Curve matching is a significant problem in computer vision and image processing.It has a wide range of applications in cultural debris splicing

medical image registration

and product testing.Given the importance of curve description and matching

scholars have conducted numerous research and have made significant progress in this field.However

several problems still exist due to the relatively high practical application requirements.At present

many common curve-matching methods can obtain acceptable classification results.However

for the geometric shape similarity problem

the results obtained by these methods cannot accurately reflect the similarity of geometric shape and are inconsistent with human cognition.An acceptable shape descriptor can effectively differentiate the target shape.Moreover

the descriptor of the target shape should remain unchanged even with the translating

rotating

and scaling of the target shape.To achieve the purpose of valid curve description

this study presents a curve description method based on arch sequence.Curve matching is usually based on the curve description method

using a certain metric to determine the degree of similarity between curves.To achieve the curve matching accurately and quickly

an arch sequence matching method based on dynamic programming is proposed according to the curve description method of the arch sequence.The similarity degree of the two curves is determined according to the similarity degree of the two arch sequences. For curve matching

the characteristic descriptor of the curve is initially defined and this descriptor is used to describe the curve.The appropriate method is used to match the curves based on the curve description.The corners of the curve are initially extracted to realize the curve description based on the arch sequence

and the curve is divided into a series of sub-curves by corners.All adjacent two sub-curves can be combined to form an arch.A contour curve can be expressed as a sequence of successive overlapping arches using an arch composed of sub-curves to represent the curve.For each arch in the arch sequence

the ratios of bow height to chord length

of bow height half-chord length to chord length

and of arc length to chord length

and the sine of the chord angle and the connection of bow high point to the midpoint of the chord are used to describe the arch.Calculating the degree of similarity between the corresponding arch sequences is necessary.Defining the distance between one arch and the other is necessary in calculating the degree of similarity between arch sequences.The ratio of bow height to chord length and other related eigenvalues are used to calculate the distance between the arches.The idea of edit distance of the string in the dynamic programming method is adopted to calculate the minimum cost of converting an arch sequence into another arch sequence

thereby obtaining the similarity between arch sequences quickly and accurately.The distance between the curves can be obtained using the edit distance between the arch sequences. The curve description and matching method based on the arch sequence are used to stitch the contours and compute the similarity of the geometric figures

thereby verifying the effectiveness of the proposed method.To verify whether this method can be applied to contour splicing

the method is initially applied to the splicing of two fragments and then to the splicing of two map contours.In the splicing experiment of fragments and map contours

the fragments and map contours are concisely stitched together using the curve description and matching method based on the arch sequence.A similarity measure is performed in a geometric test library to verify that the method can determine whether the geometries belong to the same type.In the cross-measurement experiment of geometric similarity

the curve description and the matching method based on arch sequence can accurately reflect the similarity of the graph.The similarity of the graph can accurately judge whether the two images belong to the same type.This method is used to calculate the similarity degree of the six groups of geometric shapes

thereby verifying that the method can reflect the similarity of geometric pairs.This method can provide the same result as human judgment in the comparative experiment between geometric shape and similarity.The method has better distance value to reflect the similarity of the image

compared with the method of chain code feature

multiscale invariant

shape context

and geometry complex transform(GCT). This study presents a curve description and matching method based on arch sequence.In this method

the contour curve is expressed as an arch sequence.The dynamic programming method is used to realize the curve matching based on the arch sequence.The algorithm can effectively describe

match the curve

and provide low time complexity.In this study

the curve description and matching method based on arch sequence is applied to the simulation experiment of stitching contours

the cross-measurement experiment of geometric similarity

and the comparison experiment of geometric similarity degree.The method can accurately stitch the contours

judge the similarity of the geometric figures

and provide results that are consistent with the human visual judgments.For the geometric shapes with different degrees of similarity

the distance between the arch sequences can also effectively reflect the difference.