Three-dimensional elastography method based on vision-based tactile sensor

Abstract

A three-dimensional elastography method based on a vision-based tactile sensor. The method comprises several steps, which respectively involve: performing system construction and data processing, and acquiring contact deformation data collected by a vision-based tactile sensor; performing forward simulation; performing inverse optimization; calculating gradient information inside a target object, deriving the derivative of an objective function with respect to Young's modulus, calculating the partial derivative of a resultant force with respect to an elasticity distribution, and calculating the overall gradient of the objective function with respect to Young's modulus distribution; and outputting a Young's modulus distribution obtained by means of reconstruction and outputting a quantization reliability index. The method can realize accurate reconstruction of a Young's modulus distribution inside soft objects under robotic tactile sampling, and can output a corresponding reliability index, thus having high levels of practicability.

Description

[Amended according to Rule 26, May 21, 2025] A three-dimensional elastic imaging method based on a visual-tactile sensor Technical Field

[0001] This invention relates to the field of elastic imaging technology, and in particular to a three-dimensional elastic imaging method based on a visual-tactile sensor for reconstructing the distribution of continuous Young's modulus within an elastic body. Background Technology

[0002] Elastography is an imaging method that displays the elastic distribution within soft tissues and is widely used in medical diagnostics, non-destructive testing, and other fields. Current elastography techniques mainly include Mechanical Imaging (MI), Ultrasound Elastography (USE), Magnetic Resonance Elastography (MRE), and Optical Coherence Elastography (OCE). These methods are typically based on modifications of existing imaging techniques, such as ultrasound imaging, magnetic resonance imaging, and optical coherence tomography, to achieve elasticity measurements in static or dynamic modes.

[0003] These methods, despite their varying imaging modalities, mostly comprise three key modules: a stimulus source, a sensor, and an inversion algorithm. While current methods have made some progress in terms of accuracy and clinical applicability, they still face challenges such as expensive equipment, large size, and complex operation, making them unsuitable for flexible assessment needs in robotic embedded or portable scenarios.

[0004] In addition, some studies have attempted to estimate elasticity solely through mechanical signals (such as surface deformation or force). For example, Sangpradit et al. (Finite-element modeling of soft tissue rolling indentation) proposed a tumor localization method based on finite element inversion, but this method requires knowledge of the tumor material properties or location, limiting its applicability. Olson et al. (An inverse problem approach to stiffness mapping for early detection of breast cancer: tissue phantom experiments) constructed an automated palpation system that can generate binary stiffness maps of masses using force sensors, but the equipment is bulky and has limited resolution.

[0005] On the other hand, the development of vision-based tactile sensors in recent years has provided a new technological path for elastic imaging. Vision-based tactile sensors observe the deformation of flexible surfaces after contact with objects using a camera, offering advantages such as high spatial resolution and rich information dimensions. Existing research has used these sensors to estimate properties such as the height and viscosity of liquids or the hardness and texture of solids, finding wide application in physical modeling and robot manipulation. For example, Jia et al. (Lump detection with a gelsight sensor) used the Gelsight vision-tactile sensor to observe the protrusion above a mass to identify hard lumps, demonstrating its sensitivity superior to the human hand and traditional tactile devices. However, current work largely remains at the image-level, coarse analysis level, failing to deeply construct the three-dimensional elastic distribution within the soft material.

[0006] Meanwhile, robot-assisted palpation has also become a focus of attention in recent years. Related research often employs unidirectional pressing or sliding methods, using tactile arrays to acquire two-dimensional contact pressure maps to identify abnormal tissue. With the development of machine learning, some methods have incorporated neural networks to estimate lesion depth or perform classification. However, these methods rely on large amounts of training data, and the results are often output in a classification format, making it difficult to accurately reconstruct the morphology and continuous attribute distribution of abnormal areas.

[0007] In summary, existing technologies lack an elastic imaging method that combines visual and tactile information, possesses high spatial resolution, and can reconstruct the continuous elastic distribution inside soft objects. In particular, there is still a gap in the application of this method in the context of not requiring large-scale training data and being suitable for actual robot operation. Summary of the Invention

[0008] To address the aforementioned problems, this invention discloses a three-dimensional elastic imaging method based on a visual-tactile sensor. It enables accurate reconstruction of the Young's modulus distribution within soft objects using robotic tactile sampling and can output corresponding reliability indicators.

[0009] To achieve the above objectives, the technical solution of the present invention is as follows:

[0010] A three-dimensional elastic imaging method based on a visual-tactile sensor, the method comprising the following steps:

[0011] S1, System setup and data processing: acquiring contact deformation data collected by visual-tactile sensors.

[0012] A multi-degree-of-freedom robotic arm is used to perform the pressing operation. The end effector is equipped with a visual-tactile sensor. The visual-tactile sensor is used to reconstruct the three-dimensional surface deformation field of the target object. The deformation data is registered with the posture transformation of the visual-tactile sensor to obtain the force and deformation distribution on the surface of the target object.

[0013] S2, forward simulation, establishes a forward mechanical model of the target object based on the finite element method, and obtains the deformation field of the object under the force under the current elastic modulus setting through the Newton-Raphson numerical iteration method;

[0014] S3, Inversion optimization: Construct a loss function to characterize the difference between the deformation of the simulated target object and the observed deformation;

[0015] S4. Based on the gradient backpropagation algorithm, the gradient information of the Young's modulus distribution inside the target object is obtained. The derivative of the objective function with respect to the Young's modulus is derived. By using the chain rule and according to the static equilibrium condition, the partial derivative of the resultant force with respect to the elastic distribution is calculated, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated.

[0016] S5 outputs the reconstructed Young's modulus distribution and quantification reliability index. Through derivative calculation, the gradient matrix of Young's modulus distribution with respect to surface displacement is obtained, which is used to represent the sensitivity of material stiffness change to surface deformation.

[0017] As a further improvement of the present invention, in step S2, the deformation field of the object under the force is set to u under the current elastic modulus setting. Given the force and deformation distribution data on the surface of the target object, the static equilibrium equation of the object under the action of external force under the current elastic distribution is obtained through finite element forward simulation:

[0018] Where K(u;e) is the global stiffness matrix, f o is the external force vector, and m is the mass matrix of the object, obtained through the Newton-Raphson numerical iteration method.

[0019] As a further improvement of the present invention, in step S3, given the initial elasticity prediction value, the displacement field of the object under the action of external force under the current elasticity distribution can be obtained through finite element forward simulation. Simulate deformation field With observation of tactile deformation u o To ensure consistency, the simulated contact deformation is compared with the observed deformation actually collected by the tactile sensor, and a loss function reflecting the difference between the two is constructed. The difference between simulated deformation and observed deformation can be defined as the sum of squares of the deformation errors during the contact process in frame t:

[0020] As a further improvement of the present invention, in step S4, the chain rule is as follows:

[0021] According to the static equilibrium condition, the total differential of f with respect to e yields:

[0022] Calculate the partial derivative of the resultant force with respect to the elastic distribution e, and obtain...

[0023] in From the static calculation formula, we get a1 = [1, 0, ..., 0], ..., a j = [0, ..., 1, ..., 0], j = 1, ..., m is a set of orthogonal basis vectors, m is the number of elements in the 3D geometric model, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated as follows:

[0024] in and A (i) These are the global stiffness matrix and the observation point selection matrix in the i-th sampling, respectively.

[0025] As a further improvement of the present invention, in step S5, the relationship between the Young's modulus distribution and the displacement of each node on the surface is represented by a gradient matrix. Here, the (i,j) element of the matrix represents the displacement change of node i under a small change in the Young's modulus of element j. Focusing on the deformation of each node on the observable surface, a selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the stiffness changes of each element. The calculation formula is as follows:

[0026] Where each element of M is M = [m i,j ] represents the sensitivity of the i-th surface node to the change in the Young's modulus of the j-th element, n c This refers to the number of surface nodes. A relative reliability index L(j) is defined to quantify the maximum impact of stiffness changes of each element on surface deformation.

[0027] Where L(j) represents the maximum effect of the change in Young's modulus of the j-th element on surface deformation, n s It is the number of surface nodes that the sensor contacts.

[0028] The three-dimensional elastic imaging method based on visual-tactile sensors of the present invention can reconstruct the continuous Young's modulus distribution inside soft materials. By collecting visual-tactile deformation data and combining gradient inversion algorithm and credibility analysis mechanism, it can accurately identify the internal mechanical properties of target objects and has broad application prospects. Attached Figure Description

[0029] Figure 1 shows the applicable experimental system apparatus for the three-dimensional elastic imaging method based on visual-tactile sensors of the present invention;

[0030] Figure 2 shows a schematic diagram of the overall imaging process using Figure 1;

[0031] Figure 3 shows the simulation results (model composed of two materials) obtained based on the imaging method of the present invention;

[0032] Figure 4 shows the simulation results (non-uniform material model) obtained based on the imaging method of the present invention;

[0033] Figure 5 shows three embodiments of the present invention: a silicone prosthesis containing a plastic block, a silicone prosthesis containing a cavity, and a hand joint.

[0034] Figure 6 is a comparison of the three-dimensional elastic modulus distribution map and ultrasound image of each embodiment in Figure 5 obtained using the imaging method of the present invention. Detailed Implementation

[0035] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0036] The three-dimensional elastic imaging method based on a visual-tactile sensor of the present invention includes the following steps:

[0037] S1, System setup and data processing: acquiring contact deformation data collected by visual-tactile sensors.

[0038] A multi-degree-of-freedom robotic arm is used to perform the pressing operation. The end effector is equipped with a visual-tactile sensor. The visual-tactile sensor is used to reconstruct the three-dimensional surface deformation field of the target object. The deformation data is registered with the posture transformation of the visual-tactile sensor to obtain the force and deformation distribution on the surface of the target object.

[0039] S2, forward simulation, establishes a forward mechanical model of the target object based on the finite element method, and obtains the deformation field of the object under the force under the current elastic modulus setting through the Newton-Raphson numerical iteration method;

[0040] S3, Inversion optimization: Construct a loss function to characterize the difference between the deformation of the simulated target object and the observed deformation;

[0041] S4. Based on the gradient backpropagation algorithm, the gradient information of the Young's modulus distribution inside the target object is obtained. The derivative of the objective function with respect to the Young's modulus is derived. By using the chain rule and according to the static equilibrium condition, the partial derivative of the resultant force with respect to the elastic distribution is calculated, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated.

[0042] S5 outputs the reconstructed Young's modulus distribution and quantification reliability index. Through derivative calculation, the gradient matrix of Young's modulus distribution with respect to surface displacement is obtained, which is used to represent the sensitivity of material stiffness change to surface deformation.

[0043] In step S2, under the current elastic modulus setting, the deformation field of the object under force is set to u. Given the force and deformation distribution data on the surface of the target object, the static equilibrium equation of the object under the current elastic distribution is obtained through finite element forward simulation:

[0044] Where K(u;e) is the global stiffness matrix, f o is the external force vector, and m is the mass matrix of the object, obtained through the Newton-Raphson numerical iteration method.

[0045] In step S3, given the initial elasticity estimate, the displacement field of the object under the current elasticity distribution and the action of external forces can be obtained through finite element forward simulation. Simulate deformation field With observation of tactile deformation u o To ensure consistency, the simulated contact deformation is compared with the observed deformation actually collected by the tactile sensor, and a loss function reflecting the difference between the two is constructed. The difference between simulated deformation and observed deformation can be defined as the sum of squares of the deformation errors during the contact process in frame t:

[0046] In step S4, the chain rule is as follows:

[0047] According to the static equilibrium condition, the total differential of f with respect to e yields:

[0048] Calculate the partial derivative of the resultant force with respect to the elastic distribution e, and obtain...

[0049] in From the static calculation formula, we get a1=[1,0,..,0],...,a j =[0,..1,...,0],j=1,...,m is a set of orthogonal basis vectors, where m is the number of elements in the 3D geometric model. The gradient of the overall objective function with respect to the Young's modulus distribution is calculated as follows:

[0050] in and A (i) These are the global stiffness matrix and the observation point selection matrix in the i-th sampling, respectively.

[0051] In step S5, the relationship between the Young's modulus distribution and the displacements of each node on the surface is represented by a gradient matrix. Here, the (i,j) element of the matrix represents the displacement change of node i under a small change in the Young's modulus of element j. Focusing on the deformation of each node on the observable surface, a selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the stiffness changes of each element. The calculation formula is as follows:

[0052] Where each element of M is M = [m i,j ] represents the sensitivity of the i-th surface node to the change in the Young's modulus of the j-th element, n c This refers to the number of surface nodes. A relative reliability index L(j) is defined to quantify the maximum impact of stiffness changes of each element on surface deformation.

[0053] Where L(j) represents the maximum effect of the change in Young's modulus of the j-th element on surface deformation, n s It is the number of surface nodes that the sensor contacts.

[0054] The three-dimensional elastic imaging method based on visual-tactile sensors of the present invention can reconstruct the continuous Young's modulus distribution inside soft materials. By collecting visual-tactile deformation data and combining gradient inversion algorithm and credibility analysis mechanism, it can accurately identify the internal mechanical properties of target objects and has broad application prospects.

[0055] Figure 1 shows the applicable experimental system device for the three-dimensional elastic imaging method based on visual-tactile sensors of the present invention. The proposed robot-assisted tactile elastic imaging method uses tactile information to image the invisible three-dimensional internal elastic distribution. This busy imaging method uses a physical model to estimate the stiffness distribution inside the skin and provides a reliability analysis for the elastic imaging results.

[0056] Figure 2 is a schematic diagram of the overall imaging process using Figure 1. During the i-th sampling process, the node positions and displacements on the tactile surface are acquired by pressing, and the contact force on the sensor and the contact force on the target object are calculated through forward simulation. In the optimization module, the appropriate elastic distribution is identified by minimizing the difference between the predicted deformation and the observed displacement of the target object under the action of external force.

[0057] Figure 3 shows the simulation results obtained based on the imaging method of this invention. The top row shows the actual elastic distribution, and the bottom row shows the corresponding elastic imaging results. In the figure, (a) is a cube with hard double-layer cake-like inclusions; (b) is a cube with hard annular inclusions; (c) is a cube with hard conical inclusions; (d) is a cube with softer conical inclusions; (e) is a cylinder with holes and inclusions; (f) is a hyperboloid with inclusions; and (g) is a hemisphere with multiple distributed inclusions.

[0058] Figure 4 shows the simulation results (non-uniform material model) obtained based on the imaging method of this invention. The top row shows the actual material distribution, and the bottom row shows the corresponding elastic imaging results. (a, b) Non-uniform cube; (c) Non-uniform hemisphere.

[0059] Figure 5 shows three embodiments of the present invention: (a) a silicone prosthesis containing a plastic block; (b) a silicone prosthesis containing a cavity; and (c) an in vivo hand joint.

[0060] Figure 6 is a comparison of the three-dimensional elastic modulus distribution map and ultrasound image of the various embodiments in Figure 5 obtained by the imaging method of the present invention, respectively (a) a silicone prosthesis containing a plastic block; (b) a silicone prosthesis containing a cavity; and (c) an in vivo hand joint.

[0061] This invention utilizes three-dimensional elastic imaging technology based on visual-tactile sensors to achieve elastic imaging of soft materials, silicone models containing inclusions, and in vivo hand joint tissues in a simulated environment. The process includes simulation experiments, a robot visual-tactile three-dimensional elastic imaging sampling system, sampling data processing, and nonlinear optimization solutions.

[0062] 1. Simulation Experiment:

[0063] In the simulation system, the Neo-Hookean hyperelastic material model of this invention is used to perform forward sampling on the simulation software. The implementation effect of the algorithm of this invention on software composed of two materials (containing heterogeneous materials with different geometric shapes), software with non-uniform material distribution, and software with curved surface geometry is verified, as shown in Figures 3 and 4.

[0064] 2. Robotic Vision-Tactile 3D Elastic Imaging Sampling System:

[0065] The robotic tactile three-dimensional elastography sampling system is based on the multi-degree-of-freedom Franka Emika Panda robotic arm platform, implemented by mounting a tactile sensor (Finger, Conarobot) on the end effector. This sensor has 145 marker points arranged within the sensing area to detect contact force and surface deformation, with a sampling frequency of 30Hz, meeting the requirements for experimental data acquisition. We constructed three different physical models to verify the tactile elastography method proposed in this invention: a silicone model with a rigid inlay, a silicone model with a spherical cavity, and a human hand with unknown geometry, as shown in Figure 5. The rigid inlay has a diameter of 4mm, and the cavity is formed by removing the inlay sphere. The Young's modulus of the silicone material used is approximately 0.2MPa, and the Young's modulus of the rigid inlay is approximately 2.5GPa. To avoid the influence of adhesion, we sprinkled dry fine powder on the model surface.

[0066] The model was placed on a platform directly below the tactile sensor. A robotic arm controlled the tactile sensor to press the model along the Z-axis of the global coordinate system, ensuring that the contact area fell entirely within the sensor's sensing range. Furthermore, we rotated the model to acquire tactile data along the X and Y axes from different sides. During the experiment, the maximum pressing force was controlled below 0.04 MPa to ensure sufficient deformation while avoiding damage to the model.

[0067] For the hand model, the hand is placed under the sensor. Since the hand is larger than the soft layer of the sensor, we only collect tactile data during the vertical pressing process and reconstruct the elastic distribution under the contact area.

[0068] 3. Data Processing

[0069] This invention uses a visual-tactile sensor to reconstruct a three-dimensional surface deformation field, employing a color-gradient mapping calibration method similar to that of the Gelsight structural sensor: a calibration sphere of known radius (6 mm) is pressed onto the sensor, and a hexagonal calibration block is used to determine the number of pixels per unit length. Following the method described in the reference (Gelsight wedge: Measuring high-resolution 3D contact geometry with a compact robot finger), this invention tracks pixel changes around the marked point using interpolation to obtain the distribution of deformation and force.

[0070] Using known equipment configurations, this invention extracts the transformation matrix P from the sensor's local coordinate system to the target object's coordinate system. s Including translation vector T s With rotation matrix R sWhen the sensor moves linearly along the coordinate axes without rotation, the transformation simplifies to a translation vector d. At this time, the sensor records the contact force f. s and deformation x s The above transformation can be mapped to the forces and displacements on the target object, as shown in Figure 3.

[0071] Since the node positions of the initial mesh of the target object do not perfectly match the sensor marker points, this invention performs interpolation processing on the displacement and force information at the vertices of the target object to make it an input for elastic reconstruction.

[0072] In practice, the soft surface of the sensor does not completely adhere to the object's surface. Therefore, upon initial contact, only some nodal areas possess valid tactile data. For points not in contact, this invention sets the external force to zero, and their deformation is estimated by the overall sensor transformation. To represent the target area, a virtual cube region containing the object is constructed, where blank areas, due to the existence of lower bound constraints, will exhibit minimal stiffness values ​​in elastic reconstruction.

[0073] 4. Nonlinear optimization solution:

[0074] The specific optimization steps of this invention are as follows:

[0075] ●Initialization: Set the initial Young's modulus estimate e*, which is set to a uniform distribution based on empirical values;

[0076] ● Forward Simulation: Based on the current Young's modulus distribution e, the object's response displacement field in each frame is solved using a finite element model.

[0077] ●Calculation error: Compare simulated displacement with observed displacement to construct an error loss function.

[0078] ● Gradient backpropagation: Calculated analytically using the gradient.

[0079] ●Parameter update: e is updated using the Adam optimizer in Python;

[0080] ●Convergence criterion: If the error decreases to a preset threshold, or the update step size is less than the set tolerance, the optimization is terminated and the final estimate is output. And the confidence distribution vector corresponding to the estimated value at this time.

[0081] The three-dimensional elastic imaging method based on a visual-tactile sensor of the present invention has the following advantages:

[0082] By utilizing a high spatial resolution tactile sensor, the temporal deformation field information of the object surface under external pressure is collected, which effectively improves the spatial resolution of mechanical imaging, enabling even subtle elastic changes to be accurately captured and the continuous Young's modulus distribution inside soft materials to be reconstructed.

[0083] By collecting visual and tactile deformation data and combining gradient inversion algorithm and credibility analysis mechanism, the Young's modulus of non-rigid regions inside an object can be continuously reconstructed, thereby obtaining a detailed image of elastic distribution in three-dimensional space, which is suitable for material identification of complex internal structures.

[0084] During the elastic reconstruction process, the present invention also simultaneously calculates the reliability index of the Young's modulus estimate of each unit, reflecting the reliability of the sensing results. This index provides a quality reference for the elastic reconstruction results, which helps to guide the optimization of subsequent sampling strategies or sensing strategies, and maximizes the accurate identification of the internal mechanical properties of the target object.

[0085] In summary, this invention constructs a complete modeling-optimization framework from tactile signals to internal elasticity estimation, breaking through the accuracy and interpretability bottlenecks of traditional empirical model-based methods. It achieves more stable and reliable reconstruction performance, applicable to multiple scenarios such as medical diagnosis and industrial inspection. It can be used to identify abnormal elastic regions inside objects, such as lumps, defects, and impurities, and has significant potential applications in medical palpation-assisted diagnosis and non-destructive testing of industrial materials. It is particularly suitable for elastic imaging and analysis of complex soft tissues or structures under robot assistance. By introducing physically driven finite element modeling, its application prospects are broad.

[0086] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A three-dimensional elastography method based on a visiotactile sensor, characterized by, The method comprises the following steps: S1, system building and data processing, obtaining the contact deformation data collected by the sensor, A multi-degree-of-freedom mechanical arm is used to perform pressing operation, a sensor is installed on the end effector, the three-dimensional surface deformation field of the target object is reconstructed using the sensor, the deformation data is registered with the sensor posture transformation, and the stress and deformation distribution of the surface of the target object is obtained; S2, forward simulation, a forward mechanical model of the target object is established based on the finite element method, and the deformation field of the object under stress can be obtained under the current elastic modulus setting through the Newton-Raphson numerical iteration method; S3, inversion optimization, a loss function is constructed to represent the difference between the simulated deformation of the target object and the observed deformation; S4, the Young's modulus distribution gradient information inside the target object is obtained based on the gradient back propagation algorithm optimization, the derivative of the objective function to the Young's modulus is derived, the partial derivative of the total force to the elastic distribution is calculated through the chain rule according to the static equilibrium condition, and the gradient of the overall objective function to the Young's modulus distribution is calculated; S5, output the reconstructed Young's modulus distribution and the quantitative reliability index, the gradient matrix of the Young's modulus distribution to the surface displacement is obtained through derivative calculation, and is used to represent the sensitivity of the material stiffness change to the surface deformation.

2. The three-dimensional elastography method based on the tactile vision sensor according to claim 1, wherein, The sensor in the S1 step is a visual tactile sensor.

3. The three-dimensional elastography method based on the tactile sensor according to claim 2, wherein, In the S2 step, the deformation field of the object under force is set as u under the current elastic modulus setting, and the static force balance equation of the object under the current elastic distribution under the action of external force is obtained through finite element forward simulation under the condition of the given target object surface force and deformation distribution data: Where K(u; e) is the global stiffness matrix, f o is the external force vector, and m is the mass matrix of the object, which is obtained by the Newton-Raphson numerical iteration method.

4. The three-dimensional elastography method based on tactile sensor according to claim 3, wherein, In step S3, the displacement field of the object under the current elastic distribution under the action of external force can be obtained by finite element forward simulation under the condition of the initial elastic guess value The simulation deformation field is consistent with the observed haptic deformation u o The simulated contact deformation is compared with the observed deformation actually collected by the visual haptic sensor, and a loss function reflecting the difference between the two is constructed The difference between the simulation deformation and the observed deformation can be defined as the sum of the squares of the deformation errors in the t frame contact process:

5. The three-dimensional elastography method based on tactile sensor according to claim 4, wherein, In step S4, the chain rule is: According to the static equilibrium condition, the total differential of f with respect to e is obtained: The partial derivative of the resultant force with respect to the elastic distribution e is calculated, resulting in wherein From the static calculation formula, a1 = [1, 0,.., 0],..., a j = [0,..1,..., 0], j = 1,..., m is a set of orthogonal basis vectors, m is the number of elements of the three-dimensional geometric model, and the gradient of the overall objective function to the Young's modulus distribution is calculated as follows: wherein and A (i) K and A are the global stiffness matrix and the selection matrix of the observation point in the i-th sampling, respectively.

6. The three-dimensional elastography method based on the tactile sensor according to claim 5, wherein, In step S5, the relationship between the Young's modulus distribution and the displacement of each node on the surface is represented by a gradient matrix where the (i,j) element of the matrix represents the change in displacement of the i-th node under a small change in the Young's modulus of the j-th element, focusing on the deformation of each node on the observable surface, a selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the change in the stiffness of each element, and the calculation formula is: where each element of M = [m i，j ], represents the sensitivity of the ith surface node to the change in Young's modulus of the jth element, n c is the number of surface nodes, and the relative confidence index L(j) is defined as: where L(j) represents the maximum effect of the change in Young's modulus of the jth element on the surface deformation, n s is the number of surface nodes in contact with the sensor.

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