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Heuristics and Problem Solving

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• pp 1421–1424
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• Erik De Corte 2 ,
• Lieven Verschaffel 2 &
• Wim Van Dooren 2  

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Definitions

In a general sense heuristics are guidelines or methods for problem solving. Therefore, we will first define problem solving before presenting a specific definition of heuristics.

Problem Solving

In contrast to a routine task, a problem is a situation in which a person is trying to attain a goal but does not dispose of a ready-made solution or solution method. Problem solving involves then “cognitive processing directed at transforming the given situation into a goal situation when no obvious method of solution is available” (Mayer and Wittrock 2006 , p. 287). An implication is that a task can be a problem for one person, but not for someone else. For instance, the task “divide 120 marbles equally among 8 children” may be a problem for beginning elementary school children, but not for people who master the algorithm for long division, or know how to use a calculator.

The term “heuristic” originates from the Greek word heuriskein which means “to find.” Heuristics ...

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De Corte, E., Verschaffel, L., & Op’t Eynde, P. (2000). Self-regulation: a characteristic and a goal of mathematics education. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687–726). San Diego, CA: Academic.

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Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (pp. 287–303). New York: Macmillan.

Polya, G. (1945). How to solve it . Princeton, NJ: Princeton University Press.

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Department of Education, Center for Instructional Psychology and Technology (CIP&T), Katholieke Universiteit Leuven, Dekenstraat 2, P.O. box 3773, B-3000, Leuven, Belgium

Dr. Erik De Corte, Prof. Dr. Lieven Verschaffel & Wim Van Dooren

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De Corte, E., Verschaffel, L., Van Dooren, W. (2012). Heuristics and Problem Solving. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_420

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Problem Solving

Applies critical thinking to tackle issues, overcome challenges, and implement effective solutions that lead to the desired outcomes.

As an administrator, you build upon skills as you grow within your career and move upward. The table below illustrates the various job bands (or role levels) of administrator positions at NYU. It is designed to assist with focusing on skills at your current band, and then exploring the professional development that is needed to grow to your next band opportunity.

Problem Solving by Job Band

Problem Solving Professional Development Model

Areas of focus are designed to equip individuals at each level with the skills, mindset, and strategies necessary to promote and facilitate effective teamwork and collaboration across organizational boundaries. For each of the eight NYU core competencies, there are sub-categories to fully develop the core competency and specific training areas tailored to different job bands across NYU. These designated training areas highlight the key focus areas corresponding to each competency. Login to NYU Home is required to access training resources.

Job Band 52

View problem solving-based opportunities for training, relationships, and experiences:

• Critical Thinking for Better Judgment and Decision-Making (LinkedIn Learning)
• Problem Solving Techniques (LinkedIn Learning)
• Critical Thinking and Problem-Solving (LinkedIn Learning)

To enhance your critical thinking and problem identification skills, consider engaging in developmental experiences or relationships by practicing brainstorming and problem identification with colleagues on your team, and actively seeking opportunities to improve processes within your role.

• Root Cause Analysis: Systemic Problem Prevention (LinkedIn Learning)

To enhance your root cause analysis and solution generation skills, consider engaging in developmental experiences or relationships by evaluating potential solutions with colleagues and by actively collecting data, conducting investigations, and analyzing factors to determine the underlying cause of a problem.

• Decision-Making Strategies (LinkedIn Learning)
• Project Management Simplified (LinkedIn Learning)
• Improving Your Judgment for Better Decision-Making (LinkedIn Learning)

To enhance your decision-making and implementation planning skills, consider engaging in developmental experiences or relationships by collaborating with relevant stakeholders to develop a draft implementation plan and create a draft project plan.

• Overcoming Complexity (LinkedIn Learning)
• 10 Habits of Great Problem Solvers   (LinkedIn Learning)
• Conflict Resolution Foundations   (LinkedIn Learning)
• Increase Your Flexible Thinking Skills (LinkedIn Learning)

To enhance your adaptability, flexibility, and conflict resolution skills, consider engaging in developmental experiences or relationships by participating in constructive discussions about handling conflicts on your team and contributing to a dynamic project with shifting priorities and evolving timelines.

Job Band 53

• Managing for Results (LinkedIn Learning)
• Take a More Creative Approach to Problem Solving (LinkedIn Learning)
• Coaching Yourself and Your Team from Uncertainty to Action (LinkedIn Learning)

To enhance your ability to coach and mentor for problem solving, consider engaging in developmental experiences or relationships by reviewing a problem you solved with team members and explaining your problem-solving approach, and by coaching an employee through a situation that requires problem-solving skills.

• How Leaders Drive Results and Resolve Conflict in a Hybrid Workplace (LinkedIn Learning)
• How to Handle Conflict and Escalations Before They Turn Legal (LinkedIn Learning)
• Managing Team Conflict (LinkedIn Learning)

To enhance your conflict resolution skills, consider engaging in developmental experiences or relationships by discussing conflict resolution experiences with team members to identify lessons learned and areas for improvement, and practicing resolving conflicts that arise during collaborative projects.

• LDR 005: Leading Teams (Foundations of People Leadership program) (Instructor-Led)

To enhance your ability to improve team problem-solving dynamics, consider engaging in developmental experiences or relationships by seeking out trusted peers to share insights and experiences of team problem-solving dynamics, and facilitating collaborative problem-solving exercises on your team while observing team dynamics, analyzing member interactions, and identifying patterns in problem-solving approaches.

• Leading with Stability during Times of Change and Disruption (LinkedIn Learning)
• Leading Your Team Through Change   (LinkedIn Learning)
• Driving Measurable, Sustainable Change (LinkedIn Learning)

To enhance your change management skills, consider engaging in developmental experiences or relationships by seeking guidance from change management experts or colleagues who have led successful change initiatives in the past, and actively contributing to a change initiative within NYU.

Job Band 54

• Leading Strategically (LinkedIn Learning)

To enhance your strategic problem-solving skills, consider engaging in developmental experiences or relationships by seeking guidance from mentors, senior leaders, or industry experts who have a deep understanding of strategic planning and decision-making, and formulate a problem-solving strategy and pilot it.

• Project Management: Solving Common Project Problems (LinkedIn Learning)
• Prioritizing Effectively as a Leader (LinkedIn Learning)
• Time Management for Managers (LinkedIn Learning)

To enhance your project management skills, consider engaging in developmental experiences or relationships by setting up a meeting to share best practices with the project management office at NYU and spearheading a project team, creating a project plan, setting goals and objectives, and managing project resources and timeline.

• Measuring Business Performance (LinkedIn Learning)
• Performance Management: Setting Goals and Managing Performance (LinkedIn Learning)

To enhance your performance metrics and evaluation skills, consider engaging in developmental experiences or relationships by working with your team to identify performance outcomes and consulting with Employee Systems Management, while conducting assessments and evaluations of projects, setting performance goals, defining key performance indicators, and monitoring performance against established metrics.

Job Band 55+

• Problem Solving Accross An Organization (LinkedIn Learning)

To enhance your visionary problem-solving skills, consider engaging in developmental experiences or relationships by reaching out to the Learning and Organizational Development team to seek an external coach, and creating a vision and outlining norms for innovative problem-solving on your team.

• Leading in Crisis (LinkedIn Learning)
• Executive Decision Making (LinkedIn Learning)

To enhance your strategic leadership skills in crisis management, consider engaging in developmental experiences or relationships such as participating in peer-to-peer discussions or crisis management forums, and engaging in a crisis management simulation.

• Creating a Culture of Learning (LinkedIn Learning)
• Counterintuitive Leadership Strategies for a VUCA (Volatile, Uncertain, Complex, Ambiguous) Environment (LinkedIn Learning)

To enhance your organizational learning and knowledge management skills, consider engaging in developmental experiences or relationships by seeking out peers who have experience in institutionalizing learning and promoting knowledge sharing within their departments, and experimenting with implementing a process for knowledge-sharing and collaboration, such as after-action reviews, project debriefs, or collaborative online platforms.

• Leadership Ethics (LinkedIn Learning)

To enhance your ethical decision-making skills, consider engaging in developmental experiences or relationships by participating in forums and conferences where ethical considerations are key topics of discussion, and by reviewing past decisions and case studies where ethical considerations played a significant role.

Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

• Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
• Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
• Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
• Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
• Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
• Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
• Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
• Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
• Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
• Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
• Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
• Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
• Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
• Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
• Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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Chapter 9. Cognition

Problem-Solving: Heuristics and Algorithms

Dinesh Ramoo

Approximate reading time : 11 minutes

Learning Objectives

By the end of this section, you will be able to:

• Describe the differences between heuristics and algorithms in information processing

When faced with a problem to solve, should you go with intuition or with more measured, logical reasoning? Obviously, we use both of these approaches. Some of the decisions we make are rapid, emotional, and automatic. Daniel Kahneman (2011) calls this “fast” thinking. By definition, fast thinking saves time. For example, you may quickly decide to buy something because it is on sale; your fast brain has perceived a bargain, and you go for it quickly. On the other hand, “slow” thinking requires more effort; applying this in the same scenario might cause us not to buy the item because we have reasoned that we don’t really need it, that it is still too expensive, and so on. Using slow and fast thinking does not guarantee good decision-making if they are employed at the wrong time. Sometimes it is not clear which is called for, because many decisions have a level of uncertainty built into them. In this section, we will explore some of the applications of these tendencies to think fast or slow.

We will look further into our thought processes, more specifically, into some of the problem-solving strategies that we use. Heuristics are information-processing strategies that are useful in many cases but may lead to errors when misapplied. A heuristic is a principle with broad application, essentially an educated guess about something. We use heuristics all the time, for example, when deciding what groceries to buy from the supermarket, when deciding what to wear before going out, when choosing the best route to drive through town to avoid traffic congestion, and so on. Heuristics can be thought of as aids to decision making; they allow us to reach a solution without a lot of cognitive effort or time.

The benefit of heuristics in helping us reach decisions fairly easily is also the potential downfall: the solution provided by the use of heuristics is not necessarily the best one. Let’s consider some of the most frequently applied, and misapplied, heuristics in Table CO.3 below.

In many cases, we base our judgments on information that seems to represent, or match, what we expect will happen, while ignoring other potentially more relevant statistical information. When we do so, we are using the representativeness heuristic . Consider, for instance, the data presented in the lists below. Let’s say that you went to a hospital, and you checked the records of the babies that were born on that given day. Which pattern of births do you think you are most likely to find?

• 6:31 a.m. – Girl
• 8:15 a.m. – Girl
• 9:42 a.m. – Girl
• 1:13 p.m. – Girl
• 3:39 p.m. – Boy
• 5:12 p.m. – Boy
• 7:42 p.m. – Boy
• 11:44 p.m. – Boy
• 6:31 a.m. – Boy
• 9:42 a.m. – Boy
• 3:39 p.m. – Girl
• 7:42 p.m. – Girl

Using the representativeness heuristic may lead us to incorrectly believe that some patterns of observed events are more likely to have occurred than others.

Most people think that list B is more likely, probably because list B looks more random, and matches — or is “representative of” — our ideas about randomness, but statisticians know that any pattern of four girls and four boys is mathematically equally likely. Whether a boy or girl is born first has no bearing on what sex will be born second; these are independent events, each with a 50:50 chance of being a boy or a girl. The problem is that we have a schema of what randomness should be like, which does not always match what is mathematically the case. Similarly, people who see a flipped coin come up “heads”five times in a row will frequently predict, and perhaps even wager money, that “tails” will be next. This behaviour is known as the gambler’s fallacy . Mathematically, the gambler’s fallacy is an error;: the likelihood of any single coin flip being “tails” is always 50%, regardless of how many times it has come up “heads” in the past. Think of how people choose lottery numbers. People who follow the lottery often have the impression that numbers that were chosen before are unlikely to reoccur even though the selection of numbers is random and not dependent on previous events. But the gambler’s fallacy is so strong in most people that they follow this logic all the time.

The representativeness heuristic may explain why we judge people on the basis of appearance. Suppose you meet your new next-door neighbour, who drives a loud motorcycle, has many tattoos, wears leather, and has long hair. Later, you try to guess their occupation. What comes to mind most readily? Are they a teacher? Insurance salesman? IT specialist? Librarian? Drug dealer? The representativeness heuristic will lead you to compare your neighbour to the prototypes you have for these occupations and choose the one that they seem to represent the best. Thus, your judgment is affected by how much your neighbour seems to resemble each of these groups. Sometimes these judgments are accurate, but they often fail because they do not account for base rates , which is the actual frequency with which these groups exist. In this case, the group with the lowest base rate is probably drug dealer.

Our judgments can also be influenced by how easy it is to retrieve a memory. The tendency to make judgments of the frequency or likelihood that an event occurs on the basis of the ease with which it can be retrieved from memory is known as the availability heuristic (MacLeod & Campbell, 1992; Tversky & Kahneman, 1973). Imagine, for instance, that I asked you to indicate whether there are more words in the English language that begin with the letter “R” or that have the letter “R” as the third letter. You would probably answer this question by trying to think of words that have each of the characteristics, thinking of all the words you know that begin with “R” and all that have “R” in the third position. Because it is much easier to retrieve words by their first letter than by their third, we may incorrectly guess that there are more words that begin with “R,” even though there are in fact more words that have “R” as the third letter.

The availability heuristic may explain why we tend to overestimate the likelihood of crimes or disasters; those that are reported widely in the news are more readily imaginable, and therefore, we tend to overestimate how often they occur. Things that we find easy to imagine, or to remember from watching the news, are estimated to occur frequently. Anything that gets a lot of news coverage is easy to imagine. Availability bias does not just affect our thinking. It can change behaviour. For example, homicides are usually widely reported in the news, leading people to make inaccurate assumptions about the frequency of murder. In Canada, the murder rate has dropped steadily since the 1970s (Statistics Canada, 2018), but this information tends not to be reported, leading people to overestimate the probability of being affected by violent crime. In another example, doctors who recently treated patients suffering from a particular condition were more likely to diagnose the condition in subsequent patients because they overestimated the prevalence of the condition (Poses & Anthony, 1991). After the attack on 9/11, more people died from car accidents because more people drove instead of flying in a plane. Even though the attack was an isolated incident and even though flying is statistically safer than driving, the mere fact of seeing the attack on television again and again made people think that flying was more dangerous than it is.

The anchoring and adjustment heuristic is another example of how fast thinking can lead to a decision that might not be optimal. Anchoring and adjustment is easily seen when we are faced with buying something that does not have a fixed price. For example, if you are interested in a used car, and the asking price is $10,000, what price do you think you might offer? Using $10,000 as an anchor, you are likely to adjust your offer from there, and perhaps offer $9000 or $9500. Never mind that $10,000 may not be a reasonable anchoring price. Anchoring and adjustment happens not just when we’re buying something. It can also be used in any situation that calls for judgment under uncertainty, such as sentencing decisions in criminal cases (Bennett, 2014), and it applies to groups as well as individuals (Rutledge, 1993).

In contrast to heuristics, which can be thought of as problem-solving strategies based on educated guesses, algorithms are problem-solving strategies that use rules. Algorithms are generally a logical set of steps that, if applied correctly, should be accurate. For example, you could make a cake using heuristics — relying on your previous baking experience and guessing at the number and amount of ingredients, baking time, and so on — or using an algorithm. The latter would require a recipe which would provide step-by-step instructions; the recipe is the algorithm. Unless you are an extremely accomplished baker, the algorithm should provide you with a better cake than using heuristics would. While heuristics offer a solution that might be correct, a correctly applied algorithm is guaranteed to provide a correct solution. Of course, not all problems can be solved by algorithms.

As with heuristics, the use of algorithmic processing interacts with behaviour and emotion. Understanding what strategy might provide the best solution requires knowledge and experience. As we will see in the next section, we are prone to a number of cognitive biases that persist despite knowledge and experience.

To calculate this time, we used a reading speed of 150 words per minute and then added extra time to account for images and videos. This is just to give you a rough idea of the length of the chapter section. How long it will take you to engage with this chapter will vary greatly depending on all sorts of things (the complexity of the content, your ability to focus, etc).

Problem-Solving: Heuristics and Algorithms Copyright © 2024 by Dinesh Ramoo is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Philosophers' Thinking (Heuristics and Problem-Solving‭ (‬Volume‭ ‬2)

Philosophers' Thinking (Heuristics and Problem-Solving‭ (‬Volume‭ ‬2), 2017

182 Pages Posted: 14 Apr 2017

Ulrich de Balbian

Meta-Philosophy Research Cente; Meta-Philosophy Research Center

Date Written: April 13, 2017

This section or chapter two.‭ ‬Because of its length I decided to create a second Volume‭ ‬2.‭ ‬HEURISTICS AND PROBLEM-SOLVING‭ (‬Volume‭ ‬2‭). This volume deals with details of heuristic approaches and the infinite aspects and features of‭ ‘‬problem-solving‭’ ‬and related issues. The author of the first article I quote suggests that the heuristic tools or devices he mentions will enable individuals to produce philosophy.‭ ‬He seems to think that this idea is one of the major factors that leads to the creation of philosophy. I wish to indicate,‭ ‬by citations,‭ ‬that there is much,‭ ‬much more to heuristics then the list of heuristics he suggests. I place the use of heuristic devices in the larger context of problem-solving.‭ ‬The solving of problems is of course merely one aspect of a much larger process that consist of many other features,‭ ‬steps and stages. The aim of that section and citations are to to make individuals aware of the many aspects of the process of problem conceptualization,‭ ‬investigation and solving or dissolving.‭ ‬I think it is is essential to be aware of these features of problem investigation because without such knowledge and understanding philosophers will suffer from an even greate lack of meta-cognition of the socio-cultural practice of philosophy and the doing of philosophy and of self-‭metacognition.

Suggested Citation: Suggested Citation

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JSmol Viewer

Three-dimensional dense reconstruction: a review of algorithms and datasets.

1. Introduction

2. geometrical 3d reconstruction, 2.1. overview.

• Image Acquisition : The first step is capturing multiple images or video frames of the scene or object from different angles and viewpoints. The quality and resolution of these images are crucial, as they directly impact the accuracy of the final 3D model.
• Feature Detection and Matching : Distinctive features or keypoints are identified within the images, and corresponding features across different images are matched. Common algorithms for this step include SIFT, SURF, and ORB.
• Camera Pose Estimation : Once feature correspondences are established, the relative positions and orientations of the cameras are estimated. This step is essential for reconstructing the geometry of the scene and is typically performed using methods like an essential matrix, homography matrix, or bundle adjustment.
• Depth Estimation : Depth information for each pixel is calculated, often using stereo matching or multi-view stereo techniques. This step generates a dense point cloud that represents the 3D structure of the scene or object.
• Surface Reconstruction : The dense point cloud is then transformed into a 3D mesh that represents the surface of the object or scene. Algorithms such as Poisson surface reconstruction or marching cubes are commonly used in this process.
• Texturing : In the final step, color and texture information from the original images are applied to the 3D mesh, creating a photorealistic 3D model.

2.2. Structure from Motion

2.3. shape from shading.

• Lambertian Surface : The object’s surface is assumed to follow a Lambertian reflectance model, reflecting light equally in all directions, with the reflected light intensity depending only on the angle between the light source and the surface normal [ 29 ].
• Known Lighting Conditions : The position, intensity, and color of the light source(s) are assumed to be known or estimated.
• Smooth Surface : The object’s surface is assumed to be smooth, with continuous variations in depth and surface normals.
• Single Image : SfS operates on a single image, unlike other 3D reconstruction techniques that rely on multiple images or stereo pairs.

3. Deep-Learning-Based 3D Dense Reconstruction

3.1. convolutional neural networks, 3.2. three-dimensional convolutional neural networks (3d-cnns), 3.3. recurrent neural networks (rnns) and long short-term memory (lstm), 3.4. graph neural networks (gnns).

• Input : An unordered set of 3D points, each represented by its x, y, and z coordinates.
• Transformation Networks (T-Nets) : These are mini-PointNets that learn spatial transformations to align the input point cloud. There are two T-Nets: the first predicts a 3 × 3 transformation matrix to align the point cloud and the second predicts a 64 × 64 matrix to align the features.
• Multi-Layer Perceptrons (MLPs) : Fully connected layers that learn local features for each input point. The architecture includes several MLP layers with varying numbers of neurons (e.g., 64, 128, or 1024), applying a shared weight function to each point independently, which ensures permutation invariance.
• Max Pooling : A symmetric function that aggregates local features into a global point cloud feature. Max pooling captures the most salient features of the input point cloud.
• Fully Connected Layers and Output (MLPs) : Processes the global point cloud feature to generate the final output. For classification tasks, the output layer has as many neurons as there are object classes, while, for segmentation tasks, the output layer produces per-point scores.

3.5. Generative Adversarial Networks (GANs)

• Generator : A 3D Convolutional Neural Network (CNN) that takes a random noise vector as input and produces a 3D object as output. It uses transposed 3D convolutional layers for upsampling, followed by batch normalization and ReLU activation functions. The architecture resembles a 3D U-Net, incorporating skip connections between corresponding layers to refine the generated shapes.
• Discriminator : A 3D CNN that classifies the generated 3D object as either real (from the training dataset) or fake (produced by the generator). It consists of several 3D convolutional layers with batch normalization, leaky ReLU activation functions, and a final fully connected layer with a sigmoid activation function.

3.6. Autoencoders and Variational Autoencoders (VAEs)

• Encoder : The input to the encoder is typically a 3D representation, such as a voxel grid (3D binary or scalar grid), point cloud (a set of points in 3D space), or a mesh. For voxel-based inputs, 3D convolutional layers are used to capture spatial features from the 3D grid. These layers reduce the spatial dimensions while increasing the depth of the feature maps. In the case of point clouds, layers like PointNet or PointNet++ might be used to extract features directly from the unordered set of points. After the convolutional layers, fully connected (dense) layers are used to further compress the feature representation into a latent space. This latent space is a lower-dimensional representation of the 3D input.
• Latent Space : The latent space, also known as the bottleneck layer, contains the compressed representation of the input data. It is typically a vector of fixed size that encodes the most important features necessary for reconstructing the original 3D structure. The size of the latent space is a crucial parameter that balances compression and reconstruction accuracy.
• Decoder The decoder begins with fully connected layers that take the latent space vector as input and gradually expand it back to the dimensions of the original 3D representation. For voxel-based inputs, 3D deconvolutional (transposed convolutional) layers are used to upsample the feature maps and reconstruct the 3D structure. These layers progressively increase the spatial dimensions back to the size of the original input. The output layer produces the final 3D reconstruction, typically in the form of a voxel grid, point cloud, or mesh, depending on the original input format.

3.7. Neural Radiance Fields (NeRFs)

• High-Quality Reconstructions: NeRFs can produce highly detailed and photorealistic 3D reconstructions by accurately modeling complex lighting and appearance details. This results in high-quality visual outputs that capture fine textures and intricate scene details.
• Continuous Representation: NeRFs represent 3D scenes as continuous volumetric functions, allowing for smooth interpolation and fine details that are challenging to capture with discrete representations like voxel grids.
• View Synthesis: NeRFs excel at synthesizing novel views of a scene, making them effective for applications that require generating images from new viewpoints not included in the training data.
• Flexibility: NeRFs can handle various scene types and can be adapted to different input modalities, such as RGB images and depth maps, enhancing their versatility.
• Computational Cost: Training a NeRF model can be computationally expensive and time-consuming, requiring significant GPU resources and memory. This is due to the need for fine-grained volumetric sampling and the complex nature of the optimization process.
• Data Requirements: NeRFs require a large number of input images from diverse viewpoints to produce accurate and detailed reconstructions. Acquiring and processing these images can be challenging and resource-intensive.
• Inference Speed: While NeRFs generate high-quality reconstructions, the inference process can be slow, as it involves querying the neural network for many points in the volume during rendering.
• Limited Novel Shape Generation: NeRFs are typically trained on existing scenes and may not generalize well to generating novel shapes or objects that were not part of the training data.

3.8. Transformer

4. dataset for deep-learning-based 3d dense reconstruction, 4.1. dataset review, 4.2. algorithms and dataset, 5. discussion.

• Low Texture : In scenes with minimal or no texture (e.g., flat, homogeneous surfaces), it becomes challenging to establish feature correspondences between different views. This often results in incorrect depth estimation and can lead to incomplete or noisy reconstructions [ 108 , 109 , 110 , 111 , 112 , 112 ].
• Dynamic Objects : Objects that move between frames or views introduce inconsistencies in the reconstruction process. Depth estimation and correspondence matching typically assume that the scene is static, so dynamic objects can cause errors in the reconstructed geometry [ 113 , 114 , 115 , 116 , 117 ].
• Low Image Quality : Images with low resolution, noise, or poor lighting conditions can adversely affect the performance of feature detection and matching algorithms, leading to inaccurate depth estimation and flawed reconstructions. High-quality images are crucial for robust 3D dense reconstruction [ 118 , 119 , 120 , 121 , 122 ].
• Deformation : Non-rigid or deformable objects, such as fabric or human bodies, can lead to inconsistencies in the reconstruction process. Deformations may alter an object’s appearance between views, complicating the establishment of correct feature correspondences and accurate 3D structure estimation [ 123 , 124 , 125 ].
• Drastic Scene Depth Changes : Scenes with significant depth variations, such as indoor environments with objects at varying distances, can challenge depth estimation and feature matching. Algorithms must adapt to these variations to achieve accurate reconstructions [ 110 , 126 , 127 ].
• Motion Blur : Fast-moving objects or rapid camera motion can introduce motion blur into images, making it difficult to accurately detect and match features. This can result in incorrect depth estimation and reconstruction artifacts [ 110 , 128 , 129 , 130 ].
• Adverse Illumination Conditions : Difficult lighting conditions, such as shadows, glare, or over- and under-exposure, can negatively impact feature detection and matching algorithms. Reflective or transparent surfaces may create misleading feature matches due to appearance changes depending on the viewpoint. Robust algorithms need to handle these challenging conditions to ensure accurate reconstruction [ 131 , 132 , 133 ].

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Lee, Y. Three-Dimensional Dense Reconstruction: A Review of Algorithms and Datasets. Sensors 2024 , 24 , 5861. https://doi.org/10.3390/s24185861

Lee Y. Three-Dimensional Dense Reconstruction: A Review of Algorithms and Datasets. Sensors . 2024; 24(18):5861. https://doi.org/10.3390/s24185861

Lee, Yangming. 2024. "Three-Dimensional Dense Reconstruction: A Review of Algorithms and Datasets" Sensors 24, no. 18: 5861. https://doi.org/10.3390/s24185861

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