Computer Vision

Wouldn’t it be amazing if there was a way to reduce the complexity of data while preserving its inherent structure and patterns? Well, it turns out that two powerful techniques, Principal Component Analysis (PCA) and Singular Value Decomposition (SVD), share a remarkable connection that can help us achieve just that. Let’s dive into this captivating … Read more

Have you ever wondered about the intricacies of light and how it interacts with surfaces? In this article, we will delve into the world of radiometric concepts, exploring the fundamental principles that underpin our understanding of image intensities. Join us as we unravel the mysteries of radiometry and reflectance. Angle in 2D and 3D: Understanding … Read more

Object tracking is a fundamental task in computer vision, especially when it comes to monitoring the movement of objects in dynamic environments. Traditional methods like average or median-based change detection algorithms have limitations when it comes to handling complex scenes with various distractions and changes. To overcome these challenges, a more sophisticated model is required … Read more

In the realm of 3D imaging, active illumination methods play a crucial role in capturing and reconstructing the three-dimensional structure of a scene. These methods involve projecting light patterns onto the scene and analyzing the captured images to compute depth information. Two popular active illumination methods are the intensity ratio method and phase shifting method. … Read more

Have you ever wondered how our planet came to be? Despite our vast knowledge, there is still much we don’t know about Earth and the processes that shaped it. Scientists have turned to the study of the solar system to find answers. By unraveling the mysteries of our celestial neighborhood, we gain insights into the … Read more

Introduction: When it comes to understanding the intricate language of physics, one term stands out: quantum field theory. This powerful framework allows us to describe elementary particles, delve into the forces between them, explore material properties, phase transitions, and even delve into cosmology. But what is the relationship between math and quantum field theory? Let’s … Read more

Have you ever wondered how we can extract the three-dimensional shape of an object just by observing its surface? This is made possible by a technique called photometric stereo, which provides us with the surface orientation at each point on the object. The process begins with measuring the surface normals using photometric stereo. These normals, … Read more

Have you ever wondered how a camera captures images without missing important details or introducing unwanted artifacts? The answer lies in the concept of sampling theory. In this article, we will explore the fascinating world of sampling theory and the phenomenon of aliasing in image processing. From Continuity to Discreteness: Capturing the Image When we … Read more

When it comes to the intricacies of structure from motion algorithms, one essential element to consider is the observation matrix. This matrix holds valuable insights that can greatly impact the success of the algorithm. One crucial characteristic of the observation matrix is its rank, which happens to be quite low. In this article, we will … Read more

Have you ever wondered how we, as humans, are able to perceive the shape of an object simply by looking at its shading? It’s a remarkable ability that we often take for granted. In this article, we’ll explore the intriguing field of psychophysics and delve into the experiments conducted by Vilayanur Ramachandran that shed light … Read more

Neural networks have revolutionized the field of artificial intelligence, enabling machines to learn and solve complex problems. In this article, we will explore the fundamental architecture of a neural network and how it can be trained to solve specific vision problems. Understanding Neural Network Architecture At its core, a neural network consists of interconnected layers … Read more

Tracking objects in videos can be a challenging task, especially when dealing with changes in scale, distance, lighting conditions, and occlusion. However, one approach that proves useful in certain cases is template matching. In this article, we will explore how template matching can be used as an object tracking technique. Understanding Template Matching Template matching … Read more

The human mind, with its vast imagination, has always been a subject of fascination. How do we distinguish between reality and imagination? Thanks to recent breakthroughs in biology and neuroscience, we now have a better understanding of this intriguing process. In addition, researchers are shedding light on the human microbiome, a complex ecosystem of microbes … Read more

By Tracy Seimon, Wildlife Conservation Society Director Have you ever wondered how scientific research helps us protect the rich biodiversity of our planet? As the director of the Wildlife Conservation Society’s molecular lab, located at the Bronx Zoo, I can attest to the critical role that scientific research plays in understanding and preserving our environment. … Read more

Image segmentation is a crucial task in the field of computer vision, allowing us to extract meaningful information from images by dividing them into distinct regions. One popular technique for image segmentation is the mean-shift algorithm. Unlike the k-means algorithm, mean shift overcomes the need to specify the number of clusters beforehand and is less … Read more

In the vast expanse of the universe, some of the most enigmatic phenomena are waiting to be uncovered. From gravitational waves to quantum teleportation, scientists have been making astonishing breakthroughs that push the boundaries of our understanding. Join us as we explore these remarkable achievements and the profound implications they hold for the world of … Read more

Welcome to the fascinating world of quantum computers, where reality expands beyond our imagination. Nestled inside a refrigerator, at a temperature just above absolute zero, lies a quantum computer – a technology that has the potential to revolutionize our lives with its unparalleled computational power. But what exactly are quantum computers, and how do they … Read more

Have you ever wondered how computer algorithms can detect meaningful changes in a scene? This ability is crucial for object tracking, where we want to identify and monitor moving objects in a given space. In this article, we will explore the concept of change detection and how it plays a vital role in object tracking … Read more

Have you ever wondered how our visual system interprets the world? The way we perceive colors, shapes, and shades is a fascinating subject. In this article, we’ll explore some intriguing illusions related to shading that shed light on the complexities of our visual perception. Join us on this journey as we delve into the mysteries … Read more

Image: Universality is an intriguing pattern that continues to captivate mathematicians and scientists across various disciplines. From bus systems to chicken eyes, this phenomenon reveals a hidden connection between seemingly unrelated areas of study. In this article, we will explore the concept of universality and its impact on our understanding of the world. Universality in … Read more

Image segmentation is a fundamental technique in computer vision that involves grouping pixels together based on their visual attributes or characteristics. By mapping an image to a feature space, we can identify clusters of pixels that share similar features. This process, known as segmentation, can be viewed as a clustering problem. Let’s explore how this … Read more

The journey of understanding plate tectonics has been an intriguing one. Over the past 50 years, we have made significant progress in unraveling the mysteries of Earth’s many faces. However, there is still so much we have yet to discover. Picture this: Earth, a staggering four billion years old. We can only observe a mere … Read more

Image integration and depth estimation play pivotal roles in computer vision and image processing. In the realm of uncalibrated stereo, it is crucial to compute the three-dimensional coordinates of points in a scene using the corresponding pairs of images. This estimation process involves triangulation, which relies on the known intrinsic parameters of the cameras. Estimating … Read more

Cosmology, the study of the universe’s origin and evolution, presents an abundance of enigmas waiting to be unraveled. How did the universe come into existence? How is it transforming? What lies in its future? Cynthia Chiang, an associate physics professor at McGill University, dedicates her life to exploring uncharted territories of the universe through the … Read more

Imagine a world where asking deep, difficult, and beautiful questions is not only encouraged but celebrated. This is the world that Dr. X, a physicist with an insatiable curiosity, lives in. Driven by an aesthetic sense of elegance and beauty in questioning, Dr. X traverses multiple disciplines and even time itself to find answers. Breaking … Read more

Have you ever wondered how computers can infer the shape of an object just by looking at its shading? In the world of computer vision, one technique that enables this is called “Shape from Shading.” Today, we’ll delve into the intricacies of this algorithm and explore the concept of stereographic projection. Understanding Surface Orientation To … Read more

Have you ever wondered about the incredible image sensors that nature has created? From the curious eyes of the copilia to the astonishing skin of the octopus, nature has devised some truly remarkable mechanisms. In this article, we will explore these natural image sensors and delve into the captivating world of image sensing. The Copilia: … Read more

Are you interested in calibrating your uncalibrated stereo system? Look no further! In this article, we will guide you through the process of estimating the fundamental matrix, an essential step in calibrating your system. Let’s dive in! Introduction The fundamental matrix is a three by three matrix that allows us to calibrate uncalibrated stereo systems. … Read more

Ken Ono, a prominent mathematician, has had an extraordinary journey shaped by the genius of Srinivasa Ramanujan. Ramanujan, renowned for his groundbreaking mathematical discoveries, not only inspired a Hollywood film but also played a pivotal role in Ono’s life. As a teenager, Ono found solace in Ramanujan’s story, realizing that success could be achieved beyond … Read more

Neural networks have revolutionized the field of artificial intelligence. Among the various types of neural networks, the perceptron network stands out for its ability to tackle complex problems. But what exactly is a perceptron and how does it work? Let’s dive into the intriguing realm of perceptron networks! A Single Perceptron: A Linear Classifier At … Read more

Image: Unsplash Have you ever wondered what controls your body’s internal clock? That 24-hour process that governs your sleep-wake cycle, metabolism, hormone production, and body temperature? The answer lies in the realm of circadian biology, where scientists like Dr. Carrie Partch dedicate their lives to unraveling the mysteries behind our circadian rhythms. The Quest for … Read more

Do you ever notice that different parts of a coffee mug produce different pitches when tapped? It’s not just your imagination. In fact, this peculiar phenomenon has intrigued many researchers and enthusiasts alike. So, what’s the reason behind this curious occurrence? The Symmetry of the Cup If you take a moment to tap different parts … Read more

In the world of computer vision, there are powerful techniques available to extract valuable information from binary images. For example, let’s say you have a binary image of a human body and you want to extract its skeleton. This can be achieved through an iterative process of modifying the binary image while preserving its overall … Read more

Are you curious about the fascinating world of edge detection? In the realm of computer vision, edges play a pivotal role in extracting crucial information from images. They mark the locations where image intensity experiences a rapid change. Join us on this journey as we explore the intricacies of edge detection, its theoretical framework, and … Read more

In the world of computer vision, active illumination methods have emerged as a game-changer. By controlling the lighting of a scene, these methods enable the recovery of valuable information about shape and reflectance properties with unparalleled reliability and accuracy. This article will delve into the fascinating realm of active illumination techniques, focusing on those that … Read more

Have you ever wondered how depth is computed in 3D scenes? In the world of structured light range finding, the task is to determine the depth of each point in a scene. This article will explore various methods used in structured light range finding and highlight the benefits of active illumination methods. Point-Based Range Finding … Read more

Detecting boundaries and outlining objects in images is a fascinating challenge in the field of computer vision. In this article, we will explore various techniques for boundary detection and how they can be effectively used to clean out outlines or silhouettes of objects in an image. Let’s dive in and uncover the world of boundary … Read more

Image transformations play a crucial role in shaping the way we interact with visual content. Whether it’s adjusting the brightness, applying filters, or completely changing the shape of an image, transformations enable us to enhance and manipulate images to our liking. In this article, we will delve into the world of image transformations, specifically focusing … Read more

Image processing is a fascinating field that involves transforming images to make them clearer, enhanced, or easier to analyze. In our first lecture, we covered a range of topics that laid the foundation for understanding image processing techniques. In this article, we will delve deeper into the subject, discussing the Fourier Transform, convolution, deconvolution, and … Read more

The quest to uncover the origins of life has always captivated human curiosity. From the idea of a linear evolution toward complexity to the emergence of complex cells, the search for answers continues. In this article, we delve into the work of scientists studying the deep history of life, its energy flow, and how it … Read more

Have you ever wondered how computers can detect and recognize complex shapes that cannot be easily described by equations? Well, that’s where the generalized Hough transform comes into play. In this article, we’ll explore the amazing capabilities of the generalized Hough transform and how it can be used to find intricate shapes in images. But … Read more

Have you ever wondered how images are smoothed to remove noise? In image processing, there are various techniques, and one of them is non-linear filtering. Non-linear filters, unlike linear ones, cannot be implemented as convolutions. In this article, we will explore a specific non-linear filter called median filtering and its applications in image smoothing. The … Read more

Imagine capturing a video of a captivating scene using a handheld camera. Now, envision this video not just as a sequence of moving images, but as a treasure trove of hidden information waiting to be unearthed. In Course 4 of the Techal curriculum, we dive deep into the fascinating world of computer vision, where we … Read more

Neural networks have become a sensation in the world of technology. These complex systems, inspired by the human brain, have proven to be immensely powerful in solving a wide array of problems. In this article, we will delve into the world of neural networks, exploring their structure, functionality, and their application in solving vision problems. … Read more

Computers have rapidly advanced in recent years, and their impact on various fields, including mathematics, cannot be ignored. Traditionally, mathematics has relied on human reasoning and deductive arguments to establish the truth of mathematical propositions. However, with the rise of artificial intelligence (AI) and computational tools, the role of mathematicians in proving theorems is being … Read more

Face detection has always been a fascinating challenge in the field of computer vision. To identify faces with precision, engineers have explored various approaches, one of which involves computing features known as Haar features. These features have significantly contributed to the development of more accurate and efficient face detection algorithms. The Problem of Face Detection … Read more

Welcome to the world of image processing! In this article, we’ll explore the fascinating field of transforming and analyzing images. Whether you want to remove noise, enhance blurry objects, or extract important information from images, image processing has got you covered. Enhancing Image Clarity Have you ever taken a picture at night, only to find … Read more

The world of cryptography has come a long way in ensuring secure communication and computation. In today’s technology-driven world, cryptography is used extensively, often without users even realizing it. From our cellphones to online transactions, cryptography plays a vital role in ensuring confidentiality and integrity. The Evolution of Cryptography In the past, cryptography was considered … Read more

Have you ever noticed the wind whipping around you as you cruise down the street? Have you ever disrupted a stream with a stick and witnessed the little whirlpools that form in its wake? These are examples of turbulence – the chaotic disturbances in the air and other fluids. Turbulence is everywhere, from the swirling … Read more

Have you ever wondered what lies beneath the vast ice sheets of Antarctica? It turns out that we know more about the surface of Mars than we do about the mysterious world hidden beneath the Antarctic ice. As a technology enthusiast, I am thrilled to delve into the fascinating research conducted by Professor John Prisky … Read more

Welcome to the world of Constantinos Daskalakis, a renowned professor of computer science at MIT. With a passion for data interfaces and game theory economics, Daskalakis uncovers distant truths that lie at the intersection of computing and economics. Computing the Future of Economics Daskalakis’s work delves into the practical and philosophical aspects of the interface … Read more

Life, the most intricate phenomenon on Earth, seems to emerge from the chaos of randomness. Billions of years ago, the Earth’s surface was a turbulent sea of molten lava, devoid of any discernible structure. Yet, life somehow materialized, defying the odds and challenging our understanding of how order arises from disorder. But how is this … Read more

The field of physics has experienced groundbreaking discoveries in recent years. Scientists and researchers have made significant progress in unraveling the mysteries of the universe. In this article, we will delve into some of the most remarkable breakthroughs in physics. Muon-g-2 Experiment: Shedding Light on New Physics One of the most profound discoveries in recent … Read more

Do you ever wonder how we can determine the three-dimensional shape of an object from just a single shaded image? It may seem like an impossible task, but in this article, we will explore the fascinating world of shape recovery through shading analysis. The Challenge of Shape Recovery Imagine having an image of a simple … Read more

Welcome to a fascinating journey through the vast landscape of mathematics. In this article, we will delve into the extraordinary Langlands Program, a project that has captivated mathematicians for decades. Imagine a map depicting the mathematical world, a realm shaped by centuries of brilliance, from ancient Babylonians to modern visionaries like Riemann. Within this world, … Read more

Have you ever been mesmerized by the intricate patterns of the Mandelbrot Set? This captivating mathematical creation holds many intriguing secrets, particularly within its complex fractal boundary. As we delve deeper into different regions of this boundary, we uncover astonishing features that astound the mind. From valleys of seahorses to parades of elephants, and even … Read more

Have you ever wondered what makes objects in a scene look different from each other, even under the same lighting conditions? The answer lies in their material properties and reflectance capabilities. In this article, we will explore the fascinating concept of BRDF (Bidirectional Reflectance Distribution Function) and its role in representing these properties. So, let’s … Read more

Mathematics is often viewed as an exclusive field, reserved for the intellectual elite. However, this perspective fails to acknowledge the true essence of mathematics and the benefits it can bring to everyone. In this article, we will explore the idea that math is for everybody and highlight the importance of embracing mathematics in our lives. … Read more