شناسايي مدل‌هاي سه‌بعدي در حوزه فوريه با استفاده از فشرده ‌كردن كره مشي تا رويه مدل

3D Models Recognition in Fourier Domain Using Compression of the Spherical Mesh up to the Models Surface

در اين مقاله توصيف‌گر نوين مدل سه­ بعدي در حوزه فوريه پيشنهاد شده است. به‌ منظور استخراج ويژگي در روش پيشنهادي، كره مش‌بندي‌شده محيط بر مدل، از بيرون مدل به سمت مركز آن فشرده شده، سپس طول مسيري كه رأس ­هاي كره از ابتدا تا رسيدن به رويه مدل طي مي­ كنند، محاسبه مي­شود. اين مقادير به‌منظور محاسبه تابع مسير، كه طول مسير رأس ­هاي مدل تا مركز آن است، استفاده مي­ شوند. تابع به ‌دست ‌آمده در مقابل تغييرات ايزومتريك مقاوم و براي شناسايي مد ل­هاي غير­صلب بسيار كار آمد است. در ادامه، ضرايب فوريه تابع مسير به‌عنوان بردار ويژگي محاسبه مي­ شوند و سپس بردار ويژگي استخراج‌شده در طبقه­ بند SVM مورد استفاده قرار مي­ گيرد. با بهره ­گيري از ويژگي پاسخ دامنه تبديل فوريه سيگنال­هاي حقيقي، مدل در فضايي با ابعاد كمتر، بدون از دست­دادن ويژگي­هاي ذاتي خود توصيف شده، همچنين از نرماليزاسيون حالت بي­ نياز مي­ شود. نتايج پياده­ سازي برروي پايگاه داده McGill نشان­ دهنده دقت بالاي روش پيشنهادي در طبقه­ بندي مدل­ هاي سه­ بعدي است.

Representing 3D models in diverse fields have automatically paved the way of storing, indexing, classifying, and retrieving 3D objects. Classification and retrieval of 3D models demand that the 3D models represent in a way to capture the local and global shape specifications of the object. This requires establishing a 3D descriptor or signature that summarizes the pivotal shape properties of the object. Therefore, in this work, a new shape descriptor has been proposed to recognize 3D model utilizing global characteristics. To perform feature extraction in the proposed method, the bounding meshed sphere surrounding the 3D model and concentrated from the outside toward the center of the model. Then, the length of the path which the sphere's vertices travel from the beginning to the model’s surface will be measured. These values are exploited to compute the path function. The engendered function is robust against isometric variations and it is appropriate for recognizing non-rigid models. In the following, the Fourier transform of the path function is calculated as the features vector, and then the extracted features vector is utilized in SVM classifier. By exploiting the properties of the magnitude response of the Fourier transform of the real signals, the model can be analyzed in the lower space without losing the inherent characteristics, and no more pose normalization is needed. The simulation results based on the SVM classifier on the McGill data set show the proposed method has the highest accuracy (i.e. 79.7%) among the compared related methods. Moreover, the confusion matrix for performing 70% trained SVM classifier indicates the suitable distinguishing ability for similar models and does not have a high computational complexity of model processing in 3D space.