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In this captivating PowerPoint presentation, we delve into the transformative realm of Artificial Intelligence (AI) and its profound impact on our world. Join us as we explore the intricate facets of AI, its applications, challenges, and its potential to reshape various industries.
In this captivating PowerPoint presentation, we delve into the transformative realm of Artificial Intelligence (AI) and its profound impact on our world. Join us as we explore the intricate facets of AI, its applications, challenges, and its potential to reshape various industries.
Our presentation begins with an engaging introduction to the concept of AI, demystifying its core components and algorithms. We navigate through the historical evolution of AI, from its humble beginnings to the present-day breakthroughs that have brought it into the mainstream.
Moving forward, we showcase the vast array of AI applications across diverse sectors, highlighting its capabilities in healthcare, finance, manufacturing, customer service, and more. Witness how AI-driven solutions revolutionize processes, enhance decision-making, and elevate productivity, leading to unprecedented advancements in our society.
However, no discussion on AI would be complete without addressing the challenges and ethical considerations it poses. We shed light on the potential risks, biases, and privacy concerns associated with AI systems, emphasizing the need for responsible development and deployment.
Furthermore, we delve into the cutting-edge advancements in AI research, such as machine learning, natural language processing, computer vision, and robotics. Gain insights into the future of AI and its potential to drive innovation, unlock new possibilities, and shape the way we live and work.
Throughout the presentation, captivating visuals, real-world examples, and interactive elements keep the audience engaged and ensure a dynamic learning experience. By the end of this thought-provoking session, participants will have a deeper understanding of AI's transformative power and be inspired to embrace the opportunities it presents.
Join us as we embark on an exciting journey, unraveling the mysteries of AI and discovering how it holds the key to a brighter, more intelligent future.
2. Detour: Time complexity of convolution
• Image is w x h
• Filter is k x k
• Every entry takes O(k2) operations
• Number of output entries:
• (w+k-1)(h+k-1) for full
• wh for same
• Total time complexity:
• O(whk2)
3. Optimization: separable filters
• basic alg. is O(r2): large filters get expensive fast!
• definition: w(x,y) is separable if it can be written as:
• Write u as a k x 1 filter, and v as a 1 x k filter
• Claim:
15. Why do we need to talk about resizing?
• Need to zoom in to a
region to get more details
• Can we get more details?
Louis Daguerre, 1838
16. Why do we need to talk about resizing?
• Far away objects appear
small, nearby objects appear
larger
• Need to recognize objects at
multiple scales
• Resizing images to same size
helps recognition
17. Why is resizing hard?
• E.g, consider reducing size by a factor of 2
• Simple solution: subsampling
• Example: subsampling by a factor of 2
24. Let’s look at it mathematically
• Fourier basis signals
• 𝐵𝑘 𝑛 = 𝑒
𝑖2𝜋𝑘𝑛
𝑁 , time period N/k, frequency k/N
• Suppose we sample every P pixels. Then we are only looking at the
values
• 𝐵𝑘 𝑃 , 𝐵𝑘 2𝑃 , … , 𝐵𝑘 𝑛𝑃 , …
• Consider two basis vectors 𝐵𝑘 and 𝐵𝑘+𝑁/𝑃
• 𝐵𝑘+𝑁/𝑃 𝑛𝑃 = 𝑒
𝑖2𝜋 𝑘+
𝑁
𝑃 𝑃𝑛
𝑁 = 𝑒
𝑖2𝜋𝑘𝑃𝑛
𝑇
+𝑖2𝜋𝑛(
𝑁
𝑃
)(
𝑃
𝑁
)
= 𝑒
𝑖2𝜋𝑘𝑃𝑛
𝑇
+𝑖2𝜋𝑛
= 𝑒
𝑖2𝜋𝑘𝑃𝑛
𝑁 = 𝐵𝑘(𝑛𝑃)
25. Let’s look at it mathematically
• 𝐵𝑘 𝑛𝑃 = 𝐵𝑘+
𝑁
𝑃
𝑛𝑃
• The two basis vectors look identical if we sample every P pixels
• Our eyes see the lower frequency: aliasing
• How do we avoid aliasing?
• Remove high frequencies that may be aliased
• Sample at a high enough rate (lower P)
26. Avoiding aliasing
• Suppose image has limited high frequency components
• Fourier transform of x is X
• Suppose X is non-zero only for −𝑘𝑚𝑎𝑥 to 𝑘𝑚𝑎𝑥
0 N/2
-N/2 -kmax kmax
27. Avoiding aliasing
• When sampling once every P pixels, −𝑘𝑚𝑎𝑥 is indistinguishable from
− 𝑘𝑚𝑎𝑥 + 𝑁/𝑃
• If image has both coefficients, they will get mixed
• So we want that 𝑘𝑚𝑎𝑥 < −𝑘𝑚𝑎𝑥 +
𝑁
𝑃
⇒ 2𝑘𝑚𝑎𝑥 <
𝑁
𝑃
0 N/2
-N/2 -kmax kmax
-kmax+N/P
28. Nyquist Sampling Theorem
• 2𝑘𝑚𝑎𝑥 <
𝑁
𝑃
• Basis 𝐵𝑘 has a time period of
𝑁
𝑘
or frequency of
𝑘
𝑁
•
2𝑘𝑚𝑎𝑥 <
𝑁
𝑃
⇒
2𝑘𝑚𝑎𝑥
𝑁
<
1
P
⇒ 2𝜈𝑚𝑎𝑥 < 𝜈𝑠𝑎𝑚𝑝𝑙𝑒
• Need to sample at at least twice the rate of the highest frequency
component
29. Subsampling the image
• First smooth the image to remove
high frequency components
• How should we smooth?
• One simple answer: blur with
Gaussian
• Recall that Fourier transform of
Gaussian is Gaussian
• Choose sigma so that frequencies
above
𝜈𝑠𝑎𝑚𝑝𝑙𝑒
2
get killed
38. Gaussian pyramids
[Burt and Adelson, 1983]
• In computer graphics, a mip map [Williams, 1983]
Gaussian Pyramids have all sorts of applications in computer vision
Source: S. Seitz
