Redes de telecomunicaciones

The chapter provides a classification of DFD techniques based on the method used and the mode of operation. Most approaches consider blurring as a linear shift invariant process (frequency and spatial domain) and represent the defocused image as the convolution of the focused image with the psf of lens. The blur information was then retrieved by the deconvolution process either in the frequency or spatial domain, and then related to the actual distance using the appropriate depth model. These methods offer an advantage in terms of computation and simplicity in implementation of the algorithm. The other methods (mostly statistical methods) consider the blurring as a shift variant process and retrieve a unique depth value not only along the optical axis but also along the x and y directions of the scene under investigation. These methods prove efficient since they simultaneously retrieve depth and the radiance of the scene, but are not suitable for practical purposes since they are based on error minimisation techniques which require extensive computations. Since the objective of this research was to develop a real-time depth estimation system that can be effectively implemented on a Field Programmable Gate Array (FPGA) with a usage in medical and industrial applications, the DFD methods require two images to recover the depth and hence be useful for real-time depth estimation. In terms of accuracy, DFD methods are comparable to DFF techniques [8] and require less processing time. Simon et al. [58] [59] suggested a three image technique where the blur parameter was recovered from three blurred images, but this in-turn introduced additional complexity in the image acquisition process and also failed to show good depth results [60]. After an in-depth analysis into different methods, the technique described by Watanabe and Nayar [14] based on the use of texture invariant broadband filters was chosen for implementation. Though the filters were designed in the frequency domain, the algorithm can be implemented in the spatial domain by employing five 2D convolutions and thus should be suitable for real-time implementation. In terms of accuracy, the maximum RMS error reported was 1.2% with respect to distance (which was better than comparable methods), with a depth detection error of less than 1% irrespective of the texture frequency. The main drawback of the method was the requirement for a less complicated procedure to model the rational filters for any given defocus condition. This problem was

subsequently addressed in this research work where a novel method referred as the „Two Step Polynomial Approach‟ was employed to design the rational filters (refer to chapter 4). To provide a good accuracy comparison with Watanabe‟s filters the algorithm was based on the Pillbox psf model, rather than Gaussian or Generalised Gaussian suggested by Claxton and Staunton [49]. Further the Pillbox psf model is a good approximation of a more blurred image [49] and also provided better depth results for highly blurred images as stated by Subbarao [7] [10]. The 1D equation for each of the three psf‟s are presented in Chapter 4. New research presented in this thesis also addresses: - (1) An algorithm to estimate the magnification variations between the defocused images (Chapter 3); and (2) The implementation of the DFD algorithm on the Virtex 2P FPGA (Chapter 5). Experimental results and comparison with Watanabe‟s filters are provided in these chapters.

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Introduction

One of the fundamental tasks in Image Processing is to acquire a set of images which are registered with each other but in practice this is not always possible since changes in image acquisition parameters cause misalignment. In order to compare the acquired images, the shift, rotation and scaling between the images needs to be determined. Once these differences have been estimated they can be used to correct the position of one image relative to the other. In this chapter a new method is described which was devised to effect this, as problems arise with standard methods when images have been defocused. To increase the accuracy of the depth estimation, the defocused images (near and far-focused) must be registered to compensate for magnification, and in practice, translation. Since the depth measurement method was based on Watanabe and Nayar [41], an optical method using telecentric optics was used to correct the magnification changes. This method requires the precise placement of an external aperture at the front focal plane of the lens. The method is readily suitable for real-time depth estimation since it avoids the use of any interpolation technique for registering the image and is achieved using a setup prior to depth estimation. The chapter discusses an effective technique based on Fourier analysis to measure the magnification changes between the near and the far-focussed images. Section 3.1 provides an overview of the various image registration techniques, followed by telecentric optics (Section 3.2) in which a comparison is provided between the conventional lens and telecentric lens model. Sections 3.3 and 3.4 explain the algorithm for image magnification measurement and finally Section 3.6 provides experimental results for simulated and real images.