Common Errors in MATLAB Computing

1. Forgot to convert to double. I mentioned that if you use ‘imread’ to read in an image, it will be in uint8 format. This format is less reliable than double because it does not “support” floating-point operation. It is a good idea to convert images to double format before any calculation of quantities such [...]

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Principle of Relativity: from Theoretic Physics to Visual Perception

According to wiki, “In physics, the principle of relativity is the requirement that the equations, describing the laws of physics, have the same form in all admissible frames of reference.” The importance of reference frame has been less appreciated in other sciences and it is the purpose of this blog to understand its relevance to [...]

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Understanding the Impact of Mathematics on Image Processing

This blog is a continuation of my previous blog on the relationship between mathematics and image processing and aims at more technical virtuosity than conceptual understanding. What are the most influential works by mathematicians on image processing research in the past three decades? I would say MRF in 1980s; Wavelets and PDEs in 1990s; still-too-early-to-tell [...]

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On Memory of Physical, Chemical, Biological and Social Systems

What is memory? It describes a lagging effect which causes the state of a system is not just dependent on the current input but its history. Such lagging effect can be understood by considering ferromagnetism. Permanent magnets are unique objects with memory characteristics in the inanimate world. Can a piece of iron have memory? Yes. [...]

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On Bias-Variance Dilemma and Occam’s Razor

In frequentists’ framework, there is a well-known phenomenon called bias-variance dilemma: a simple model tends to have lower variance but introduce higher bias; a more complex model could reduce the bias at the price of higher variance. Therefore, it is often necessary to find a tradeoff and avoid over-complicated models. The preference of simple models [...]

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Deductive Logic vs. Inductive Reasoning

For a long period I was baffled by the relationship between mathematical and physical sciences (like Platonism vs. Aristotelian). If mathematics and physics are about the study of mentally reproducible and experimentally reproducible objects respectively, which one is more fundamental? Especially in view of the increasing influence of mathematics on science and engineering (for better [...]

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What is Research-Based Learning?

How do we learn? Nobody knows for sure. We might know how we learn to play basketball (it takes a lot of practice) or how we learn to write computer programs (it takes a lot of thinking); but we don’t have a definite answer to an effective learning strategy for generic things including college education. [...]

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Energy-related Challenge and Supply-Demand Principle

Energy preservation (First law of thermodynamics) is likely to be one of the most important principles in the physical world. Because of this principle, we know perpetual motion is impossible. However, nobody knows exactly what is energy; what we can do is to measure it in some way or another. Therefore, it is also called [...]

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Blackboard-based Teaching vs. Powerpoint-based Teaching

I have been teaching EE465 for seven straight years. In the first few trials, I used totally blackboard-based teaching and closed-book exams. It is kind of easy to teach concepts related to binary images such as morphological filtering on blackboard because they are simply mathematical objects (e.g., set operations). But students did not like too [...]

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Ten Years After Receiving My Doctor of Philosophy

Francis Bacon said, “History make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend”. Newton’s epoch-making achievement is his “Mathematical Principles of Natural Philosophy”. Today we just call it classical mechanics or Newtonian mechanics. In a letter written from Einstein to Thornton in 1944, “So many people today [...]

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