21.
  3. (c)
    Two graphs with the same geometric structure may have different interpretations.
  4. (d)
    Sort the vertices first, list all possible constraints for each vertex in turn, and verify them one by one.
  [Hint] Refer to the example in Table 10.2 for analysis.