PhD student/-s in mathematics - Hiring in process/Finished, not possible to apply

Research subject

Mathematics

Work duties

The doctoral students positions are mainly devoted to postgraduate studies, but include 20% department service, usually teaching. The research area for the current call is mathematical methods and models within computer vision, image analysis, feature extraction, machine learning, statistical methods, optimization and tracking.

Research projects

There are two possible research projects available, listed below, and we are planning to fill one or two positions. Please note in the application which project(s) you are interested in.

 1) Optimization methods for matrix factorization, dimensionality reduction and neural networks

 In recent years there has been a dramatic increase in performance of recognition, classification and segmentation systems due to deep learning approaches. Still there is very little theoretical understanding of the reason for this improvement. Furthermore, training with these models requires solving very large scale non-convex optimization problems and it is unclear under what conditions these can be reliably solved. In this project we will study mathematical optimization methods for learning and dimensionality reduction approaches related to matrix factorization. We will develop effective and reliable algorithms that scale well beyond today's standard and apply these to computer vision applications. Additionally, we aim to characterize what different learning architectures can achieve and provide theoretical limits on their performance. From an application point of view our main focus will be to address problems in computer vision related to 3D-reconstruction and understanding of dynamic scenes from image data. The project is a part of the Wallenberg AI, Autonomous Systems and Software Program. (Contact: Carl Olsson)

2) Computer vision for smart systems

The development of computer vision, machine learning and robotics has come a long way but there remains a lot of work to merge the technologies into a functioning integrated system to give us truly smart robots. The use of robotic computer vision today is limited to very specific scenarios or controlled laboratory environments. In the interdisciplinary project Semantic Mapping and Visual Navigation for Smart Robots, which recently has received funding from the Swedish Foundation for Strategic Research, we rely on expertise from computer vision, machine learning, automatic control and optimization in order to take the current state-of-the-art in autonomous systems to the next level of perception, cognition and navigation, and towards key capabilities of robots able to effectively act in the real world. For demonstration, the project will develop an autonomous system for the visual inventory inspection of a supermarket using small-scale, low-cost quadcopters. The system will provide a complete solution for visual navigation and 3D mapping where not only scene geometry is modelled, but also semantic constraints are integrated. The research is relevant for many industrial applications, such as self-driving cars, unmanned ground vehicles, scene modeling and inspection in general. The main goal of the PhD project is to develop novel methods for scene understanding (in terms of semantic structure from motion) and localization using both vision and other sensors. This typically involve robust estimation techniques, structure from motion estimation and machine learning. (Contact: Karl Åström, Carl Olsson)

Admission requirements

A person meets the general admission requirements for third-cycle courses and study programmes if he or she:

• has been awarded a second-cycle qualification, or
• has satisfied the requirements for courses comprising at least 240 credits of which at least 60 credits were awarded in the second cycle, or
• has acquired substantially equivalent knowledge in some other way in Sweden or abroad.

 A person meets the specific admission requirements for third cycle studies in mathematics if he or she has:

• at least 90 credits of relevance to the subject area, of which at least 60 credits from the second cycle and a specialised project of at least 30 second-cycle credits in the field, or
• a second second-cycle degree in a relevant subject.
• In practice this means that the student should have achieved a level of knowledge in mathematics that corresponds to that of Master of Science programs in Engineering Mathematics or Engineering Physics or a Masters degree in mathematics or applied mathematics.

Additional requirements:

• Very good oral and written proficiency in English.
• The candidate is expected to have programming skills.

Assessment criteria 

Selection for third-cycle studies is based on the student's potential to profit from such studies. The assessment of potential is made primarily on the basis of academic results from the first and second cycle. Special attention is paid to the following:

• Knowledge and skills relevant to the thesis project and the subject of study.
• An assessment of ability to work independently and to formulate and tackle research problems.
• Written and oral communication skills.
• Other experience relevant to the third-cycle studies, e.g. professional experience.

Consideration will also be given to good collaborative skills, drive and independence, and how the applicant, through his or her experience and skills, is deemed to have the abilities necessary for successfully completing the third cycle programme.

Additional merits:

• Programming experience (C++, java, matlab, python).
• Skills in developing structure from motion algorithms.
• Skills in deep learning research.

Terms of employment

Only those admitted to third cycle studies may be appointed to a doctoral studentship. Third cycle studies at LTH consist of full-time studies for 4 years. A doctoral studentship is a fixed-term employment of a maximum of 5 years (including 20% departmental duties). Doctoral studentships are regulated in the Higher Education Ordinance (1993:100), chapter 5, 1-7 §§.

Instructions on how to apply

Applications shall be written in English and include a cover letter stating the reasons why you are interested in the position and in what way the research project corresponds to your interests and educational background. The application must also contain a CV, degree certificate or equivalent, and other documents you wish to be considered (grade transcripts, contact information for your references, letters of recommendation, etc.).