KR20240068968A - Method and apparatus for detecting reflection symmetry based on shape signature - Google Patents

Abstract

The present invention discloses a method and apparatus for detecting reflection symmetry based on shape signatures. According to the invention, a processor; and a memory connected to the processor, wherein the memory converts a two-dimensional input image into a one-dimensional Radon signal, and performs a line integral of the one-dimensional Radon signal within a preset direction range or a line integral between the input image and an arbitrary line. Calculate a shape signature obtained through intersection set, calculate a merit profile representing the degree of reflection at each position of the one-dimensional Radon signal from the shape signature, and use the merit profile to select the two of the plurality of symmetry axis candidate directions. A reflection symmetry detection device using a shape signature stored program instructions executed by the processor to determine an optimal symmetry axis direction for a dimensional input image is provided.

Description

Method and apparatus for detecting reflection symmetry based on shape signature}

The present invention relates to a method and device for detecting reflection symmetry based on shape signatures.

The symmetry properties of nature and artifacts can be used to simplify shape representation in computer vision systems.

Additionally, the symmetrical structure facilitates the vision system in various tasks such as object recognition, object detection, etc.

Reflection symmetry detection, also known as mirror symmetry or bilateral symmetry detection, determines whether a shape can be decomposed into two parts.

Recently, interest in symmetry detection has been increasing in the field of computer vision.

Existing methods mainly deal with shape symmetry in binary images or symmetry of objects in natural images.

However, existing reflection symmetry detection has the problem of incompletely detecting the symmetry axis due to limited space.

JP Public Patent Publication 2007-536644

In order to solve the problems of the prior art described above, the present invention seeks to propose a reflection symmetry detection method and device based on shape signatures that can efficiently remove erroneous symmetry axis candidates.

In order to achieve the above-described object, according to one embodiment of the present invention,

A reflection symmetry detection device using a shape signature, comprising: a processor; and a memory connected to the processor, wherein the memory converts a two-dimensional input image into a one-dimensional Radon signal, and performs a line integral of the one-dimensional Radon signal within a preset direction range or a line integral between the input image and an arbitrary line. Calculate a shape signature obtained through intersection set, calculate a merit profile representing the degree of reflection at each position of the one-dimensional Radon signal from the shape signature, and use the merit profile to select the two of the plurality of symmetry axis candidate directions. A reflection symmetry detection device using a shape signature stored program instructions executed by the processor to determine an optimal symmetry axis direction for a dimensional input image is provided.

The shape signature may include an R-signature obtained from the line integration of the one-dimensional Radon signal and a LIP-signature obtained through the intersection of the input image and an arbitrary line.

The R-signature can be defined by the equation below.

[Equation]

here, is a two-dimensional function is the Radon transform defined as, is the Dirac delta function, silver is a straight line, and θ is the angle that L makes with the y-axis, , ρ is the radial distance from the origin to L

The LIP-signature can be defined by the equation below.

[Equation]

here, is the intersection between the input image D and an arbitrary line I and direction θ, s is the value moving away from the origin, is the largest intersection set in the θ direction, Is is the projection of D in the θ direction on the line, is a direction set, Is lim

A preset threshold can be applied to the peaks of the merit profile to determine the optimal symmetry axis direction.

The shape signature and the merit profile have one or more peaks in a predetermined direction θ, and the merit profile may emphasize some of the peaks appearing in the shape signature.

The merit profile can be calculated using the similarity of forward and reverse circular shifts at angles in each direction.

The program commands are:

The optimal symmetry axis direction can be verified by determining whether the Radon projection and its inverse version are the same in the optimal symmetry axis direction.

According to another aspect of the present invention, there is provided a reflection symmetry detection method using a shape signature in a device including a processor and a memory, comprising: converting a two-dimensional input image into a one-dimensional Radon signal; Calculating a shape signature obtained through a line integral of the one-dimensional Radon signal or an intersection of the input image and an arbitrary line within a preset direction range; calculating a merit profile representing the degree of reflection at each location of the one-dimensional Radon signal from the shape signature; and determining an optimal symmetry axis direction for the two-dimensional input image among a plurality of symmetry axis candidate directions using the merit profile.

According to another aspect of the present invention, a computer program stored in a computer-readable recording medium that performs the above method is provided.

According to the present invention, there is an advantage in that the reflection symmetry axis direction of the input image can be accurately detected through the shape signature and merit profile.

Figure 1 is a diagram for explaining Radon transformation.
Figure 2 shows two components and This is a diagram showing how to process and calculate the LIP-signature.
Figure 3 is a diagram showing the original shape and mirror shape and the R/LIP-signature calculated therefrom;
Figure 4 is a diagram showing the robustness of the R/LIP-signature calculated from two types of deer.
Figure 5 is a diagram showing a process for detecting a reflection symmetry axis of an arbitrary shape according to this embodiment.
Figure 6 is a diagram for explaining the process of detecting the axis of reflection symmetry according to this embodiment.
Figure 7 is a diagram showing the merit profiles of two shape signatures.
Figure 8 shows direction candidate 0 and This is a diagram showing a method for verifying reflection symmetry.
Figure 9 is a diagram showing the configuration of a reflection symmetry detection device according to this embodiment.

Since the present invention can make various changes and have various embodiments, specific embodiments will be illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to specific embodiments, and should be understood to include all changes, equivalents, and substitutes included in the spirit and technical scope of the present invention.

The terms used in this specification are merely used to describe specific embodiments and are not intended to limit the invention. Singular expressions include plural expressions unless the context clearly dictates otherwise. In this specification, terms such as “comprise” or “have” are intended to designate the presence of features, numbers, steps, operations, components, parts, or combinations thereof described in the specification, but are not intended to indicate the presence of one or more other features. It should be understood that this does not exclude in advance the possibility of the existence or addition of elements, numbers, steps, operations, components, parts, or combinations thereof.

In addition, the components of the embodiments described with reference to each drawing are not limited to the corresponding embodiments, and may be implemented to be included in other embodiments within the scope of maintaining the technical spirit of the present invention, and may also be included in separate embodiments. Even if the description is omitted, it is natural that a plurality of embodiments may be re-implemented as a single integrated embodiment.

In addition, when describing with reference to the accompanying drawings, identical or related reference numbers will be assigned to identical or related elements regardless of the drawing symbols, and overlapping descriptions thereof will be omitted. In describing the present invention, if it is determined that a detailed description of related known technologies may unnecessarily obscure the gist of the present invention, the detailed description will be omitted.

This embodiment detects reflection symmetry using Radon-transformed R-Signature and LIP-Signature, and uses a merit profile combining them to remove incorrect symmetry axis direction. proposes.

In the following, the R-Signature and LIP-Signature will be examined in detail, and the reflection symmetry detection method proposed in this embodiment will be described in detail.

We first explain the shape signature based on the Radon transform.

is called a two-dimensional function, is called the Dirac delta function, Is is a straight line, where θ is the angle that L makes with the y-axis, , ρ is defined as the radial distance from the origin to L.

The Radon transform of f, expressed as , is calculated by calculating the line integral as follows: It is a function defined in the space of .

Here, the function Is If it is, it is limited to 1, otherwise it is limited to 0.

Figure 1 is a diagram for explaining Radon transformation.

As shown in Figure 1, D is a binary shape represented by f.

Definition 1: Radial distance for projection θ and are respectively and am.

The Radon projection of D in the θ direction denoted by It is defined as

more precisely am.

Next, the R-signature is explained, which is expressed as follows.

The integral computed over a radial slice of the Radon image of Makes invariant to transformation and scaling. This is the multiplication factor except scaling factor at It occurs from and is periodic with period π.

LIP-Signature is intended to represent the geometric properties of an object in projection space and is defined as follows.

Definition 2: is the intersection between D and any line I and direction θ, with s moving away from the origin.

is the largest intersection set in the θ direction. am.

Is is the projection of D in the θ direction on the line.

Direction set Considering go represents.

thus second It is called the LIP-signature for.

From LIP-Signature constant for the rotation of Go to

Figure 2 shows two components and This is a diagram showing how to process and calculate the LIP-signature.

Figure 3 is a diagram showing the original shape and mirror shape and the R/LIP-signature calculated therefrom;

Figure 4 is a diagram showing the robustness of the R/LIP-signature calculated from two types of deer. One is the normal shape and the other is a deterioration of the first shape to take into account the non-linear deformation of the contour.

It can be seen that the LIP-signature and R-signature of this shape are almost identical. Figure 3 also shows the R/LIP-signature and its mirrored shape. The symmetry property of this signature is used for symmetry detection described below.

Figure 5 is a diagram showing a process for detecting an axis of reflection symmetry of an arbitrary shape according to this embodiment.

Referring to FIG. 5, this embodiment converts a two-dimensional symmetry detection problem into a one-dimensional symmetry detection problem ((a) of FIG. 5).

Conversion to a one-dimensional symmetry detection problem is the process of converting a given input image (shape) D into a one-dimensional Radon signal.

Next, a shape signature (R/LIP-signature) is calculated from the one-dimensional Radon signal (Figure 5(b)).

Then, a merit profile is calculated from the corresponding signature to highlight candidates for the symmetry axis direction (Figure 5(c)).

Through a verification process referring to the merit profile, incorrect candidates are removed and a symmetry measure indicating how good the detected symmetry axis direction is is calculated (Figure 5(d)).

Finally, the axis of symmetry for the input image is detected ((e) in Figure 5).

Below, we describe some theoretical results on the R-signature that can serve as a basis for a new approach to reflection symmetry detection.

R-signature is chosen as a useful tool for shape analysis because it is robust against noise, nonlinear deformation, and is invariant to similarity transformation.

The problem of detecting and measuring the reflection symmetry of an arbitrary shape D is transformed into measuring the reflection symmetry in an R-signature.

Due to the fact that is periodic with period π about θ, the projection set It may be sufficient to consider only the R-signatures, making a series of discrete predictions. Consider a set of

Theorem 1: D is the direction When including reflection symmetry, the R-signature is also and is reflection symmetrical.

Proof: axis direction from Let's look at Figure 6a, which has reflection symmetry.

direction Consider an arbitrary intersection line L1 of the shape D that is at a distance ρ from the root (intersection point) of the system coordinates. this is means.

now second for It is regarded as a symmetrical line segment of .

Because this is the axis of symmetry of D It should be the intersection line in Figure D.

According to the Radon transform definition am.

Because of am. From the description above If this condition is also satisfied.

thus Such as and There is a bijection in between.

Accordingly am.

thus and here am. thus Is is reflection symmetrical.

Without losing generality Assuming that It is displayed as Is is perpendicular to

class Is It should be noted that it is a reflection of .

These intersection lines are angle makes

direction (i.e. Considering the direction), each of these intersection lines is calculated as follows:

and am.

Because, am.

thus, am.

Because ( ) As follows this direction It can also be said to be reflection symmetrical.

Below, we will explain that the LIP-signature related to reflection symmetry detection has similar properties to the R-signature.

Theorem 2: D is the direction If it contains reflection symmetry, the LIP-signature also and is reflection symmetrical.

Proof: Axis direction Consider a shape with reflection symmetry (see Figure 6b).

and (each and )go and Suppose we want to denote each of the longest intersection sets (respective projections) of .

Thanks to the symmetry property of D, and get

this is It means that

As a result, the LIP-signature is is reflection symmetrical.

According to the definition above, and am.

Therefore each It is the largest intersection set and projection of D in the direction class do This is a parameter that corresponds to the direction.

On the other hand, and each direction It can be redefined as the longest intersection and projection of D.

in other words, am. Therefore, the LIP-signature is also is reflection symmetrical.

From Theorems 1 and 2, we can see that R-signature and LIP-signature have similar properties with respect to reflection symmetry. Accordingly, by checking the reflection symmetry properties of these signatures, candidates for the symmetry axis direction of the shape can be detected.

The complexity of the reflection detection problem converted from the two-dimensional domain to the one-dimensional domain is reduced.

The degree of reflection symmetry at each location of the one-dimensional signal is measured by comparing the similarity between the one-dimensional signal and the circular inverse signal at this location, considering the following definitions.

Below, the merit profile is explained in detail.

Definition 3: Given is called a vector of n elements.

This is called the forward (backward) circular movement of x in step i. is defined as follows.

In particular, the inversion of x, called I(x), is It is defined as

If the vector x is and is equal, then it has reflection symmetry at index k.

To measure the degree of reflection symmetry of x at position k and Estimate the similarity between According to this embodiment, using Pearson correlation and Measures the similarity between For simplicity, we consider two vectors X and Y with the same dimension.

The similarity between them is defined as follows:

where n is the number of elements in vector and is the average value of

The value ranges from 1 to +1 and indicates how similar X is to Y.

Reflection symmetry detection of the shape is effectively detected by considering the merit profile calculated from the above-described R-signature and LIP-signature.

For this purpose, in this embodiment, each angle Measures the similarity between forward and backward circular movements.

If this similarity is high, the angle is a good candidate for the direction of reflection symmetry.

Figure 7 is a diagram showing the merit profiles of two shape signatures.

The first row of Figure 7 represents a shape with only one reflection symmetry axis, and the second row represents a shape with two reflection symmetry axes orthogonal.

It can be seen that the merit profile of a shape with such single/multiple axes of symmetry has two peaks close to 1.

Also, according to Theorems 1 and 2, the following results can be obtained.

1) The axis of reflection symmetry is In the case of direction, its merit profile is respectively and has two peaks close to 1.

2) Direction A peak close to 1 does not mean that a given shape has reflection symmetry in that direction.

The above results are used to eliminate erroneous reflection symmetry axis directions.

A smooth Merit profile ensures that there are exactly two peaks close to 1 for each symmetry direction. Therefore, in this embodiment, incorrect detection of multiple axes of symmetry can be prevented.

To detect the true symmetry direction of shape D considering the merit profile, we need to remove the incorrect candidates predicted by Theorems 1 and 2.

For this purpose, the following verification process is performed.

Based on the following Theorems 3 and 4, the candidate direction ( ) Check whether the Radon projection is symmetrical.

Theorem 3: D is the direction Including reflection symmetry in to ensure reflection symmetry exists and here is variable.

Proof: Figure 6c shows shape D and direction From the axis of reflection symmetry represents.

Assume D is in the first quadrant of the coordinate system.

The distance between and the roots of the coordinate system is am.

now direction from the left of In D and any line (i.e. ) is considered.

class The distance between am.

silver is a symmetric segment of L for .

D is the axis of reflection symmetry Because it has silver direction It should be the intersection line with shape D in . The distances between and the roots of the coordinate system are respectively It is clear that

also, and silver direction Since it is the intersection line with shape D in and It can be inferred.

also, Because We get the result, where am.

this is go This means that it is reflection symmetrical.

Summary 4. go If D is not reflection symmetric about There is no reflection symmetry in direction.

Proof: D is the axis of reflection symmetry direction is reflection symmetrical (see Figure 6d).

go and the distance between the roots of the coordinate system.

Is Because there is no reflection symmetry about to make it happen exists.

The two sides of (i.e. class ) direction from Considering the intersection line with D at and the distance between them is Let it be.

and and therefore This happens.

this is class this This means that it cannot be symmetrical.

Therefore D is cannot be accepted as an axis of symmetry. This contradiction proves the conclusion of the proposed theorem.

Candidate symmetry axis directions via Theorems 3 and 4 Radon projection to check if is reflection symmetric (in other words, ) can be introduced.

Based on this solution If and only if is reflection symmetrical This is a good symmetrical direction. Figure 8 shows direction candidate 0 and This is a diagram showing a method for verifying reflection symmetry.

Radon projection in direction 0 (indicated by the red line in Figure 8a). has reflection symmetry, but direction (blue dotted line) shows the corresponding radon projection on the line in Figure 8(a). is not reflection symmetric.

To measure the symmetrical characteristics of the Radon projection described above, the Pearson correlation coefficient as shown in Equation 3 is used to determine the direction. determines how much symmetry reliability there is.

For candidate verification, Radon projection This is the reverse version It is symmetrical only if it is identical.

thus and By estimating the similarity between We can define the symmetry scale of D.

In equation 4: The degree of symmetry is expressed as -1 to +1.

A negative range means no symmetry at all, so for a truly effective symmetry measurement, must be located between 0 and 1. Therefore the threshold is used to suppress unimportant symmetry candidates.

Below, two methods for detecting reflection symmetry are described.

In practice, the main problem in reflection symmetry detection is determining the direction of reflection. direction Once detected, the symmetry reflection axis can be easily defined as a line passing through the center of the shape.

Algorithm 1 presents a moment-based method to detect the center of an arbitrary binary shape, and then focuses on detecting the direction of reflection symmetry.

As shown in Figure 5, the shape signature of a given shape is calculated, and a direction candidate is detected with a peak close to 1 through their merit profile.

Afterwards, if the obtained measurement value is greater than the threshold, the symmetry axis direction candidate is displayed as the symmetry axis direction along with the symmetry measurement value.

According to this embodiment, two thresholds are used to remove unimportant candidates.

first threshold is used to remove non-significant peaks detected in the merit profile, and the two second thresholds is the symmetry measure used to suppress incorrect candidates in the next step.

In theory, the conditions for detecting real reflection symmetry are am.

These parameters have their own threshold values for simplicity in Algorithm 2. can be replaced with , and to ensure symmetrical detection quality, can be considered.

Figure 9 is a diagram showing the configuration of a reflection symmetry detection device according to this embodiment.

As shown in FIG. 9, it may include a processor 900 and a memory 902 that stores instructions executable by the processor.

It may include a central processing unit (CPU) capable of executing computer programs or other virtual machines.

Memory 902 may include a non-volatile storage device, such as a non-removable hard drive or a removable storage device. Removable storage devices may include compact flash units, USB memory sticks, etc. Memory may also include volatile memory, such as various types of random access memory.

Program instructions executable by a processor are stored in the memory 902, and here, memory can be defined as a recording medium that stores a computer program.

Program instructions according to this embodiment perform a process of detecting reflection symmetry in an input image.

More specifically, the program instructions convert a two-dimensional input image into a one-dimensional Radon signal, and a shape signature obtained through line integration of the one-dimensional Radon signal within a preset direction range or intersection of the input image with an arbitrary line. Calculate a merit profile representing the degree of reflection at each position of the one-dimensional Radon signal from the shape signature, and use the merit profile to determine the optimal 2-dimensional input image among a plurality of symmetry axis candidate directions. Determine the direction of the axis of symmetry.

Here, the shape signature may include an R-signature obtained from the line integration of the one-dimensional Radon signal and a LIP-signature obtained through the intersection of the input image and an arbitrary line.

Additionally, program instructions may determine the optimal symmetry axis direction by applying a preset threshold to a peak of the merit profile, wherein the shape signature and the merit profile have one or more peaks in a predetermined direction θ, The merit profile can highlight some of the peaks that appear in the shape signature.

The merit profile according to this embodiment can be calculated using the similarity of forward and reverse circular shifts at angles in each direction.

The above-described embodiments of the present invention have been disclosed for illustrative purposes, and those skilled in the art will be able to make various modifications, changes, and additions within the spirit and scope of the present invention, and such modifications, changes, and additions will be possible. should be regarded as falling within the scope of the patent claims below.

Claims (10)

A reflection symmetry detection device using a shape signature,
processor; and
Including a memory connected to the processor,
The memory is,
Convert the two-dimensional input image into a one-dimensional Radon signal,
Calculate a shape signature obtained through the line integral of the one-dimensional Radon signal or the intersection of the input image and an arbitrary line within a preset direction range,
Calculate a merit profile representing the degree of reflection at each location of the one-dimensional Radon signal from the shape signature,
To determine the optimal symmetry axis direction for the two-dimensional input image among a plurality of symmetry axis candidate directions using the merit profile,
A reflection symmetry detection device using a shape signature storing program instructions executed by the processor. According to paragraph 1,
The shape signature includes an R-signature obtained from the line integration of the one-dimensional Radon signal and a LIP-signature obtained through the intersection of the input image and an arbitrary line. According to paragraph 2,
The R-signature is a reflection symmetry detection device defined by the equation below.
[Equation]

here, is a two-dimensional function is the Radon transform defined as, is the Dirac delta function, silver is a straight line, and θ is the angle that L makes with the y-axis, , ρ is the radial distance from the origin to L According to paragraph 2,
The LIP-signature is a reflection symmetry detection device defined by the equation below.
[Equation]

here, is the intersection between the input image D and an arbitrary line I and direction θ, s is the value moving away from the origin, is the largest intersection set in the θ direction, Is is the projection of D in the θ direction on the line, is a direction set, Is lim According to paragraph 1,
The program commands are:
A reflection symmetry detection device that determines the optimal symmetry axis direction by applying a preset threshold to peaks of the merit profile. According to clause 5,
The shape signature and the merit profile have one or more peaks in a predetermined direction θ, and the merit profile emphasizes some of the peaks appearing in the shape signature. According to paragraph 1,
A reflection symmetry detection device wherein the merit profile is calculated using the similarity of forward and reverse circular shifts at angles in each direction. According to paragraph 1,
The program commands are:
A reflection symmetry detection device that verifies the optimal symmetry axis direction by determining whether a Radon projection and its inverse version are the same in the optimal symmetry axis direction. A reflection symmetry detection method using a shape signature in a device including a processor and memory, comprising:
Converting a two-dimensional input image into a one-dimensional Radon signal;
Calculating a shape signature obtained through a line integral of the one-dimensional Radon signal or an intersection of the input image and an arbitrary line within a preset direction range;
calculating a merit profile representing the degree of reflection at each location of the one-dimensional Radon signal from the shape signature; and
A reflection symmetry detection method comprising determining an optimal symmetry axis direction for the two-dimensional input image among a plurality of symmetry axis candidate directions using the merit profile. A computer program stored in a computer-readable recording medium that performs the method according to claim 9.