CN118570273A - A monocular depth estimation method based on surface normal vector and neural radiance field - Google Patents

Abstract

The present invention discloses a monocular depth estimation method based on surface normal vectors and neural radiation fields, so as to solve the problems that the depth estimation method based on deep learning in the prior art has ambiguity and cannot handle occlusion and low-texture areas. The monocular depth estimation method of the present invention includes: 1. Acquiring a depth prior map based on surface normal vectors and a depth estimation model; 2. Guiding neural radiation field training based on depth prior; 3. Rendering an accurate depth map based on neural radiation field and Gaussian filtering. The method based on surface normal vectors adds geometric constraints to the projection points, effectively alleviating the ambiguity problem in monocular depth estimation. The monocular depth estimation method based on neural radiation fields does not rely on the estimated correspondence and cross-view reprojection depth for optimization, but directly optimizes the volume. Through the good view synthesis effect of the neural radiation field, problems such as occlusion and highlights in monocular depth estimation can be effectively solved.

Description

A monocular depth estimation method based on surface normal vector and neural radiance field

Technical Field

The present invention belongs to the field of computer vision, and in particular relates to a monocular depth estimation method based on surface normal vectors and neural radiation fields.

Background Art

In recent years, more and more autonomous driving industries have adopted pure visual perception solutions. Depth information represents the three-dimensional structure of the scene, which is important for understanding the geometric relationship of objects in the scene. It has been widely used in fields such as three-dimensional reconstruction, autonomous driving, and face recognition. The goal of depth estimation is to obtain the distance to the object and ultimately obtain a depth map, which provides depth information for a series of tasks (such as 3D reconstruction, SLAM, and decision-making). The mainstream distance measurement methods on the market are monocular, stereo, and based on RGB-D cameras.

Existing monocular depth estimation methods usually adopt a cost volume-based architecture to solve the multi-view stereo problem. However, due to the lack of reasoning constraints, the predicted depth maps across views are usually inconsistent and often violate photometric consistency. The current mainstream monocular depth estimation network obtains learning-based priors from single image depth estimation for optimization to generate accurate and consistent depth maps. However, existing methods lack solutions to the problem of insufficient features in low-texture areas in specific problems, and it is difficult to deal with the problem of depth ambiguity in the absence of global information. At the same time, since monocular images are two-dimensional images, multiple three-dimensional spatial points are often obtained during projection, which makes the monocular depth estimation task ambiguous. Therefore, a monocular depth estimation method based on surface normal vectors and neural radiation fields is needed to improve the accuracy of the original monocular depth estimation method.

The surface normal vector-based method adds geometric constraints to the projection points, effectively alleviating the ambiguity problem in monocular depth estimation. The monocular depth estimation method based on neural radiance field does not rely on the estimated correspondence and cross-view reprojection depth for optimization, but directly optimizes the volume. The good view synthesis effect of neural radiance field can effectively solve the problems of occlusion and highlight in monocular depth estimation.

Summary of the invention

The purpose of the present invention is to provide a monocular depth estimation method based on surface normal vector and neural radiation field, so as to solve the problems of ambiguity, occlusion and highlight that appear in the monocular depth estimation of the prior art.

The technical solution of the present invention is as follows:

The present invention first provides a monocular depth estimation method based on surface normal vector and neural radiation field, comprising the following steps:

1) Construct an initial surface normal vector and depth estimation model, and use an image dataset with depth labels for training to obtain a trained surface normal vector and depth estimation model;

2) Input the image set to be processed captured by the monocular camera in a multi-view scene into the trained surface normal vector and depth estimation model to obtain a depth prior atlas;

3) The image set to be processed captured by the monocular camera is input into the neural radiation field, and the neural radiation field is guided to perform three-dimensional reconstruction of the image set to be processed based on the depth prior atlas obtained in step 2), so as to obtain a rendered depth image set;

4) Use Gaussian filtering to filter and optimize the rendered depth image set, and finally obtain the optimized depth image set as the monocular depth estimation result.

As a preferred solution of the present invention, the surface normal vector and depth estimation model includes a depth estimation module, a surface normal vector estimation module and a geometric consistency optimization module; the depth estimation module is used to extract depth features in the input image and output a predicted depth map; the surface normal vector estimation module is used to extract a multi-scale feature map in the input image and output a surface normal vector; the geometric consistency optimization module is used to predict the depth in the depth map according to the multi-scale feature map constraints and change along the direction of the surface normal vector to finally obtain a depth prior map.

As a preferred solution of the present invention, the image set to be processed is input into the neural radiation field, and the neural radiation field is guided by the depth prior atlas obtained in step 2) to perform three-dimensional reconstruction on the image set to be processed, including the following steps:

3.1) Project the depth prior atlas obtained in step 2) into three-dimensional space according to the depth information, transform and project a depth prior map in the depth prior atlas to other camera perspectives and compare it with the depth information of other camera perspectives, so as to obtain the error map corresponding to the depth prior map at each perspective, and traverse all the depth prior maps in the depth prior atlas;

3.2) Determine the range of neural radiation field sampling based on the error map;

3.3) Within the determined neural radiation field sampling range, the image set to be processed is three-dimensionally reconstructed to obtain a rendered depth image set.

The present invention also provides a monocular depth estimation system based on surface normal vector and neural radiation field, comprising:

The model building module is used to build the initial surface normal vector and depth estimation model, and use the image dataset with depth labels for training to obtain the trained surface normal vector and depth estimation model;

A depth prior map acquisition module is used to input the image set to be processed into the trained surface normal vector and depth estimation model to obtain a depth prior map set;

A three-dimensional reconstruction module is used to input the image set to be processed into the neural radiation field, and guide the neural radiation field to perform three-dimensional reconstruction on the processed image set based on the depth prior atlas obtained by the depth prior map acquisition module to obtain a rendered depth image set;

The Gaussian filter module is used to use Gaussian filtering to filter and optimize the rendered depth image set, and finally obtain the optimized depth image set as the monocular depth estimation result.

The present invention further provides a terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned monocular depth estimation method based on surface normal vectors and neural radiation fields when executing the computer program.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention uses surface normal vectors as auxiliary information for depth estimation, thus overcoming the inaccuracy problem of monocular depth estimation in texture-poor areas in the prior art. Existing methods often have difficulty in providing reliable depth information on surfaces lacking obvious textures, while surface normal vectors provide additional geometric constraints, enabling the model to better understand the scene structure, thereby improving the accuracy of depth estimation in these areas.

The present invention adopts the volume rendering technology of neural radiation field, thus overcoming the accuracy problem of monocular depth estimation in textureless or low-texture areas in the prior art. Neural radiation field can synthesize images from different perspectives and provide depth information even in texture-poor areas, thereby improving the comprehensiveness and accuracy of depth estimation.

The present invention combines the scene representation of neural radiance fields with depth prior knowledge, thus improving the robustness of depth estimation in dynamic scenes and occlusion. By leveraging the scene representation capabilities of neural radiance fields, the model can better understand and predict occlusion relationships, and provide reliable depth information even in complex scenes with dynamic objects or occlusions.

The present invention uses the weighted visual weight of the Gaussian filter for optimization, thereby solving the technical problem of edge blur in depth estimation. By adjusting the parameters of the Gaussian filter, especially the standard deviation, unnecessary noise can be removed while maintaining edge clarity, thereby improving the accuracy of the depth map at the object boundary.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a diagram showing the process of obtaining depth prior based on surface normal vector and depth estimation model;

Figure 2 is a flowchart of neural radiation field training;

Figure 3 is a flowchart of neural radiation field rendering;

FIG4 is a diagram of a monocular depth estimation method based on surface normal vectors and neural radiation fields;

Figure 5 is a flowchart of monocular depth estimation based on surface normal vectors and neural radiation fields.

DETAILED DESCRIPTION

The present invention is further described and illustrated below in conjunction with specific embodiments. The embodiments are merely exemplary of the present disclosure and do not define the scope of limitation. The technical features of each embodiment of the present invention may be combined accordingly without conflicting with each other.

As shown in Figures 4 and 5, the present invention provides a monocular depth estimation method based on surface normal vectors and neural radiation fields to solve the problem that the depth estimation method based on deep learning in the prior art has ambiguity and cannot handle occlusion and low-texture areas. Specifically, it includes:

1) Obtaining depth prior based on surface normal vector and depth estimation model; the depth map generated by the existing depth estimation method may be discontinuous or broken, while the surface normal vector provides the direction information of the pixel point in three-dimensional space. This geometric information is integrated into the depth estimation process as a hard constraint, which helps the model to make more reasonable depth inference in areas lacking texture or occlusion. By enforcing the consistency between the depth map and the normal vector field, the model can reduce the ambiguity caused by illumination changes or material similarity and improve the geometric accuracy of the depth map. At the boundaries and corners of objects, the depth changes are particularly drastic, and the surface normal vector provides rich shape information in such areas. Combined with this information, the model can better define the boundaries of objects and generate clearer and more accurate edges. The monocular depth estimation model combined with the surface normal vector not only enhances the accuracy and robustness of depth estimation, but also broadens its application scope in a variety of complex scenes. It is a key link in promoting the advancement of three-dimensional vision technology. The image set to be processed captured by the monocular camera in a multi-view scene is input into the trained surface normal vector and depth estimation model to obtain a depth prior atlas.

As shown in Figure 1, the process of obtaining a depth prior map based on the surface normal vector and the depth estimation model is as follows:

1.1) Depth and surface normal estimation; First, the depth estimation model is used as a feature extractor. The image to be processed captured by the input monocular camera in a multi-view scene is subjected to a series of depth-separable convolutions and point convolutions to gradually reduce the spatial resolution, increase the number of channels, and extract high-level semantic features. At the end of the encoder, multiple bottleneck layers are used to further compress the features and reduce the computational burden. The decoder part is responsible for upsampling the encoded features and restoring them to the original image size while gradually increasing the details. This part is implemented by combining upsampling, skip connections with the features of the encoder, and using convolutional layers. Skip connections help preserve local details and improve the accuracy of reconstruction. Finally, the decoder outputs a depth map of the same size as the input image, where each pixel contains the estimated depth information of the pixel's location. During training, the MSE loss and SSIM loss functions are used. In order to promote the smoothness and geometric consistency of the depth map, a smoothing term of variational (Total Variation, TV) regularization is added to the loss function. The depth estimation model is supervised learning on an image dataset with precise depth labels, and the total loss function is It is expressed as:

, ,

in, is the depth map predicted by the model, is the real depth map, N is the number of samples, is the average image brightness, is the standard deviation of pixel values, , , L is the dynamic range of grayscale, which is related to the type of image data, represents the gradient of the depth map at position i; is a hyperparameter that balances the weights of each loss term.

In surface normal vector estimation, features are extracted from the image to be processed captured by the input monocular camera in a multi-view scene, and a multi-scale feature extraction function is used to extract a multi-scale feature map. Assume that the input image is , the multi-scale feature extraction function is , then the obtained multi-scale feature map can be expressed as Based on multi-scale feature maps , the surface normal vector of each pixel is estimated through the convolutional neural network CNN. The normal vector prediction function is , then ,in is the surface normal vector of each pixel in the multi-scale feature map, Convolutional neural network used in the surface normal estimation module.

1.2) Depth map consistency optimization process: After the predicted depth map is obtained by the depth estimation model, in order to ensure that the predicted depth map is geometrically consistent with the corresponding surface normal vector, this method constructs a geometric consistency optimization model. The specific implementation method is as follows;

For a pixel The surface normal vector and the estimated depth value , Normal vector coordinates; use the camera's geometric model to express geometric consistency. Assuming that the pinhole camera model is known, there is an internal parameter matrix , rotation matrix and translation vector , then the three-dimensional space point corresponding to the pixel point It can be expressed as:

Furthermore, the normal vector of this space point in the world coordinate system is Should be consistent with the estimated normal vector In order to optimize the consistency, this method constructs a loss function to minimize the deviation between the depth gradient and the normal vector, so that the estimated depth value is coordinated with the normal vector information:

in, Loss function of the geometric consistency optimization module; is the predicted depth map Z at pixel position The depth gradient at reflects the direction of depth change. is the surface normal vector at the same position, is a scalar coefficient that reflects the relationship between the depth change rate and the normal vector direction. , the depth changes in the predicted depth map can be constrained to be along the direction of the surface normal vector to finally obtain a depth prior map, thereby enhancing the geometric rationality of the depth estimation.

2) Guide neural radiance field training based on depth prior: The existing neural radiance field sampling method is layered sampling, but in the sampling process of rendering depth map, since the pixel values predicted by all sampling points corresponding to pixels with poor texture along the camera light are roughly the same, the depth map obtained by rendering sampling by the existing method deviates from the actual situation to a large extent. After obtaining the depth prior map, in order to distribute the sampling range more accurately, this method uses an adaptive depth prior to guide the sampling of the neural radiance field.

As shown in Figure 2, the neural radiation field sampling process based on depth prior is as follows:

The obtained depth prior atlas is projected into three-dimensional space according to the depth information, and an image in the depth prior atlas is transformed and projected to other camera perspectives for comparison with the depth information of other camera perspectives, so as to obtain the error map corresponding to the depth map at each perspective. The formula is as follows:

in It is a picture The depth value corresponds to the projection of the spatial point onto the image The corresponding two-dimensional coordinates of the middle and rear are, It is projected onto the graph The depth value of the two-dimensional coordinate is then expressed through an error map to describe the accuracy and credibility of the depth prior map; is the rotation matrix from image i to image j, is the translation vector from image i to image j, is the corresponding depth value in Figure i, The intrinsic characteristics of the camera; is the depth error.

The sampling range under the camera perspective is determined according to each perspective error map, where the sampling on pixels with smaller errors is concentrated around the depth prior, while the sampling on pixels with larger errors still uses the original neural radiation field formula. The formula for the sampling range is as follows:

Among them, D is the depth prior map, e is the error map, and To define the upper and lower limits of the range; is the starting sampling point of the ray under the guidance of the depth prior map, is the termination sampling point of the ray under the guidance of the depth prior map, As the contents of the same scene may be greatly different in different perspectives, resulting in low confidence in a large number of regions, the algorithm only uses the four other perspectives with the smallest error value to calculate the average value.

Neural radiance fields are trained to transform input images into a continuous, differentiable scene representation, allowing new views to be rendered from arbitrary perspectives.

As shown in Figure 3, the specific training steps are as follows:

2.1) Ray generation: For each pixel in the training image, the ray from the camera center through the pixel is calculated using the known camera intrinsics and extrinsics. ,in is the camera center, is the ray direction, are the ray parameters.

2.2) Volume rendering, in ray The sampling range is obtained based on the depth prior. Points .

Through a multi-layer perceptron neural network , given the location of each sampling point and the ray direction , the network predicts the color of the point and bulk density .

The color of each pixel along the ray is calculated using the classic volume rendering formula and transmittance :

in, is the distance between adjacent sampling points, From the starting point of the ray to The cumulative transmittance of the sampling points is is an exponential function.

2.3) Loss function and optimization: The training goal of the neural radiation field is to minimize the difference between the reconstructed image and the actual image. The loss is taken as the loss function, i.e.

in, is the predicted color calculated from the volume rendering formula, is the actual observed pixel color.

Use Adam optimizer to update network parameters to reduce the loss function .

2.4) Iterative training: After multiple iterations, randomly select rays from the data set for forward propagation and backward propagation, and gradually adjust the network parameters until the loss converges.

The training of the neural radiation field continuously optimizes the network parameters so that the images synthesized from any perspective are as close as possible to the actual captured images, thereby achieving three-dimensional reconstruction of the scene.

3) Rendering accurate depth map based on neural radiation field and Gaussian filter; The three-dimensional scene of the scene is obtained through neural radiation field, similar to color rendering, and the depth map is obtained by volume rendering. Since the depth is equal to the ray in the sampling process middle The value of , so the rendered depth map The formula is as follows:

is the distance between adjacent sampling points, From the starting point of the ray to The cumulative transmittance of the sampling points is is an exponential function.

The 3D reconstructed depth map learned by the neural radiation field may have insufficient depth continuity and noise. This method uses Gaussian filtering to further filter and optimize the 3D reconstructed depth map. Since the 3D reconstructed depth map obtained by neural radiation field rendering should be highly consistent with the real input, if there is an error between the two, it means that the learned neural radiation field information is defective, and the depth information of the corresponding area is often wrong. Therefore, the 3D reconstructed image obtained by rendering can be optimized by Gaussian filtering and the error between the input 3D reconstructed image. The specific formula of the filtering optimization function is:

in, represents a Gaussian filter, Represents the rendered depth map. represents the convolution operation, and express The square of the norm, that is, the square of the Euclidean distance, represents the target image; represents the filtering optimization function. This loss function tries to find a Gaussian filtered rendered image that is as close as possible to the target image.

The monocular depth estimation method based on surface normal vector and neural radiation field of the present invention not only uses surface normal vector as auxiliary information of depth estimation, providing additional geometric constraints; it also uses volume rendering technology of neural radiation field (NeRF), which can synthesize images from different perspectives and provide depth information even in texture-poor areas; the present invention also optimizes the weighted visual weight of Gaussian filter, and by adjusting the parameters of Gaussian filter, especially standard deviation, it can remove unnecessary noise while maintaining edge clarity; so that the present invention performs well in multiple performance indicators such as mean absolute error (MAE), mean square error (MSE) and relative error (Rel), not only significantly improving the accuracy, but also showing excellent ability in processing complex scenes, texture-poor areas and boundary details. In addition, compared with the existing monocular depth estimation method, the method of the present invention also has significant advantages in operation efficiency and robustness, proving the potential and value of the method of the present invention in practical applications.

Based on the same inventive concept, a monocular depth estimation system based on surface normal vector and neural radiation field is also provided in this embodiment, including:

A model building module is used to build an initial surface normal vector and depth estimation model, and train it using an image dataset with depth labels to obtain a trained surface normal vector and depth estimation model;

A depth prior map acquisition module is used to input the image set to be processed into the trained surface normal vector and depth estimation model to obtain a depth prior map set;

A three-dimensional reconstruction module is used to input the image set to be processed into the neural radiation field, and guide the neural radiation field to perform three-dimensional reconstruction on the processed image set based on the depth prior atlas obtained by the depth prior map acquisition module to obtain a rendered depth image set;

The Gaussian filter module is used to use Gaussian filtering to filter and optimize the rendered depth image set, and finally obtain the optimized depth image set as the monocular depth estimation result.

For the system embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment, and the implementation methods of the remaining modules will not be repeated here. The system embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

The embodiments of the system of the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus such as a computer. The system embodiments can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, the corresponding computer program instructions in the non-volatile memory are read into the memory by the processor of any device with data processing capabilities and run.

An embodiment of the present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned monocular depth estimation method based on surface normal vectors and neural radiation fields when executing the computer program.

The above-mentioned embodiments only express several implementation methods of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. For ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims (10)

1. A monocular depth estimation method based on a surface normal vector and a neural radiation field, comprising the steps of:

1) Constructing an initial surface normal vector and a depth estimation model, and training by using an image data set with a depth label to obtain a trained surface normal vector and a trained depth estimation model;

2) Inputting a to-be-processed image set captured by a monocular camera in a multi-view scene into a trained surface normal vector and a depth estimation model to obtain a depth priori atlas;

3) Inputting the image set to be processed into a nerve radiation field, guiding the nerve radiation field to carry out three-dimensional reconstruction on the image set to be processed based on the depth priori graph set obtained in the step 2), and obtaining a rendered depth image set;

4) And filtering and optimizing the rendered depth image set by using Gaussian filtering, and finally obtaining the optimized depth image set as a monocular depth estimation result.

2. The monocular depth estimation method based on surface normal vector and neural radiation field of claim 1, wherein the surface normal vector and depth estimation model comprises a depth estimation module, a surface normal vector estimation module, and a geometric consistency optimization module; the depth estimation module is used for extracting depth characteristics in an input image and outputting a predicted depth map; the surface normal vector estimation module is used for extracting a multi-scale feature map in an input image and outputting a surface normal vector; the geometric consistency optimization module is used for predicting depth in the depth map according to multi-scale feature map constraint and finally obtaining a depth priori map along the surface normal vector direction.

3. The method of monocular depth estimation based on surface normal vectors and neural radiation fields according to claim 2, wherein the depth estimation module uses a weighted sum of mean square error loss function, structural similarity loss function and variational regularized smooth term loss as the total loss function in the training process.

4. The monocular depth estimation method based on surface normal vector and neural radiation field according to claim 2, wherein the surface normal vector estimation module extracts a multiscale feature map from an input image using a multiscale feature extraction function, and estimates a surface normal vector of each pixel point of the multiscale feature map by a convolutional neural network, expressed as:

Wherein, For the surface normal vector of each pixel of the multi-scale feature map,A convolutional neural network used for the surface normal vector estimation module,For a multi-scale feature extraction function,Is an input image.

5. The method of monocular depth estimation based on surface normal vectors and neural radiation fields of claim 2, wherein the loss function of the geometric consistency optimization module causes the depth in the predicted depth map to vary along the surface normal vector direction by minimizing the deviation between the depth gradient in the predicted depth map and the surface normal vector; the loss function is:

Wherein, Is a predictive depth mapAt the pixel positionA depth gradient at the point where the depth is greater,Is the pixel locationThe normal vector of the surface at which the position is located,Is a scalar coefficient; the loss function of the module is optimized for geometric consistency.

6. The monocular depth estimation method based on the surface normal vector and the neural radiation field according to claim 1, wherein the depth prior atlas obtained based on the step 2) guides the neural radiation field to perform three-dimensional reconstruction on the image set to be processed, and the method comprises the following steps:

3.1 Projecting the depth prior map set obtained in the step 2) into a three-dimensional space according to the depth information, converting and projecting one depth prior map in the depth prior map set under other camera view angles and comparing the depth information of the other camera view angles, so as to obtain error maps corresponding to the depth prior map under each view angle, and traversing all the depth prior maps in the depth prior map set;

3.2 Determining a range of neural radiation field samples based on the error map;

3.3 In the determined nerve radiation field sampling range, carrying out three-dimensional reconstruction on the image set to be processed to obtain a rendered depth image set.

7. The method of monocular depth estimation based on surface normal vector and neural radiation field of claim 6, wherein the determining the range of neural radiation field samples based on the error map is expressed as:

Wherein, As a depth-prior map,In the form of an error map,AndUpper and lower limits of the range predefined; for the initial sampling point of the nerve radiation field under the guidance of the depth prior map, Terminating sampling points of the nerve radiation field under the guidance of the depth priori map; As a function of the value.

8. The method for monocular depth estimation based on surface normal vector and neural radiation field according to claim 1, wherein the filtering optimization is performed on the rendered depth image set by a filtering optimization function minimizing gaussian filtering, and the formula of the filtering optimization function is:

Wherein, The gaussian filter is represented by the number of the filters,Representing the depth map after rendering of the image,A convolution operation is represented and is performed,Representation ofThe square of the norm,Representing the target image as an optimized depth image; representing a filtering optimization function.

9. A monocular depth estimation system based on a surface normal vector and a neural radiation field, comprising:

The model construction module is used for constructing an initial surface normal vector and a depth estimation model, and training by using an image data set with a depth label to obtain a trained surface normal vector and a trained depth estimation model;

the depth prior image acquisition module is used for inputting the image set to be processed into the trained surface normal vector and the depth estimation model to obtain a depth prior image set;

The three-dimensional reconstruction module is used for inputting the image set to be processed into the nerve radiation field, guiding the nerve radiation field to carry out three-dimensional reconstruction on the processed image set based on the depth priori graph set obtained by the depth priori graph acquisition module, and obtaining a rendered depth image set;

and the Gaussian filtering module is used for filtering and optimizing the rendered depth image set by using Gaussian filtering, and finally obtaining the optimized depth image set as a monocular depth estimation result.

10. A terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the surface normal vector and neural radiation field based monocular depth estimation method according to any one of claims 1 to 8 when the computer program is executed.