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Toru Tamaki
このレクチャーでは，コンピュータビジョンやパターン認識，画像処理などで使われる数式や考え方，数学的手法を学びます．基礎的な連立方程式の解き方とその解釈，微分と最適化，回帰とスパースモデリング，制約付き最適化問題と凸最適化，識別などの基本的な考え方を，数式を通して理解し，いくつかの問題についてはPythonコードを使って理解を深めます．特に連立方程式Ax=bというよく見かける数式を題材に，顔画像の近似問題としていろいろな手法が定式化できること，また解き方があることを学びます．
Register for this course and see more details by visiting:
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What's inside
Syllabus
はじめに
レクシャースライドPDFです．ファイルは***slide.pdfです（映像撮影時の古いものも残してありますが，新しいほうは誤植などを修正してあります）．
演習問題の解答例のファイルは***answer.pdfです．
演習用のコードはリンクのgithubを参照してください．
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Syllabus
はじめに
レクシャースライドPDFです．ファイルは***slide.pdfです（映像撮影時の古いものも残してありますが，新しいほうは誤植などを修正してあります）．
演習問題の解答例のファイルは***answer.pdfです．
演習用のコードはリンクのgithubを参照してください．
Read more
Traffic lights
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Explores mathematical formulations, concepts, and techniques used in computer vision, pattern recognition, and image processing
Provides a foundation in linear equations, differential calculus, regression analysis, and constrained optimization
Offers a practical approach with Python code demonstrations to enhance understanding
Emphasizes the interpretation of the widely encountered equation Ax=b in various contexts
Suitable for learners with a background in linear algebra and a desire to apply mathematical concepts to real-world problems
Requires familiarity with basic programming concepts and Python syntax
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Reviews summary
コンピュータビジョン数学基礎とpython実装
学習者によると、このコースはコンピュータビジョンにおける数学的基礎を深く、かつ実践的に学ぶのに非常に効果的です。特に、線形代数や微分、最適化といった複雑な概念も、丁寧な解説とPythonでの豊富な実装例を通して明確に理解できると高く評価されています。これにより、理論と実践の橋渡しがなされ、研究や開発への応用に繋がると多くの学生が述べています。一方で、ある程度の数学的・プログラミング的基礎知識が必須であり、前提知識がないと難易度が高いと感じる学習者もいるため、受講には注意が必要です。しかし、その専門性と質は、この分野を深く追求したい方には必修とも言える内容です。
実世界への応用例が多く、講師の説明が非常に論理的です。
"今後の研究や開発に役立つと確信しています。"
"講師の説明も非常に論理的で、疑問点を残しません。コンピュータビジョン分野に進む人には必修と言える内容です。"
"コンピュータビジョンにおいて数学がなぜ重要なのか、どう役立つのかを、具体的な数式とPythonコードで丁寧に解説してくれます。"
複雑な数式をPythonコードで実践的に学べます。
"数式とPythonコードの関連付けが素晴らしく、理論と実践の橋渡しをしてくれます。"
"数式とPythonコードの融合が秀逸で、理論が実装にどう落とし込まれるのかを明確に示してくれます。特に、Ax=bの解釈から顔画像近似への応用は目から鱗でした。"
"Pythonでの演習も理解を深めるのに役立ちました。"
コンピュータビジョンの数学的基礎を深く掘り下げます。
"このコースは、コンピュータビジョンで必要となる数学の基礎を非常に深く理解させてくれました。"
"今まで曖昧だった数学の概念が、このコースで一気にクリアになりました。特に、一般化逆行列やヤコビ行列、ヘッセ行列の物理的意味や、それがコンピュータビジョンでどう使われるのかが非常に分かりやすかったです。"
"非常に深い内容で、数学の基礎を固めるには最適です。"
受講には確固たる数学とプログラミングの基礎が必須です。
"前提知識としてある程度の数学力がないと、途中で挫折する可能性もあります。"
"私のような数学があまり得意ではない人間には、かなり難しく感じました。"
"全くの初心者にはハードルが高いかもしれません。Pythonでの実装は理解を助けますが、こちらもプログラミング経験がないと厳しいかもしれません。"
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Review Linear Algebra Foundations
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Brush up on the concepts of linear algebra, such as matrix operations, vector spaces, and linear transformations, to strengthen your understanding of the mathematical foundation used in this course.
Browse courses on
Linear Algebra
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Show steps
Show steps
- Review notes and textbooks from previous linear algebra courses
- Complete practice problems and exercises to test your understanding
- Watch online lectures or tutorials to reinforce key concepts
Join a Matrix Theory Study Group
Show steps
Engage with fellow students or classmates to discuss concepts, share insights, and work through problems collaboratively. This interactive activity will enhance your understanding and provide support.
Browse courses on
Linear Algebra
Show steps
Show steps
Show steps
- Reach out to classmates or form a study group with interested individuals
- Establish a regular meeting schedule and set clear goals for each session
- Take turns presenting concepts, solving problems, and facilitating discussions
Solve Practice Matrix Problems
Show steps
Engage in regular practice of solving matrix problems to improve your computational skills and deepen your understanding of matrix theory.
Browse courses on
Matrix Operations
Show steps
Show steps
Show steps
- Find online problem sets or textbooks with practice exercises
- Allocate dedicated time for solving these problems on a regular basis
- Review your solutions and identify areas for improvement
Three other activities
Expand to see all activities and additional details
Show all six activities
Solve Differential Calculus Practice Problems
Show steps
Sharpen your differential calculus skills by regularly practicing problem-solving. This will strengthen your understanding of the concepts and improve your ability to apply them.
Browse courses on
Derivatives
Show steps
Show steps
Show steps
- Find online problem sets or textbooks with practice exercises
- Allocate dedicated time for solving these problems on a regular basis
- Review your solutions and identify areas for improvement
Explore Advanced Matrix Analysis Tutorials
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Seek out specialized tutorials or online courses to expand your knowledge of advanced matrix analysis techniques and their applications in various fields.
Browse courses on
Singular Value Decomposition
Show steps
Show steps
Show steps
- Identify reputable online platforms or educators offering tutorials
- Review the course content and select tutorials that align with your interests
- Follow the tutorials, complete the exercises, and engage in discussions
Create Visualizations of Matrix Transformations
Show steps
Enhance your understanding of matrix transformations by creating visual representations using tools like Python or MATLAB. This hands-on activity will solidify your grasp of the geometric interpretations.
Browse courses on
Linear Transformations
Show steps
Show steps
Show steps
- Choose a matrix transformation and its corresponding geometric operation
- Write a program to generate a visual representation of the transformation
- Experiment with different transformation parameters and observe the resulting effects
Career center
Learners who complete コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題 will develop knowledge and skills
that may be useful to these careers:
Computer Vision Engineer
Computer Vision Engineer
Computer Vision Engineers design and develop software that enables computers to interpret and understand visual data. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, is closely aligned with this field as it provides a solid foundation in the mathematical principles underlying computer vision, including linear algebra, optimization, and numerical methods. By understanding these concepts, you can better grasp the algorithms and techniques used in computer vision systems.
Data Scientist
Data Scientist
Data Scientists use their expertise in statistical modeling, machine learning, and data analysis to extract insights from data. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can provide you with a strong foundation in the mathematical principles and techniques used in data science, including linear algebra, optimization, and numerical methods. These concepts are essential for developing and implementing data-driven solutions.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical methods to solve complex problems in various industries. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can help you build a solid foundation in the mathematical principles and techniques used in operations research, including linear algebra, optimization, and numerical methods. These concepts are essential for modeling and solving problems related to resource allocation, scheduling, and decision-making.
Market Researcher
Market Researcher
Market Researchers conduct research to understand consumer behavior and market trends. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can provide you with a strong foundation in the mathematical principles and techniques used in market research, including linear algebra, optimization, and numerical methods. These concepts are essential for designing and analyzing research studies and interpreting data to gain insights into consumer behavior.
Business Analyst
Business Analyst
Business Analysts analyze business processes and data to identify areas for improvement. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can provide you with a strong foundation in the mathematical principles and techniques used in business analysis, including linear algebra, optimization, and numerical methods. These concepts are essential for understanding and analyzing business processes, identifying inefficiencies, and developing data-driven solutions.
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data to solve problems in various fields. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding statistical models, data analysis techniques, and hypothesis testing.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can provide you with a strong foundation in the mathematical principles and techniques used in software development, including linear algebra, optimization, and numerical methods. These concepts are essential for understanding and implementing software algorithms and data structures.
Data Analyst
Data Analyst
As a Data Analyst, you will handle the collection, cleaning, analysis, and presentation of data to derive meaningful insights. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can help you build a foundation in the mathematical concepts and techniques frequently used in data analysis. Its focus on linear algebra, optimization, and numerical methods can provide you with a strong understanding of data manipulation, modeling, and interpretation.
Data Engineer
Data Engineer
Data Engineers design and build systems for storing, managing, and processing data. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding data structures, algorithms, and data management techniques.
Economist
Economist
Economists study and analyze economic data to understand economic trends and develop policies. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding econometric models, data analysis techniques, and economic forecasting.
Actuary
Actuary
Actuaries use mathematical and statistical models to assess and manage risk in the insurance and finance industries. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for developing and implementing actuarial models.
Financial Analyst
Financial Analyst
Financial Analysts use financial data and models to make investment recommendations and provide financial advice. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding and implementing financial models and making informed investment decisions.
Consultant
Consultant
Consultants provide expert advice and guidance to businesses on various issues. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding complex business problems, developing solutions, and communicating effectively with clients.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical models to assess risk and make informed decisions in the financial industry. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for developing and implementing financial models.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers develop and implement machine learning models to automate tasks and solve complex problems. This course, コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題, can be useful in building your foundation for this role, as it covers topics like linear algebra, optimization, and numerical methods. These concepts are essential for understanding and implementing machine learning algorithms.
For more career information including salaries, visit:
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Reading list
We've selected 14 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
コンピュータビジョン数学基礎：数式とPythonで学ぶ最適化と最小二乗問題.
コンピュータビジョンの分野における標準的な教科書であり、基本的なアルゴリズムや手法を網羅的に解説しています。
PyTorchライブラリを使用したディープラーニングの手法を解説しており、コンピュータビジョンにおける画像認識や物体検出などのタスクに役立ちます。
TensorFlowライブラリを使用したディープラーニングの手法を解説しており、コンピュータビジョンにおける画像認識や物体検出などのタスクに役立ちます。
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この本は、深層学習の基礎をわかりやすく解説しています。畳み込みニューラルネットワーク、リカレントニューラルネットワーク、敵対的生成ネットワークなど、コンピュータビジョンで用いられるアルゴリズムを体系的に学ぶことができます。
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この本は、コンピュータビジョンのアルゴリズムと応用をわかりやすく解説しています。画像処理、物体認識、物体検出など、コンピュータビジョンで用いられるアルゴリズムを体系的に学ぶことができます。
この本は、凸最適化の手法をわかりやすく解説しています。線形計画法、二次計画法、円錐計画法など、コンピュータビジョンで用いられる凸最適化の手法を体系的に学ぶことができます。
この本は、ガウス過程の基礎をわかりやすく解説しています。ガウス過程のモデル、学習アルゴリズム、応用など、コンピュータビジョンで用いられるガウス過程の概念を体系的に学ぶことができます。
この本は、ベイズネットワークの基礎をわかりやすく解説しています。ベイズネットワークの構造、確率的推論、学習アルゴリズムなど、コンピュータビジョンで用いられるベイズネットワークの概念を体系的に学ぶことができます。
この本は、機械学習で用いられる最適化の手法をわかりやすく解説しています。勾配降下法、確率的勾配降下法、ニュートン法など、コンピュータビジョンで用いられる最適化の手法を体系的に学ぶことができます。
この本は、数値最適化の手法をわかりやすく解説しています。勾配降下法、ニュートン法、共役勾配法など、コンピュータビジョンで用いられる最適化の手法を体系的に学ぶことができます。
この本は、情報理論、推論、学習アルゴリズムの基礎をわかりやすく解説しています。エントロピー、KLダイバージェンス、ベイズ推定など、コンピュータビジョンで用いられる確率的モデリングの概念を体系的に学ぶことができます。
この本は、機械学習の基礎をわかりやすく解説しています。教師あり学習、教師なし学習、強化学習など、コンピュータビジョンで用いられる機械学習の概念を体系的に学ぶことができます。
この本は、線形代数の基礎をわかりやすく解説しています。行列、ベクトル、線形写像など、コンピュータビジョンで用いられる数学を体系的に学ぶことができます。
この本は、確率過程の基礎をわかりやすく解説しています。マルコフ過程、ポアソン過程、ブラウン運動など、コンピュータビジョンで用いられる確率過程の概念を体系的に学ぶことができます。
For more information about how these books relate to this course, visit:
OpenCourser.com/course/zrioay/konpiyu
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