El hash geométrico es un método utilizado en visión por computadora y reconocimiento de patrones para identificar objetos en una escena mediante la comparación de sus características geométricas con una base de datos precalculada. Fue desarrollado a finales de los años 1980 por Yehezkel Lamdan y Haim J. Wolfson, y se volvió influyente en el campo del reconocimiento de objetos basado en modelos. La técnica destaca por su capacidad para manejar occlusiones parciales y su invarianza ante transformaciones geométricas comunes, lo que la convierte en una alternativa robusta a los enfoques anteriores de coincidencia de plantillas.
La idea central del hash geométrico es representar cada modelo de objeto como un conjunto de puntos de características (como esquinas, bordes o puntos de interés) y luego codificar sus relaciones espaciales en una tabla hash. Durante el reconocimiento, una escena consultada se procesa extrayendo sus propios puntos de características, y la tabla hash se utiliza para votar por los modelos candidatos. Este proceso de votación permite que el sistema pueda rápidamente hypotetizar qué modelo podría estar presente, incluso cuando solo se ve un subconjunto de las características del objeto.
Desarrollo Histórico
El hash geométrico surgió de la investigación en geometría computacional y visión por computadora durante los años 1980. Lambert y Wolfson introdujeron el concepto en un artículo de 1988 titulado "Geometric hash: un esquema general y eficiente de reconocimiento basado en modelos inedición", presentado en la Conferencia Internacional de la IEEE sobre Visión por Computadora. El enfoque se basó en trabajos anteriores sobre hash y coincidencia geométrica, pero introdujo una forma novedosa de indexar las características del modelo, lo que hacía que el reconocimiento fuera rápido y tolerante a ruido.
La técnica ganó popularidad en los años 1990, especialmente en aplicaciones como inspección de piezas industriales, robótica y imágenes médicas. También se adaptó para su uso en biología molecular para la comparación de estructuras de proteínas, donde se podían combinar las disposiciones geométricas de átomos o residuos Choros en diferentes moléculas. A principios de los años 2020, el hash geométrico sigue siendo un concepto fundamental en visión por computadora, aunque ha sido ampliamente reemplazado por métodos basados en aprendizaje profundo en muchas aplicaciones prácticas.
Resumen del Algoritmo
El algoritmo de hash geométrico funciona en dos fases: preprocesamiento y reconocimiento. En la fase de preprocesamiento, para cada modelo en la base de datos, se extraen y no se eliminan puntos de características. Para cada par ordenado de puntos (o una base, típicamente dos puntos que definen un marco de coordenadas, el algoritmo calcula las coordenadas de todos los demás puntos relativas a esa base. Estas coordenadas relativas se almacenan luego en una tabla hash, con la base y el identificador del modelo como valor asociado.
Durante el reconocimiento, se extraen los puntos de características de la escena, y el algoritmo selecciona un par de puntos aleatorio como base candidata. Calcula las coordenadas relativas de los puntos restantes de la escena usando esta base y las busca en la tabla hash. Cada coincidencia incrementa un voto para el modelo y la base correspondientes. Después de procesar todas las bases posibles (o una submuestra seleccionada), se selecciona el modelo con el mayor número de votos como la mejor coincidencia. El algoritmo luego verifica la coincidencia, alignna el modelo con la escena y comprueba su consistencia.
Este enfoque es invariante ante traslación, rotación y escala uniforme porque las coordenadas relativas se calculan en un marco normalizado. También permite occlusiones parciales porque solo se necesita que un subconjunto de las características del modelo esté presente en la escena para que se acumulen suficientes votos.
Aplicaciones en Visión por Computadora
El hash geométrico se ha aplicado en varios dominios donde se requiere un reconocimiento de objetos robusto. En la automatización industrial, se usaba para colocar piezas en una cinta transportadora, donde las piezas podían estar rotadas o escaladas en relación con una referencia. En robótica, ayudaba a los robots a identificar y agarrar objetos en entornos desordenados. La excelencia del método a la ocultación lo hacía adecuado para tareas como reconocer objetos parcialmente ocultos en una pila.
En imágenes médicas, el hash geométrico se usaba para alinear estructuras anatómicas en imágenes de rayos X o resonancia magnética, facilitando tareas como el registro de imágenes y la planificación quirúrgica. En biología molecular, facilitaba la comparación de estructuras 3D de proteínas, donde el objetivo era encontrar patrones de plegado similares a pesar de las variaciones en secuencias de aminoácidos. Estas aplicaciones aprovechaban la la capacidad técnica para combinar configuraciones geométricas sin requerir una correspondienta explícita entre puntos individuales.
Comparación con Enfoques Modernos
Con el auge de los objetos moleculares y la enseñanza en los años 2010, el hash geométrico se ha vuelto menos prominente en los “en. Enojs” de “sinon de “el” “de” “objeto”. 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