A method for quantifying aesthetic features of classical gardens in the Yangtze River Delta region

Abstract

This invention discloses a method for quantifying the aesthetic characteristics of classical gardens in the Jiangnan region. First, the coordinate data of six types of landscape elements in classical Jiangnan gardens—semi-open buildings, solid buildings, roads, etc.—are preprocessed, including null value cleanup, unit standardization, and deduplication of road points. Then, a greedy algorithm and a depth-first search algorithm are used to optimize the tour path, calculating path-related parameters to obtain a fun index, thus quantifying the aesthetic appeal of the path. Next, a scoring system is constructed by combining the distribution density of landscape elements and spatial openness variations to obtain a comprehensive score for the sense of illusion. Finally, an aesthetic feature vector is constructed, and after standardization, a weighted cosine similarity is used to calculate the aesthetic similarity between different gardens. This invention is the first to construct a three-dimensional quantitative model of "fun appeal-illusion sense-similarity," transforming abstract garden aesthetics into calculable indicators. It possesses innovation, scientific rigor, practicality, and scalability, and can be widely applied to scenarios such as garden heritage protection, modern landscape design optimization, and smart tourism path planning.

Description

Technical Field

[0001] This invention relates to a feature quantification method, specifically a method for quantifying garden aesthetic features. Background Technology

[0002] Classical gardens in the Jiangnan region are a treasure of traditional Chinese aesthetics. With "changing scenery with every step," "finding grandeur in small spaces," and "harmony between man and nature" as their core design concepts, their aesthetic value is widely recognized. However, for a long time, research on the aesthetic characteristics of classical gardens in Jiangnan has relied heavily on subjective qualitative descriptions such as "profound artistic conception" and "balanced density," lacking scientific and unified quantitative indicators and modeling methods, making it difficult to accurately and objectively depict and analyze the aesthetic characteristics of these gardens.

[0003] Existing garden-related analysis techniques mostly focus on a single research dimension, which has obvious limitations: some studies only optimize garden tour routes through shortest path algorithms, ignoring the "fun" experience brought by the diversity of landscapes and failing to quantify the aesthetic feelings brought by path changes; some studies only discuss the "illusionary feeling" of garden space at the level of subjective feelings, without establishing an objective quantitative system based on spatial characteristics and element distribution; and comparative studies on the aesthetic similarity between gardens lack unified feature selection standards and calculation methods, resulting in poor reproducibility of analysis results and difficulty in promoting and applying them within the industry.

[0004] With the continuous application of digital technology in the field of gardening, the quantitative research of garden aesthetics has become a key requirement for breaking through the limitations of traditional research and promoting the scientific inheritance and innovative application of garden cultural heritage. Therefore, it is urgent to construct a multi-dimensional, operable, and highly universal quantitative method for the aesthetic characteristics of classical gardens in Jiangnan, transforming abstract garden aesthetic concepts into calculable and verifiable quantitative indicators. Summary of the Invention

[0005] Purpose of the invention: In view of the above-mentioned existing technology, this invention proposes a quantitative method for the aesthetic characteristics of classical gardens in Jiangnan, so as to accurately depict the changes in garden paths, spatial experience and the commonalities of aesthetics among gardens.

[0006] Technical solution: Beneficial Effects: This invention, by constructing a three-dimensional quantitative model of "fun, illusion, and similarity," achieves the scientific quantification of the aesthetic characteristics of classical gardens in Jiangnan. Compared with existing technologies, it has the following significant beneficial effects: 1. For the first time, a three-dimensional quantitative system of "fun, illusion, and similarity" for classical gardens in the Jiangnan region was constructed, which transforms abstract garden aesthetic concepts such as "different views with each step" and "seeing the big in the small" into calculable and verifiable quantitative indicators, filling the gap in traditional garden aesthetics research that relies solely on qualitative descriptions.

[0007] 2. By integrating various digital technologies such as greedy algorithms, depth-first search (DFS), and weighted cosine similarity, the system achieves efficient optimization of the optimal path, accurate calculation of feature parameters, and objective comparison of similarity between gardens. The entire quantification process is logically rigorous and the steps are clear. The analysis results are repeatable and verifiable, thus enhancing the scientific nature of garden aesthetics research.

[0008] 3. All quantitative indicators and algorithm parameters are adapted to the scale and design characteristics of classical gardens in Jiangnan, such as a 2m road deduplication radius, a 5m mountain and water proximity attenuation scale, and an 8m hard and soft landscape neighborhood radius. At the same time, it supports the custom adjustment of parameters such as thresholds and weights, which can be adapted to the quantitative analysis of classical gardens in Jiangnan of different scales and styles. It is easy to operate and highly practical.

[0009] 4. The quantitative methods and indicator systems provided by this invention are highly transferable and can be widely applied to various scenarios such as the valuation of garden heritage, the optimization of modern landscape design, and the planning of smart tourism routes. They can provide data support for the restoration and protection of garden heritage, and also provide quantitative references for modern landscape design to draw upon the aesthetic characteristics of classic gardens. Attached Figure Description

[0010] Figure 1 Flowchart of a method for quantifying the aesthetic characteristics of classical gardens in Jiangnan; Figure 2 A map showing the optimized pathways of Yu Garden, a classical garden in the Jiangnan region. Figure 3 A diagram showing the optimized pathways in the Lingering Garden, a classical garden in the Jiangnan region. Detailed Implementation

[0011] The invention will now be further explained with reference to the accompanying drawings.

[0012] like Figure 1 As shown, a method for quantifying the aesthetic characteristics of classical gardens in the Jiangnan region is presented, with the following specific steps: Step 1: Collect multimodal data of classical gardens in the Jiangnan region, including coordinate data of landscape elements and plant crown diameter data. The landscape elements include semi-open buildings, solid buildings, roads, artificial hills, water features, and plants. Import all data into MATLAB software for preprocessing, specifically including: (1) Cleaning up null and outlier values: Remove invalid data with null coordinates (NaN); define the garden area by the extreme values ​​of the coordinates of the physical buildings, and delete the coordinates of abnormal landscape elements that exceed the area; where the extreme values ​​of the coordinates of the physical buildings are: x_min=min(x coordinate of physical building), x_max=max(x coordinate of physical building), y_min=min(y coordinate of physical building), y_max=max(y coordinate of physical building).

[0013] (2) Unit unification: Convert the millimeter-level coordinates of all landscape elements to meter-level units, and synchronously complete the unit conversion from millimeter to meter for plant crown diameter data to ensure that all data scales are consistent.

[0014] (3) Road point deduplication: Construct a circular neighborhood with a radius of 2m, and filter the road coordinate points. When the Euclidean distance between the candidate road point and the selected road point is less than 2m, the candidate point is determined to be a duplicate point and is removed to avoid data redundancy in subsequent path calculation.

[0015] Step 2: Focusing on the "complexity" of garden paths and the "diversity" of landscapes, an algorithm is used to optimize the best tour route and calculate path characteristics, ultimately obtaining a "fun index" to quantify the aesthetic appeal of the garden paths. This includes: (1) Path optimization: A greedy algorithm is used to find the optimal tour path within the garden area defined by the physical buildings. The greedy algorithm uses the "minimum distance from the current point to the unvisited point" as the local optimum standard, and the path points must satisfy the coordinate range x∈[x_min,x_max], y∈[y_min,y_max], and the distance between adjacent path points ≤5m. The depth-first search (DFS) algorithm is used to traverse all path nodes and supplement isolated path segments to ensure that the optimal tour path has no isolated points and good connectivity.

[0016] (2) Calculation of key features: Calculate the three core feature parameters of the optimal tour path, namely: total path length L, which is obtained by accumulating the Euclidean distances of adjacent road points; number of turning points Nt, which is calculated by the vector angle formula for the included angle of three consecutive points. When the included angle is <120°, it is determined to be a turning point. The number of all turning points that meet the conditions is counted; number of intersections Nc, which is determined by the difference in the sign of the cross product of line segment vectors to determine whether the path line segments intersect. The total number of intersections formed by the intersection is counted.

[0017] The specific method for determining the intersection points is as follows: For the path segment p1p2 formed by nodes p1 and p2, and the path segment p3p4 formed by nodes p3 and p4, where the coordinates of node p1 are (p1.x, p1.y), the coordinates of node p2 are (p2.x, p2.y), the coordinates of node p3 are (p3.x, p3.y), and the coordinates of node p4 are (p4.x, p4.y), the cross product of the vectors is calculated as follows: d1 = (p2.x - p1.x)(p4.y - p3.y) - (p2.y - p1.y)(p4.x - p3.x), d2 = (p1.x - p3.x)(p4.y - p3.y) - (p1.y - p3.y)(p4.x - p3.x), d3=(p1.x-p2.x)(p3.y-p4.y)-(p1.y-p2.y)(p3.x-p4.x), d4=(p2.x-p3.x)(p3.y-p4.y)-(p2.y-p3.y)(p3.x-p4.x), When d1>0 and d2<0 and d3>0 and d4<0, or d1<0 and d2>0 and d3<0 and d4>0, it is determined that the two line segments intersect, that is, there is an intersection point at that position.

[0018] (3) Calculation of interest index: Combining the complexity of the path and the characteristics of landscape changes, the interest index is defined as Int=(Nt+Nc)×1000 / L. The higher the interest index Int value, the stronger the aesthetic interest of the garden tour path.

[0019] Step 3: Focusing on the core spatial experience of "seeing the grand in the small" in classical Jiangnan gardens, a scoring system is constructed through two dimensions: the density of landscape element distribution and the changes in spatial openness and closure. This ultimately yields a comprehensive score for the sense of illusion, quantifying the illusory aesthetic characteristics of the garden space, specifically including: (1) Calculation of element distribution score: The distance matrix of all landscape elements is calculated by using the pdist function. After converting it into a square matrix, the minimum distance between each element and other elements is extracted. The average value of all minimum distances is obtained to get the distribution density of landscape elements. The minimum value eps is set. When the distribution density is ≥ eps, the element distribution score = 1 / maximum density. The higher the element distribution score, the sparser the distribution of garden landscape elements and the stronger the sense of spatial transparency.

[0020] (2) Calculation of opening and closing change score: Set the open space threshold to 20m and the enclosed space threshold to 10m, traverse all valid road points and count the distance between all road point pairs; when the distance between road point pairs is >20m, it is judged as open space, and the sense of opening and closing is +1; when the distance between road point pairs is <10m, it is judged as enclosed space, and the sense of opening and closing is -1; accumulate the sense of opening and closing values ​​of all road point pairs to obtain the opening and closing change score.

[0021] (3) Calculation of the overall score of illusion: The element distribution score and the opening and closing change score are directly added together to obtain the illusion score. The formula is: Illusion score = element distribution score + opening and closing change score. The higher the value of the illusion score, the stronger the dynamic experience (illusion) of the garden space from "enclosed" to "open".

[0022] Step 4: Integrate the garden's appeal, path features, spatial characteristics, and cultural aesthetic features to construct a multi-dimensional aesthetic feature vector. Through standardization and weighted cosine similarity calculation, compare the aesthetic feature similarities among different classical gardens in the Jiangnan region. Specifically, this includes: (1) Constructing an aesthetic feature vector: Integrate the indicators obtained from the above quantification with the newly added cultural aesthetic indicators to form an aesthetic feature vector F=[Int, Nt, Nc, L, element distribution score, opening and closing change score, Φ_SW, B_HS].

[0023] Among them, Φ_SW is the proximity index between the tour route and the garden's landscape elements, reflecting the degree of proximity between the tour route and the garden's landscape elements. It is calculated using a distance decay model, and the formula is: Φ_SW=0.5×(mean(Aw)+mean(Ar)), where mean(·) represents the arithmetic mean, Aw is the water affinity index, and Ar is the rock affinity index. Aw=exp(-d_w / τ_w), Ar=exp(-d_r / τ_r), where d_w is the distance from the path point to the nearest water body, d_r is the distance from the path point to the nearest artificial hill, and τ_w is the distance from the water body to the nearest rockery. The distance attenuation scale, τ_r, is the distance attenuation scale of the artificial hill. In this embodiment, both τ_w and τ_r are set to 5m. B_HS is the hard-soft balance index, which reflects the design concept of "combining hard and soft" in gardens. It is calculated by the difference in distribution density between hard and soft landscapes. The calculation formula is: B_HS=mean(1-|ρ_H-ρ_S| / (ρ_H+ρ_S+eps)), where ρ_H is the distribution density of hard landscapes in a neighborhood with a radius of 8m, and ρ_S is the distribution density of soft landscapes in the same neighborhood. Hard landscapes are the combination of buildings and artificial hills, and soft landscapes are the combination of water bodies and plants.

[0024] (2) Feature vector standardization: The Z-score standardization method is used to eliminate the scale difference of different feature indicators. The calculation formula is: Fz=(F-MU) / SIG, where MU is the mean of the aesthetic feature vectors F1 and F2 of the two gardens to be compared, i.e., MU=(F1+F2) / 2, and the standard deviation SIG=√[((F1-MU)²+(F2-MU)²) / 2]+eps, where eps represents an arbitrarily small positive number.

[0025] (3) Weighted cosine similarity calculation: The weighted cosine similarity between the two gardens to be compared is calculated based on the preset weight vector. The weight vector w is set to [0.15,0.10,0.10,0.10,0.15,0.15,0.12,0.13] by default. The similarity value S_cos is obtained by dividing the weighted dot product by the product of the weighted vector magnitudes. The closer S_cos is to 1, the more similar the aesthetic features of the two gardens are. The closer it is to 0, the greater the difference in the aesthetic features of the two gardens are.

[0026] The following uses Yu Garden, a classical garden in the Jiangnan region, as an example to explain in detail the specific implementation process of this method: 1. Data Acquisition and Preprocessing The coordinate data of landscape elements in Yu Garden were obtained, including 32 semi-open buildings, 48 ​​solid buildings, 156 original points of roads, 12 artificial hills, 8 water bodies, and 64 plants, including crown diameter data for plants. After importing into MATLAB, null values ​​for 6 road points and outliers for 4 plant coordinates outside the garden area were cleaned up. Millimeter coordinates were converted to meters, and plant crown diameters were converted from "1200mm" to "1.2m". The road points were deduplicated with a 2m radius, resulting in 128 valid road points. The garden area was defined by the coordinates of solid buildings: x∈[-150,220]m, y∈[0,200]m.

[0027] 2. Implement with quantifiable elements of fun. (1) Path optimization: The greedy algorithm obtains the optimal path, with the path points being 1→8→15→…→128 in sequence. The DFS algorithm is used to supplement two isolated paths to ensure connectivity. (2) Calculation of key features: path length L=147.26m, turning points Nt=36, intersection points Nc=46; (3) Calculation of fun index: Int=(36+46)×1000 / 147.26≈556.85, indicating that the Yu Garden path is quite interesting.

[0028] 3. Quantitative Implementation of Illusory Sense (1) Element distribution score: The distance matrix is ​​calculated using the pdist function, and the average minimum distance is 3.2m. The element distribution score is 1 / 3.2≈0.3125. (2) Opening and closing change score: 128 road point pairs were counted, totaling 8128 groups, of which 125 pairs were open points with a width of >20m and 43 pairs were enclosed points with a width of <10m. The opening and closing change score = 125 - 43 = 82. (3) Illusionary feeling score: 0.3125+82=82.3125, reflecting that the illusionary feeling of Yu Garden is more prominent.

[0029] 4. Implementation of similarity quantification (1) Feature vector construction: hydrophilic Aw=0.821, stony Ar=0.890, Φ_SW=0.8557, hardscape density ρ_H=0.021, softscape density ρ_S=0.018, B_HS=0.7234, feature vector F=[556.85,36,46,147.26,0.3125,82,0.8557,0.7234]; (2) Similarity comparison: The weighted cosine similarity S_cos=-0.3536 was calculated between the feature vector F2=[482.17,28,39,132.54,0.286,75,0.792,0.685] of Liuyuan Garden, indicating that the two have significant differences in aesthetic features, which is consistent with the actual garden style of "Yuyuan Garden is compact and Liuyuan Garden is spacious".

[0030] Figure 2 This is a map showing the optimized path layout for Yu Garden. Figure 3 This is a map showing the optimized path layout of the Lingering Garden, with coordinates in meters. The dark green lines represent the optimal tour path obtained through a greedy algorithm and a depth-first search (DFS) algorithm. Purple dots represent semi-open buildings, black dots represent solid buildings, yellow dots represent road points, red dots represent artificial hills, cyan dots represent water features, and green circles represent plants, with the size of the green circles proportional to the plant crown diameter. The map includes a 20m scale and a north arrow, which visually demonstrates the optimal path layout and the spatial distribution characteristics of various landscape elements.

[0031] The results of this embodiment show that the fun index, illusion score, and similarity value between gardens obtained by the quantification method of the present invention can accurately reflect the actual aesthetic characteristics of classical gardens in Jiangnan, and are highly consistent with the design style and spatial characteristics of the gardens, thus verifying the feasibility, effectiveness, and accuracy of the method of the present invention.

[0032] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for quantifying the aesthetic characteristics of classical gardens in the Jiangnan region, characterized in that, include: Step 1: Collect multimodal data of classical gardens in Jiangnan, including coordinate data of landscape elements and crown diameter data of plants. The landscape elements include semi-open buildings, solid buildings, roads, rockeries, water bodies, and plants; preprocess all data. Step 2: Based on the greedy algorithm, find the optimal tour path within the space defined by the physical buildings, calculate the total length L, the number of turning points Nt, and the number of intersections Nc of the optimal tour path, and calculate the fun index Int using the formula Int=(Nt+Nc)×1000 / L. Step 3: Construct a scoring system based on two dimensions: the distribution density of landscape elements and the changes in spatial openness and closure, and finally obtain a comprehensive score for the sense of illusion; Step 4: Construct a multi-dimensional aesthetic feature vector. After standardizing the feature vector, use the weighted cosine similarity formula to calculate the aesthetic similarity between different gardens, thus achieving a comparison of the aesthetic feature similarity between different classical gardens in Jiangnan.

2. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 1, characterized in that, In step 1, the preprocessing includes: cleaning up null values ​​and outliers outside the garden area in the data, converting millimeter-level coordinates to meter-level units, and using circular neighborhood filtering to select road points and remove duplicate points; wherein, the boundary of the garden area is defined by the extreme values ​​of the coordinates of the physical buildings, and the extreme values ​​of the coordinates of the physical buildings are: x_min=min(physical building x coordinate), x_max=max(physical building x coordinate), y_min=min(physical building y coordinate), y_max=max(physical building y coordinate), and the coordinates of landscape elements outside this coordinate range are judged as outliers.

3. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 1, characterized in that, In step 2, the optimal tour path is found within the space defined by the physical building based on the greedy algorithm. Specifically, the greedy algorithm takes the minimum distance from the current point to the unvisited point as the local optimum standard, and the path points must satisfy the coordinate range x∈[x_min,x_max], y∈[y_min,y_max], and the distance between adjacent path points ≤ a preset threshold. The path nodes are traversed by the depth-first search algorithm to ensure that there are no isolated points on the path.

4. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 1, characterized in that, In step 2, the total path length L is obtained by summing the Euclidean distances between adjacent road points; The calculation method for the number of turning points Nt is as follows: the included angle of three consecutive points is calculated using the vector included angle formula. When the included angle is less than a preset angle threshold, it is determined to be a turning point. The number of all turning points that meet the conditions is counted. The number of intersection points Nc is determined by the difference in the sign of the cross product of line segment vectors to determine whether the path line segments intersect. The total number of intersection points formed by the intersection is counted.

5. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 4, characterized in that, In step 2, the specific method for determining the intersection points is as follows: For the path segment p1p2 formed by nodes p1 and p2, and the path segment p3p4 formed by nodes p3 and p4, the coordinates of node p1 are (p1.x, p1.y), the coordinates of node p2 are (p2.x, p2.y), the coordinates of node p3 are (p3.x, p3.y), and the coordinates of node p4 are (p4.x, p4.y). The cross product of the vectors is calculated as follows: d1 = (p2.x - p1.x)(p4.y - p3.y) - (p2.y - p1.y)(p4.x - p3.x), d2 = (p1.x - p3.x)(p4.y - p3.y) - (p1.y - p3.y)(p4.x - p3.x). d3=(p1.x-p2.x)(p3.y-p4.y)-(p1.y-p2.y)(p3.x-p4.x), d4=(p2.x-p3.x)(p3.y-p4.y)-(p2.y-p3.y)(p3.x-p4.x), When d1>0 and d2<0 and d3>0 and d4<0, or d1<0 and d2>0 and d3<0 and d4>0, it is determined that the two line segments intersect, that is, there is an intersection point at that position.

6. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 1, characterized in that, Step 3 specifically includes: calculating the distance matrix of all landscape elements using the pdist function, extracting the minimum distance between each element and other elements and calculating the average to obtain the distribution density, and calculating the element distribution score according to element distribution score = 1 / maximum density, where density ≥ minimum value eps; Set an openness threshold and an enclosure threshold, and count the distance between all road point pairs. When the distance is greater than the openness threshold, the sense of openness / closure increases by 1; when the distance is less than the enclosure threshold, the sense of openness / closure decreases by 1. Accumulate the scores to obtain the openness / closure change score. The overall illusion score is calculated by adding the element distribution score to the opening and closing change score.

7. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 1, characterized in that, In step 4, the aesthetic feature vector F = [Int, Nt, Nc, L, element distribution score, opening and closing change score, Φ_SW, B_HS]; where Φ_SW is the water affinity index, calculated as: Φ_SW = 0.5 × (mean(Aw) + mean(Ar)), mean(·) represents the arithmetic mean, Aw is the water affinity index, Ar is the rock affinity index, Aw = exp(-d_w / τ_w), Ar = exp(-d_r / τ_r), d_w is the distance from the path point to the nearest water body, and d_r is the distance from the path point to the nearest artificial hill; B_HS is the hard and soft balance index, calculated as: B_HS = mean(1-|ρ_H-ρ_S| / (ρ_H+ρ_S+eps)), ρ_H is the distribution density of hard scenery in the neighborhood, ρ_S is the distribution density of soft scenery in the same neighborhood, hard scenery is the combination of buildings and artificial hills, and soft scenery is the combination of water bodies and plants.

8. The method for quantifying the aesthetic characteristics of classical gardens in Jiangnan according to claim 7, characterized in that, In step 4, the weighted cosine similarity between the two gardens to be compared is calculated based on the preset weight vector. The weight vector w is set to [0.15, 0.10, 0.10, 0.10, 0.15, 0.15, 0.12, 0.13]. The similarity value S_cos is obtained by dividing the weighted dot product by the product of the weighted vector magnitudes. The closer S_cos is to 1, the more similar the aesthetic features of the two gardens are. The closer S_cos is to 0, the greater the difference in the aesthetic features of the two gardens are.

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