In this paper, we review an auxiliary function approach to independent component analysis (ICA) and independent vector analysis (IVA). The derived algorithm consists of two alternative updates: 1) weighted covariance matrix update and 2) demixing matrix update, which include no tuning parameters such as a step size in the gradient descent method. The monotonic decrease of the objective function is guaranteed by the principle of the auxiliary function method. The experimental evaluation shows that the derived update rules yield faster convergence and better results than natural gradient updates. An efficient implementation on a mobile phone is also presented.
We propose a new method of the surface orientation (normal vector) imager being independent upon non-Lambertian reflectance components.
It consists of six light sources at vertices of a hexagon and the three-phase correlation image sensor (3PCIS) for demodulating the amplitude and phase of reflected light at two illumination modes. To separate the Lambertial and the specular reflectance components, the light sources first illuminate the object in six phases being different in 2π/6 between the neighbors (the dipole modulation mode) and then in three phases being different in 4π/6 each other
(the quadrapole modulation mode). In the dipole modulation mode,
the amplitude and phase depend both on the Lambertian reflectance (surface orientation) and on the non-Lambertian reflectance (specular strength). In the quadrapole modulation mode, the former component is eliminated and only the latter component remains. Subtracting it from the dipole modulation result, we obtain the surface orientation map based on the photometric stereo principle. We implemented the method using CMOS 64x64 pixel 3PCIS and successfully reconstructed the normal vector maps for various non-Lambertian object.
We propose a novel system for real-time three-dimensional surface orientation measurement. The advantages of our method are: (1) single frame capture of normal vector distribution, (2) dense, pixel-wise capture of normal vectors, and (3) independence on surface reflectance and background illumination. This system consists of two components; one is the sinusoidally amplitude-modulated three-phase (3P) light sources at vertices of a triangle and another is the three-phase correlation image sensor (3PCIS) for demodulating the amplitude and phase of reflected light from the surface. Based on the photometric stereo principle, the phase and amplitude can be easily converted to the azimuth and inclination, respectively, of the normal vector of the surface. We implemented this system using our CMOS 64 × 64 pixel 3PCIS developed by us and successfully reconstructed the normal vector map in its frame rate (30Hz).