CN118071585A - Rapid resampling method, system and device for remote sensing image and storage medium - Google Patents
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Abstract
The invention discloses a method, a system, a device and a storage medium for rapidly resampling a remote sensing image, wherein the method comprises the following steps: determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm; establishing a target grid for storing an array of required sampling point data, wherein the size of the array is [ target grid image height ] [ target grid image width ] [ interpolation calculation required sampling point number ]; the last one-dimensional order of the array is fixed; processing the sampling point data of the remote sensing image one by one, and assigning any sampling point data to a target grid array around the sampling point data; after all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not; if the data in the array is missing, a distance weighting algorithm is used for processing; if the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
Description
Technical Field
The invention relates to the technical field of remote sensing data processing, in particular to a method, a system, a device and a storage medium for rapidly resampling remote sensing images.
Background
Due to the satellite platform, the image sensor, the earth itself and other aspects, the remote sensing image has geometrical distortion which is difficult to avoid. Therefore, the first step of processing the original data of the satellite remote sensing image is to geometrically position the image pixels, namely to determine the geographic longitude and latitude of the image pixels, and then to resample the original image data to generate a high-precision remote sensing image product. The geometric positioning method of the satellite remote sensing image pixels is mature, and the positioning precision of the satellite remote sensing image pixels reaches the sub-pixel level.
Image resampling is an essential operation in image processing, and is an indispensable step in remote sensing data processing, whether the geometric positioning is performed, or the following geometric fine correction, elevation correction, orthographic correction, or common operations such as image zooming-in, zooming-out, and rotation. Image resampling is specifically a process of acquiring pixel values on a target grid according to a set pixel aggregation or interpolation rule by using a set of sampling points (coordinates on the target grid after an original image pixel value plus transform operation). The common interpolation methods include a nearest neighbor method, bilinear interpolation, surface fitting interpolation, bicubic interpolation and the like, and the difference between different interpolation methods is in calculation timeliness and precision, and the interpolation methods need to be selected according to actual requirements.
Taking bilinear interpolation as an example, the method uses the values of the four nearest neighbor input sample points to determine the value on the target grid. For basic image scaling, rotation and other operations, the corresponding relation between the original image grid and the target grid can be determined very simply, namely, which four input sampling points are the nearest points required by bilinear interpolation is determined. However, for operations such as geometric positioning, the transformed sample point coordinates are irregular, and the nearest four points required for bilinear interpolation are to be obtained, and conventional methods can only traverse the entire sample point data set, which is even more time-consuming than interpolation computation.
To solve the efficiency problem of finding the nearest neighbor sample point, the conventional approach is to block the entire sample point data set to reduce the size of the traversing sample point data set, or to speed up the finding efficiency by a method similar to a half-search. But the remote sensing image is generally very large (10 8 sampling points), and even if the sampling point data is segmented, hundreds to tens of sampling points still need to be searched. Therefore, the efficiency of the traditional resampling method cannot meet the requirement of the real-time processing of the modern satellite remote sensing image.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method, a system, a device and a storage medium for rapidly resampling a remote sensing image.
The invention aims at realizing the following technical scheme:
In a first aspect, the present invention provides a method for rapidly resampling a remote sensing image, including:
Determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
establishing an array for storing the data of the required sampling points, wherein the size of the array is [ target raster image height ] [ target raster image width ] [ interpolation calculation required sampling point number ];
the rule for storing the sampling point data in the array is as follows:
Sequentially storing the data of sampling points of different orientations of the target grid point in the positions in the corresponding array from the nearest upper left position by taking the target grid point as the center according to the clockwise sequence;
processing the remote sensing image sampling point data one by one, and assigning each sampling point data to a surrounding target grid array;
After all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
Based on the above, the set resampling interpolation algorithm is the nearest neighbor method, and the array assignment is performed in the following manner:
Firstly judging whether the array in the target grid has a value or not, if not, directly assigning a value;
If the distance d1 between the sampling point and the target grid is judged, and if the distance d1 between the sampling point and the target grid is smaller than d2, the value is assigned.
Based on the above, the set resampling interpolation algorithm is a bilinear interpolation algorithm, and the array assignment is performed in the following manner:
Sample point data with image coordinates (I, J) is formed by rounding down floorI, floorJ coordinate values, and ceilI and ceilJ are formed by rounding up coordinate values, so that the sample point data is assigned to the upper left point target grid array [ floorI ] [ floorJ ] [3], the upper right point target grid array [ floorI ] [ ceilJ ] [4], the lower left point target grid array [ ceilI ] [ floorJ ] [2] and the lower right point target grid array [ ceilI ] [ ceilJ ] [1].
Based on the above, the set resampling interpolation algorithm is a bicubic interpolation algorithm, and the array assignment is performed in the following manner:
the sampling point assigns values to the surrounding 16 target grid point arrays, and assigns values of i and j to arrays [ floorI +i ] [ floorJ +j ] [ i ] 4+j ], respectively [ -1,0,1,2].
Based on the above, the method for performing interpolation calculation to complete resampling comprises the following steps:
f(P)＝f(S1)
Where f (P) is a pixel value interpolated from the target grid point P, and f (S 1) is an image pixel value at the sampling point S 1.
Based on the above, the method for performing interpolation calculation to complete resampling comprises the following steps:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y denote the coordinates of the target grid point P, x 1,x2,x3,x4 is the abscissa of the sampling point S 1,S2,S3,S4, R 1 is the interpolation point of S 1,S2 at P x, R 2 is the interpolation point of S 3,S4 at P x, and y 1,y2 is the ordinate of R 1,R2, respectively.
Based on the above, the method for performing interpolation calculation to complete resampling comprises the following steps:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y represents the coordinates of the target grid point P, x 1,y2 is S i of the sampling point S i, i takes values 1 to 16, and k is a kernel function of the bicubic interpolation algorithm.
In a second aspect, the present invention provides a rapid resampling system for remote sensing images, comprising:
The sampling point number determining module is used for determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
The array establishing module is used for establishing an array for storing the data of the required sampling points, and the size of the array is [ target raster image height ] [ target raster image width ] [ number of the sampling points required by interpolation calculation ];
the rule for storing the sampling point data in the array is as follows:
Sequentially storing the data of sampling points of different orientations of the target grid point in the positions in the corresponding array from the nearest upper left position by taking the target grid point as the center according to the clockwise sequence;
The assignment module is used for processing the remote sensing image sampling point data one by one and assigning each sampling point data to a surrounding target grid array;
A resampling module for: after all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
In a third aspect, the present invention provides a computer device, including a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the remote sensing image rapid resampling method when executing the computer program.
In a fourth aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the remote sensing image fast resampling method.
Compared with the prior art, the invention has outstanding substantive characteristics and remarkable progress, and in particular has the following beneficial effects:
① The traditional resampling calculation efficiency is improved by 3-4 times;
② The difficulty of algorithm realization is avoided;
③ The result is reliable and can be applied to oversized images.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related art, the drawings that are required to be used in the embodiments or the related technical descriptions will be briefly described, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to the drawings without inventive effort for those skilled in the art.
Fig. 1 is a schematic diagram of a sample point distribution.
Fig. 2 is a schematic diagram of which target grid points the sampling points will be used in interpolation calculation, taking the nearest neighbor method as an example (red points P represent target grid points and black star points S represent sampling points).
Fig. 3 is a schematic diagram of sample points used in interpolation calculation by which target grid points are used (red points P represent target grid points, and black star points S represent sample points) taking bicubic interpolation as an example.
Fig. 4 is a flow chart of resampling calculation according to the present invention.
Fig. 5 is a diagram of a sampling point orientation corresponding to the bilinear interpolation algorithm array of the present invention.
FIG. 6 is a plot of the sample point orientations corresponding to the bicubic interpolation algorithm array of the present invention.
FIG. 7 is a comparison of the time-consuming improvement before and after resampling calculation.
Fig. 8 is a functional block diagram of a computer device of the present invention.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
After the satellite remote sensing data is geometrically positioned, the distribution of the coordinate points of the sampling points on the target grid is extremely irregular, as shown in fig. 1, asterisks represent the sampling points, and grid crossing points represent the target grid points. In interpolation computation, one or more sampling points near the target grid point need to be found, so that in order to avoid the search traversal, reverse thinking can be performed, and data of one sampling point can appear in interpolation computation of which target grid points, and obviously only can be used by the target grid points around the coordinates of the sampling point.
Taking the nearest neighbor method as an example, as shown in fig. 2, in the interpolation calculation, the S33 sampling point is only used by the target grid points P33, P34, P43, P44; taking bicubic interpolation as an example, as shown in fig. 3, in the interpolation calculation, the S33 sampling point is only used by 16 target grid points such as P22 to P55, and is not searched by other target grid points. Therefore, the problem of searching the sampling points can be equivalent to the problem of using the sampling points by whom, so that the time-consuming searching process in the resampling process is directly avoided.
As shown in fig. 4, the present invention provides a rapid resampling method for remote sensing images, which includes:
step 1: determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
Such as nearest neighbor algorithm, 1 sampling point is needed; bilinear interpolation algorithm, 4 sampling points are needed; the bicubic interpolation algorithm requires 16 sample points.
Step 2: establishing an array for storing the data of the required sampling points, wherein the size of the array is [ target raster image height ] [ target raster image width ] [ interpolation calculation required sampling point number ];
the rule for storing the sampling point data in the array is as follows:
Sequentially storing the data of sampling points of different orientations of the target grid point in the positions in the corresponding array from the nearest upper left position by taking the target grid point as the center according to the clockwise sequence;
As shown in FIG. 5, in the bilinear interpolation algorithm, [1] stores the sampling point at the upper left position of the target grid, [2] stores the sampling point at the upper right position, [3] stores the sampling point at the lower right position, and [4] stores the sampling point at the lower left position in the array. Similarly, bicubic interpolation is shown in fig. 6.
Step 3: and processing the remote sensing image sampling point data one by one, and assigning each sampling point data to a surrounding target grid array.
Taking the nearest neighbor algorithm as an example, firstly judging whether values exist in an array in a target grid or not, if no values exist, directly assigning values; if the distance d1 between the sampling point and the target grid is judged, and if the distance d1 between the sampling point and the target grid is smaller than d2, the value is assigned.
Taking bilinear interpolation algorithm as an example, if the sampling point data with the image coordinates (I, J) is given by floorI, floorJ as the coordinate value, the coordinate value is rounded downwards, the ceilI is given by ceilJ as the coordinate value, and the coordinate value is rounded upwards, the sampling point data is assigned to the upper left point target grid array [ floorI ] [ floorJ ] [3], to the upper right point target grid array [ floorI ] [ ceilJ ] [4], to the lower left point target grid array [ ceilI ] [ floorJ ] [2], and to the lower right point target grid array [ ceilI ] [ ceilJ ] [1].
Taking bicubic interpolation algorithm as an example, the sampling points assign values to the surrounding 16 target grid point arrays, and assign values to arrays [ floorI +i ] [ floorJ +j ] [ i ] 4+j ], i and j values [ -1,0,1,2].
Step 4: after all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
Taking the nearest neighbor algorithm as an example, the method for performing interpolation calculation to finish resampling comprises the following steps:
f(P)＝f(S1)
Where f (P) is a pixel value interpolated from the target grid point P, and f (S 1) is an image pixel value at the sampling point S 1.
Taking bilinear interpolation algorithm as an example, the method for performing interpolation calculation to finish resampling comprises the following steps:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y denote the coordinates of the target grid point P, x 1,x2,x3,x4 is the abscissa of the sampling point S 1,S2,S3,S4, R 1 is the interpolation point of S 1,S2 at P x, R 2 is the interpolation point of S 3,S4 at P x, and y 1,y2 is the ordinate of R 1,R2, respectively.
Taking bicubic interpolation algorithm as an example, the method for performing interpolation calculation to finish resampling comprises the following steps:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y represents the coordinates of the target grid point P, x 1,y2 is S i of the sampling point S i, i takes values 1 to 16, and k is a kernel function of the bicubic interpolation algorithm;
k is defined as follows, where the parameter a generally takes the value-0.5:
In order to illustrate the advanced nature of the resampling process after the improvement of the invention, the image data of a satellite with a scene image and the size of 6G is taken, and the resampling results of the three interpolation algorithms before and after the improvement are compared. First, the accuracy of the result is that whether the images obtained by the two resampling flows are identical. By comparing the sample point data of each target grid participating in interpolation calculation, no difference is found, indicating that the present invention is feasible. Then a comparison of the calculation time consumption is made, as shown in fig. 7. It can be seen that avoiding the search improves the computational efficiency by a factor of 3-4 with the improved resampling process of assigning values to the target grid array.
Based on the same inventive concept, the embodiment of the application also provides a remote sensing image rapid resampling system. The implementation of the solution provided by the system is similar to the implementation described in the above method, so the specific limitation in the embodiments of the rapid resampling system for remote sensing image provided below may be referred to as the limitation of the method hereinabove, and will not be repeated herein.
In one exemplary embodiment, a remote sensing image rapid resampling system is provided, comprising:
The sampling point number determining module is used for determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
The array establishing module is used for establishing an array of a target grid for storing the data of the required sampling points; the size of the array is [ target raster image height ] [ target raster image width ] [ number of sampling points required by interpolation calculation ]; the last dimension of the array stores sampling points in different directions, and the sequence is fixed;
The assignment module is used for processing the remote sensing image sampling point data one by one and assigning each sampling point data to a surrounding target grid array;
A resampling module for: after all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
The various modules in the system described above may be implemented in whole or in part by software, hardware, and combinations thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
In one exemplary embodiment, a computer device is provided, which may be a terminal. As shown in fig. 8, the computer apparatus further includes a processor, a memory, an input/output interface, a communication interface, a display unit, and an input device. The processor, the memory and the input/output interface are connected through a system bus, and the communication interface, the display unit and the input device are connected to the system bus through the input/output interface. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The input/output interface of the computer device is used to exchange information between the processor and the external device. The communication interface of the computer device is used for carrying out wired or wireless communication with an external terminal, and the wireless mode can be realized through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. The computer program, when executed by the processor, implements the steps of the method for rapidly resampling remote sensing images. The display unit of the computer device is used for forming a visual picture, and can be a display screen, a projection device or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be a key, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by those skilled in the art that the structure shown in FIG. 8 is merely a block diagram of some of the structures associated with the present inventive arrangements and is not limiting of the computer device to which the present inventive arrangements may be applied, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
In one exemplary embodiment, a computer readable storage medium is provided, on which a computer program is stored, which when executed by a processor, implements the steps of a method for fast resampling of remote sensing images.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, database, or other medium used in embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical Memory, high density embedded nonvolatile Memory, resistive random access Memory (ReRAM), magneto-resistive random access Memory (Magnetoresistive Random Access Memory, MRAM), ferroelectric Memory (Ferroelectric Random Access Memory, FRAM), phase change Memory (PHASE CHANGE Memory, PCM), graphene Memory, and the like. Volatile memory can include random access memory (Random Access Memory, RAM) or external cache memory, and the like. By way of illustration, and not limitation, RAM can be in various forms such as static random access memory (Static Random Access Memory, SRAM) or dynamic random access memory (Dynamic Random Access Memory, DRAM), etc. The databases referred to in the embodiments provided herein may include at least one of a relational database and a non-relational database. The non-relational database may include, but is not limited to, a blockchain-based distributed database, and the like. The processor referred to in the embodiments provided in the present application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, or the like, but is not limited thereto.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. The rapid resampling method for the remote sensing image is characterized by comprising the following steps of:
Determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
establishing an array for storing the data of the required sampling points, wherein the size of the array is [ target raster image height ] [ target raster image width ] [ interpolation calculation required sampling point number ];
the rule for storing the sampling point data in the array is as follows:
Sequentially storing the data of sampling points of different orientations of the target grid point in the positions in the corresponding array from the nearest upper left position by taking the target grid point as the center according to the clockwise sequence;
processing the remote sensing image sampling point data one by one, and assigning each sampling point data to a surrounding target grid array;
After all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
2. The method for rapidly resampling a remote sensing image according to claim 1, wherein:
the set resampling interpolation algorithm is the nearest neighbor method, and array assignment is carried out by adopting the following modes:
Firstly judging whether the array in the target grid has a value or not, if not, directly assigning a value;
If the distance d1 between the sampling point and the target grid is judged, and if the distance d1 between the sampling point and the target grid is smaller than d2, the value is assigned.
3. The method for rapidly resampling a remote sensing image according to claim 1, wherein:
The set resampling interpolation algorithm is a bilinear interpolation algorithm, and array assignment is carried out in the following mode:
Sample point data with image coordinates (I, J) is formed by rounding down floorI, floorJ coordinate values, and ceilI and ceilJ are formed by rounding up coordinate values, so that the sample point data is assigned to the upper left point target grid array [ floorI ] [ floorJ ] [3], the upper right point target grid array [ floorI ] [ ceilJ ] [4], the lower left point target grid array [ ceilI ] [ floorJ ] [2] and the lower right point target grid array [ ceilI ] [ ceilJ ] [1].
4. The method for rapidly resampling a remote sensing image according to claim 1, wherein:
the set resampling interpolation algorithm is a bicubic interpolation algorithm, and array assignment is carried out in the following mode:
the sampling point assigns values to the surrounding 16 target grid point arrays, and assigns values of i and j to arrays [ floorI +i ] [ floorJ +j ] [ i ] 4+j ], respectively [ -1,0,1,2].
5. The method for rapidly resampling a remote sensing image according to claim 2, wherein the method for performing interpolation calculation to complete resampling is as follows:
f(P)＝f(S1)
Where f (P) is a pixel value interpolated from the target grid point P, and f (S 1) is an image pixel value at the sampling point S 1.
6. The method for rapidly resampling a remote sensing image according to claim 3, wherein the method for performing interpolation calculation to complete resampling is as follows:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y denote the coordinates of the target grid point P, x 1,x2,x3,x4 is the abscissa of the sampling point S 1,S2,S3,S4, R 1 is the interpolation point of S 1,S2 at P x, R 2 is the interpolation point of S 3,S4 at P x, and y 1,y2 is the ordinate of R 1,R2, respectively.
7. The method for rapidly resampling a remote sensing image according to claim 4, wherein the method for performing interpolation calculation to complete resampling is as follows:
Wherein f (P) is a pixel value obtained by interpolation of the target grid point P, and f (S 1) is an image pixel value of the sampling point S 1; x, y represents the coordinates of the target grid point P, x 1,y2 is S i of the sampling point S i, i takes values 1 to 16, and k is a kernel function of the bicubic interpolation algorithm.
8. A remote sensing image rapid resampling system, comprising:
The sampling point number determining module is used for determining the number of sampling points required by interpolation calculation according to a set resampling interpolation algorithm;
The array establishing module is used for establishing an array for storing the data of the required sampling points, and the size of the array is [ target raster image height ] [ target raster image width ] [ number of the sampling points required by interpolation calculation ];
the rule for storing the sampling point data in the array is as follows:
sequentially storing sampling point data of different orientations of the target grid point in positions in the corresponding array from the nearest upper left position by taking the target grid point as a center according to a clockwise sequence;
The assignment module is used for processing the remote sensing image sampling point data one by one and assigning each sampling point data to a surrounding target grid array;
A resampling module for: after all the sampling point data are assigned to the arrays in the target grid, checking whether all the arrays have values or not;
if the data in the array is missing, a distance weighting algorithm is used for processing;
If the data in the array is complete, carrying out interpolation calculation on the grid points one by one to finish resampling.
9. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method for fast resampling of remote sensing images of any of claims 1 to 4.
10. A computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor performs the steps of the remote sensing image fast resampling method of any of claims 1 to 4.
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| CN202410212918.6A Pending CN118071585A (en) | 2024-02-26 | 2024-02-26 | Rapid resampling method, system and device for remote sensing image and storage medium |
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