Almost all mesh processing procedures cause some more or less visible changes in the appearance of objects represented by polygonal meshes. In many cases, such as mesh watermarking, simplification or lossy compression, the objective is to make the change in appearance negligible, or as small as possible, given some other constraints. Measuring the amount of distortion requires taking into account the final purpose of the data. In many applications, the final consumer of the data is a human observer, and therefore the perceptibility of the introduced appearance change by a human observer should be the criterion that is taken into account when designing and configuring the processing algorithms. In this review, we discuss the existing comparison metrics for static and dynamic (animated) triangle meshes. We describe the concepts used in perception-oriented metrics used for 2D image comparison, and we show how these concepts are employed in existing 3D mesh metrics. We describe the character of subjective data used for evaluation of mesh metrics and provide comparison results identifying the advantages and drawbacks of each method. Finally, we also discuss employing the perception-correlated metrics in perception-oriented mesh processing algorithms.

Development of geometry data compression techniques in the past years has been limited by the lack of a metric with proven correlation with human perception of mesh distortion. Many algorithms have been proposed, but usually the aim has been to minimise mean squared error, or some of its derivatives. In the field of dynamic mesh compression, the situation has changed with the recent proposal of the STED metric, which has been shown to capture the human perception of mesh distortion much better than previous metrics. In this paper we show how existing algorithms can be steered to provide optimal results with respect to this metric, and we propose a novel dynamic mesh compression algorithm, based on trajectory space PCA and Laplacian coordinates, specifically designed to minimise the newly proposed STED error. Our experiments show that using the proposed algorithm, we were able to reduce the required data rate by up to 50% while preserving the introduced STED error.

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Advances in both graphics hardware and scanning technology have allowed for retrieving and rendering complex 3D models with thousands of vertices. With the recent popularity gain of interactive web applications, the data size is beginning to be the tightest bottleneck, especially for detailed 3D animations. The MPEG-4 standard was recently supplemented with an algorithm for compression of dynamic triangle meshes called Frame-based Animated Mesh Compression, which is considered the state of the art in this area. We have thoroughly analysed the algorithm and identified some weak spots and unclarities. In this paper, we present several improvements and optimisations, which attempt to resolve the problems we found. These changes result in combined performance gain of up to 32 percent on tested datasets.

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