Three-dimensional elastic imaging method based on visual tactile sensor

Abstract

The invention discloses a three-dimensional elastic imaging method based on a visual tactile sensor, which belongs to the technical field of elastic imaging and comprises the following steps: system building and data processing, acquisition of contact deformation data acquired by the visual tactile sensor, forward simulation and inversion optimization. Calculating internal gradient information of a target object; deducing a derivative of a target function to Young modulus; calculating a partial derivative of resultant force to elastic distribution; calculating a gradient of the whole target function to Young modulus distribution; according to the method, the Young modulus distribution in the soft object can be accurately reconstructed under robot touch sampling, corresponding credibility indexes can be output, and the practicability is high.

Description

Technical Field

[0001] The present invention relates to the technical field of elastic imaging, and in particular to a three-dimensional elastic imaging method based on visual-tactile sensors, which is used to reconstruct the distribution of continuous Young's modulus inside an elastic body. Background Art

[0002] Elastography is an imaging method that reveals the elastic distribution within soft tissues and is widely used in medical diagnosis, non-destructive testing, and other fields. Existing elastography techniques primarily include mechanical imaging (MI), ultrasound elastography (USE), magnetic resonance elastography (MRE), and optical coherence elastography (OCE). These methods are typically modified from existing imaging technologies, such as ultrasound, magnetic resonance imaging, and optical coherence tomography, to measure elasticity in static or dynamic modes.

[0003] Despite varying imaging modalities, these methods generally incorporate three key components: a stimulus source, a sensor, and an inversion algorithm. While current methods have achieved some progress in accuracy and clinical applicability, they still face challenges such as expensive equipment, bulky size, and complex operation, making them unsuitable for elasticity assessment 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 the known material properties or location of the tumor and has limited applicability. Olson et al. (An inverse problem approach to stiffness mapping for early detection of breast cancer: tissue phantom experiments) built an automatic palpation system that can generate a binary stiffness map of the tumor 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 technical path for elastic imaging. Vision-based tactile sensors use cameras to observe the deformation of flexible surfaces after contact with objects, and have advantages such as high spatial resolution and rich information dimensions. Existing studies have used this type of sensor to estimate the height and viscosity of liquids or the hardness and texture of solids, which have been widely used in the fields of physical modeling and robotic manipulation. For example, Jia et al. (Lump detection with a gelsight sensor) used the Gelsight vision-based tactile sensor to observe the bulge above the lump to identify hard lumps, and proved that its sensitivity was better than that of human hands and traditional tactile devices. However, existing work mostly stays at the rough analysis level of the image, and fails to deeply construct the three-dimensional elastic distribution inside the soft body.

[0006] At the same time, robot-assisted palpation has also become a focus of attention in recent years. Related studies often use unidirectional pressing or sliding methods to obtain two-dimensional contact pressure maps through tactile arrays to identify abnormal tissue. With the development of machine learning, some methods have introduced neural networks to estimate lesion depth or perform classification and identification. However, these methods rely on large amounts of training data, and the results are often output in a classified form, making it difficult to accurately restore the morphology of the abnormal area and the distribution of continuous attributes.

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

[0008] To address the above issues, the present invention discloses a 3D elastic imaging method based on visual-tactile sensors. This method can accurately reconstruct the Young's modulus distribution inside soft objects under robot tactile sampling and output corresponding credibility indicators.

[0009] In order to achieve the above object, 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 construction and data processing, obtaining contact deformation data collected by sensors,

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

[0013] S2, forward simulation, builds a forward mechanical model of the target object based on the finite element method. The Newton-Raphson numerical iteration method can be used to obtain the deformation field of the object under the current elastic modulus setting;

[0014] S3, inversion optimization, constructs 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 back propagation algorithm optimization, obtains the gradient information of the Young's modulus distribution inside the target object, derives the derivative of the objective function with respect to the Young's modulus, calculates the partial derivative of the resultant force with respect to the elastic distribution through the chain rule according to the static equilibrium condition, and calculates the gradient of the overall objective function with respect to the Young's modulus distribution;

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

[0017] As a further improvement of the present invention, the sensor in step S1 is a visual-tactile sensor.

[0018] As a further improvement of the present invention, in step S2, the deformation field of the object under the current elastic modulus setting is set to u. Under the condition of the force and deformation distribution data of the target object surface, the static equilibrium equation of the object under the external force under the current elastic distribution is obtained through finite element forward simulation:

[0019]

[0020] 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.

[0021] As a further improvement of the present invention, in step S3, under the condition that the initial elastic guess value is given, the displacement field of the object under the external force under the current elastic distribution can be obtained by finite element forward simulation. Simulate deformation field and observed tactile deformation u o The simulated contact deformation is compared with the actual observed deformation collected by the visual tactile sensor, and a loss function reflecting the difference between the two is constructed. It represents the difference between the simulated deformation and the observed deformation and can be defined as the sum of the squares of the deformation errors during the contact process of frame t:

[0022]

[0023] As a further improvement of the present invention, in step S4, the chain rule is:

[0024]

[0025] According to the static equilibrium condition, the total differential of f with respect to e can be obtained:

[0026]

[0027]

[0028] Calculate the partial derivative of the resultant force with respect to the elastic distribution e, and obtain According to 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 in the three-dimensional geometric model, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated as follows:

[0029]

[0030] in and A (i) are the global stiffness matrix and the selection matrix of observation points in the i-th sampling respectively.

[0031] 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 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, the selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the stiffness change of each element. The calculation formula is:

[0032]

[0033] Where each element of M = [m i，j ], represents the sensitivity of the i-th surface node to the change of the Young's modulus of the j-th element, n c is the number of surface nodes, and the relative credibility index L(j) is defined to quantify the maximum impact of the stiffness change of each element on the surface deformation:

[0034]

[0035] 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 that the sensor contacts.

[0036] 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 it with a gradient inversion algorithm and a credibility analysis mechanism, it can achieve accurate identification of the internal mechanical properties of the target object, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The present invention shows an applicable experimental system device for the three-dimensional elastic imaging method based on visual tactile sensors;

[0038] Figure 2 Shows the use of Figure 1 Schematic diagram of the overall imaging process;

[0039] Figure 3 The figure shows the simulation results (model composed of two materials) obtained based on the imaging method of the present invention;

[0040] Figure 4 The figure shows the simulation results (non-uniform material model) obtained based on the imaging method of the present invention;

[0041] Figure 5 The objects of the three embodiments of the present invention are a silicone prosthesis containing a plastic block, a silicone prosthesis containing a cavity, and a palmar joint;

[0042] Figure 6 The imaging method of the present invention is used to obtain Figure 5 Comparison of the three-dimensional elastic modulus distribution diagram and ultrasound image of each embodiment. DETAILED DESCRIPTION

[0043] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0044] The three-dimensional elastic imaging method based on the visual-tactile sensor of the present invention comprises the following steps:

[0045] S1: System construction and data processing: acquiring contact deformation data collected by a visual-tactile sensor. Using a multi-degree-of-freedom robotic arm to perform a 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 then aligned with the posture transformation of the visual-tactile sensor to obtain the force and deformation distribution on the target object's surface.

[0046] S2, forward simulation, builds a forward mechanical model of the target object based on the finite element method. The Newton-Raphson numerical iteration method can be used to obtain the deformation field of the object under the current elastic modulus setting;

[0047] S3, inversion optimization, constructs a loss function to characterize the difference between the deformation of the simulated target object and the observed deformation;

[0048] S4, based on the gradient back propagation algorithm optimization, obtains the gradient information of the Young's modulus distribution inside the target object, derives the derivative of the objective function with respect to the Young's modulus, calculates the partial derivative of the resultant force with respect to the elastic distribution through the chain rule according to the static equilibrium condition, and calculates the gradient of the overall objective function with respect to the Young's modulus distribution;

[0049] S5 outputs the reconstructed Young's modulus distribution and quantitative credibility index. Through derivative calculation, the gradient matrix of the Young's modulus distribution to the surface displacement is obtained to represent the sensitivity of the material stiffness change to the surface deformation.

[0050] In step S2, the deformation field of the object under the current elastic modulus setting is set to u. Given the force and deformation distribution data of the target object surface, the static equilibrium equation of the object under the external force under the current elastic distribution is obtained through finite element forward simulation:

[0051]

[0052] 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.

[0053] In step S3, under the condition of the initial elastic guess value, the displacement field of the object under the external force under the current elastic distribution can be obtained through finite element forward simulation. Simulate deformation field and observed tactile deformation u o The simulated contact deformation is compared with the actual observed deformation collected by the tactile sensor, and a loss function reflecting the difference between the two is constructed. It represents the difference between the simulated deformation and the observed deformation and can be defined as the sum of the squares of the deformation errors during the contact process of frame t:

[0054]

[0055] In step S4, the chain rule is:

[0056]

[0057] According to the static equilibrium condition, the total differential of f with respect to e can be obtained:

[0058]

[0059] Calculate the partial derivative of the resultant force with respect to the elastic distribution e, and obtain According to 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 in the three-dimensional geometric model, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated as follows:

[0060]

[0061] in and A (i) are the global stiffness matrix and the selection matrix of observation points in the i-th sampling respectively.

[0062] In step S5, the relationship between the Young's modulus distribution and the displacement of each node on the surface is represented by the gradient matrix 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, the selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the stiffness change of each element. The calculation formula is:

[0063]

[0064] Where each element of M = [m i，j ], represents the sensitivity of the i-th surface node to the change of the Young's modulus of the j-th element, n c is the number of surface nodes, and the relative credibility index L(j) is defined to quantify the maximum impact of the stiffness change of each element on the surface deformation:

[0065]

[0066] 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 that the sensor contacts.

[0067] 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 it with a gradient inversion algorithm and a credibility analysis mechanism, it can achieve accurate identification of the internal mechanical properties of the target object, and has broad application prospects.

[0068] Figure 1It is an applicable experimental system device for the three-dimensional elastic imaging method based on visual tactile sensors in 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 adopts a physical model to estimate the stiffness distribution inside the skin and provide credibility analysis for the elastic imaging results.

[0069] Figure 2 It is the use of Figure 1 Schematic diagram of the overall imaging process. During the i-th sampling process, the node positions and displacements on the tactile surface are acquired by pressing, and the contact forces on the sensor and 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 external force.

[0070] Figure 3 These are simulation results obtained using the imaging method of the present invention. The top row shows the actual elastic distribution, and the bottom row shows the corresponding elastic imaging results. The figures show (a) a cube with a hard double-layer cake-like inclusion; (b) a cube with a hard ring-shaped inclusion; (c) a cube with a hard conical inclusion; (d) a cube with a softer conical inclusion; (e) a cylinder with holes and inclusions; (f) a hyperbolic solid with inclusions; and (g) a hemisphere with multiple distributed inclusions.

[0071] Figure 4 These are the simulation experiment results (non-uniform material model) obtained based on the imaging method of the present invention. The upper row shows the actual material distribution, and the lower row shows the corresponding elastic imaging results. (a, b) Non-homogeneous cube; (c) Non-homogeneous hemisphere.

[0072] Figure 5 The objects of the three embodiments of the present invention are respectively (a) a silicone prosthesis comprising a plastic block; (b) a silicone prosthesis comprising a cavity; (c) and a

[0073] Figure 6 The imaging method of the present invention is used to obtain Figure 5 Comparison of the three-dimensional elastic modulus distribution diagram and ultrasound image of each embodiment, respectively, (a) a silicone prosthesis containing a plastic block; (b) a silicone prosthesis containing a cavity; (c) and an in vivo palmar joint.

[0074] The present invention realizes elastic imaging of soft objects, silicone models containing inclusions, and in-vivo palm joint tissues in a simulation environment based on the three-dimensional elastic imaging technology of visual-tactile sensors, including simulation experiments, a robot visual-tactile three-dimensional elastic imaging sampling system, sampling data processing, and nonlinear optimization solution.

[0075] Simulation experiment:

[0076] In the simulation system, the present invention samples the Neo-Hookean hyperelastic material model to perform forward sampling on the simulation software. The algorithm of the present invention is verified to be effective on software composed of two materials (containing heterogeneous objects of different geometric shapes), software with uneven material distribution, and software with curved surface geometry. Figure 3 、 4 .

[0077] Robotic visual-tactile 3D elastic imaging sampling system:

[0078] The robotic visual-tactile three-dimensional elastic imaging sampling system is based on the multi-degree-of-freedom Franka Emika Panda robotic arm platform and is realized by installing a visual-tactile sensor (Finger, Conarobot) on the end effector. The sensor has 145 markers arranged inside the sensing area to detect contact force and surface deformation. The sampling frequency is 30Hz, which meets the requirements of experimental data acquisition. We constructed three different physical models to verify the tactile elastic imaging method proposed in this invention, including: a silicone model with hard embedded objects, a silicone model with spherical cavities, and a real human palm with unknown geometric structure, such as Figure 5 As shown in the figure, the diameter of the hard insert is 4 mm, and the cavity is formed by pulling out the embedded ball. The Young's modulus of the silicone material used is approximately 0.2 MPa, and the Young's modulus of the hard insert is approximately 2.5 GPa. To avoid the influence of viscosity, we sprinkled dry fine powder on the surface of the model.

[0079] The model was placed on a platform directly below the tactile sensor. The 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 completely within the sensor's sensing range. Furthermore, we rotated the model to obtain tactile data along the X- and Y-axes from different sides. During the experiment, the maximum pressing force was kept below 0.04 MPa to ensure sufficient deformation while avoiding damage to the model.

[0080] For the palm model, the hand is placed at rest under the sensor. Since the palm is larger than the soft layer of the sensor, we only collect tactile data during vertical pressing and reconstruct the elastic distribution under the contact area.

[0081] Data processing;

[0082] This method uses visual-tactile sensors to reconstruct the 3D surface deformation field. It employs a color-gradient mapping calibration method similar to the Gelsight structured sensor: a calibration sphere with a known radius (6 mm) is pressed against the sensor, and a hexagonal calibration block is used to determine the number of pixels per unit length. Following the method described in the paper (Gelsight wedge: Measuring high-resolution 3D contact geometry with a compact robot finger), this method uses interpolation to track the pixel changes around the marker point to obtain the distribution of deformation and force.

[0083] With the help of known device configuration, the present invention extracts the transformation matrix P from the sensor local coordinate system to the target object coordinate system. s , including the translation vector T s With the rotation matrix R s When the sensor moves linearly along the coordinate axis without rotation, the transformation is simplified to the translation vector d. At this time, the contact force f recorded by the sensor is s and deformation x s The above transformation can be mapped to the force and displacement on the target object, such as Figure 3 .

[0084] Since the node positions of the initial grid of the target object do not completely match the sensor markers, the present invention interpolates the displacement and force information on the vertices of the target object to make them the elastic reconstruction input.

[0085] In practice, the sensor's soft layer doesn't completely conform to the object's surface. Therefore, upon initial contact, valid tactile data is only present in certain node regions. For untouched points, the present invention sets the external force to zero, and estimates their deformation using the overall sensor transformation. To represent the target area, a virtual cube containing the object is constructed. Due to the lower bound constraint, the blank areas will appear as minimal stiffness values in the elastic reconstruction.

[0086] Nonlinear optimization solution:

[0087] The specific optimization steps of the present invention are as follows:

[0088] Initialization: Set the initial Young's modulus estimate e*, which is set to a uniform distribution based on empirical values;

[0089] Forward simulation: Based on the current Young's modulus distribution e, the finite element model is used to solve the object response displacement field in each frame.

[0090] Calculation error: Compare the simulated displacement with the observed displacement and construct the error loss function

[0091] Gradient back propagation: Calculated by the analytical expression of the gradient

[0092] Parameter update: Use the Adam optimizer in Python to update e;

[0093] Convergence judgment: If the error drops to the 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 credibility distribution vector corresponding to the estimated value at this time.

[0094] The three-dimensional elastic imaging method based on visual tactile sensors of the present invention has the following advantages:

[0095] Using high-spatial-resolution tactile sensors to collect temporal deformation field information on the surface of an object under external pressure, the spatial resolution of mechanical imaging is effectively improved, allowing even subtle elastic changes to be accurately captured and the continuous Young's modulus distribution within soft materials to be reconstructed.

[0096] By collecting visual and tactile deformation data and combining it with a gradient inversion algorithm and credibility analysis mechanism, the Young's modulus of the non-rigid region inside the object can be continuously reconstructed to obtain a detailed image of the elastic distribution in three-dimensional space, which is suitable for material identification of complex internal structures.

[0097] During the elastic reconstruction process, the present invention also synchronously calculates the credibility index of the estimated value of Young's modulus of each unit to reflect the reliability of the perception result. This index provides a quality reference for the elastic reconstruction result, helps guide the optimization of subsequent sampling strategies or perception strategies, and maximizes the accurate recognition of the internal mechanical properties of the target object.

[0098] In summary, the present 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, achieving more stable and reliable reconstruction performance. It is suitable for multiple scenarios such as medical diagnosis and industrial inspection, and can be used to identify abnormal elastic areas inside objects, such as lumps, defects, impurities, etc. It has important application potential 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 physics-driven finite element modeling, it has broad application prospects.

[0099] It should be noted that the above content merely illustrates the technical idea of the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A three-dimensional elastic imaging method based on visual tactile sensors, characterized in that: The method comprises the following steps: S1, system construction and data processing, obtaining contact deformation data collected by sensors, A multi-degree-of-freedom robotic arm is used to perform the pressing operation. The end effector is equipped with a sensor, which is used to reconstruct the three-dimensional surface deformation field of the target object. The deformation data is aligned with the sensor posture transformation to obtain the force and deformation distribution on the target object surface. S2, forward simulation, builds a forward mechanical model of the target object based on the finite element method. The Newton-Raphson numerical iteration method can be used to obtain the deformation field of the object under the current elastic modulus setting; S3, inversion optimization, constructs a loss function to characterize the difference between the deformation of the simulated target object and the observed deformation; S4, based on the gradient back propagation algorithm optimization, obtains the gradient information of the Young's modulus distribution inside the target object, derives the derivative of the objective function with respect to the Young's modulus, calculates the partial derivative of the resultant force with respect to the elastic distribution through the chain rule according to the static equilibrium condition, and calculates the gradient of the overall objective function with respect to the Young's modulus distribution; S5 outputs the reconstructed Young's modulus distribution and quantitative credibility index. Through derivative calculation, the gradient matrix of the Young's modulus distribution to the surface displacement is obtained to represent the sensitivity of the material stiffness change to the surface deformation.

2. The three-dimensional elastic imaging method based on visual tactile sensor according to claim 1, characterized in that: The sensor in step S1 is a visual-tactile sensor.

3. The three-dimensional elastic imaging method based on visual tactile sensor according to claim 2, characterized in that: In step S2, the deformation field of the object under the current elastic modulus setting is set to u. Given the force and deformation distribution data of the target object surface, the static equilibrium equation of the object under the external force under the current elastic distribution is obtained through finite element forward simulation: f(u;e,f o )=∫0K(u;e)du-A(uu′)-(m T girlfriend o )=0 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 elastic imaging method based on visual tactile sensor according to claim 3, characterized in that: In step S3, under the condition of the initial elastic guess value, the displacement field of the object under the external force under the current elastic distribution can be obtained through finite element forward simulation. Simulate deformation field and observed tactile deformation u o The simulated contact deformation is compared with the actual observed deformation collected by the visual tactile sensor, and a loss function reflecting the difference between the two is constructed. It represents the difference between the simulated deformation and the observed deformation and can be defined as the sum of the squares of the deformation errors during the contact process of frame t:

5. The three-dimensional elastic imaging method based on visual tactile sensor according to claim 4, characterized in that: In step S4, the chain rule is: According to the static equilibrium condition, the total differential of f with respect to e can be obtained: Calculate the partial derivative of the resultant force with respect to the elastic distribution e and get in According to 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 in the three-dimensional geometric model, and the gradient of the overall objective function with respect to the Young's modulus distribution is calculated as follows: in and A (i) are the global stiffness matrix and the selection matrix of observation points in the i-th sampling respectively.

6. The three-dimensional elastic imaging method based on visual tactile sensor according to claim 5, characterized in that: In step S5, the relationship between the Young's modulus distribution and the displacement of each node on the surface is represented by the gradient matrix 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, the selection matrix S is introduced to obtain the sensitivity matrix M of the surface nodes to the stiffness change of each element. The calculation formula is: Where each element of M = [m i，j ], represents the sensitivity of the i-th surface node to the change of the Young's modulus of the j-th element, n c is the number of surface nodes, and the relative credibility index L(j) is defined to quantify the maximum impact of the stiffness change of each element on the surface deformation: where L(j) represents the maximum effect of the change in Young’s modulus of the jth element on the surface deformation, and ns is the number of surface nodes contacted by the sensor.

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